JOHNS OPKJNSUNIVERSITY CIRCULARS.

Publis/~edwit/z t~4e approbatiw’zoft/ie BoardofTrustees.

No. 11.] BALTIMORE, JULY, 1881. [PRIcE5 CENTS.

CALENDAIR, ACADEMIC YEAR, 1881-82.

September20. NextTermBegins.September21—24. Examinationsfor Matriculation.September27. InstructionsResumed:Assemblyof all theOfficersandStudentsin HopkinsHall.December23—January3. Recess.February22. CommemorationDay.April 7—10. SpringRecess.June9. NextTermCloses.

CONTENTS.PAGE. PAGE.

Calendar 137 German:Meetingsof UniversitySocieties, 187 AdvancedCourses 142AcademicStaff: Major andMinor Courses 142

PresidentandProfessors 138 RomanceLa.nguages:Lecturers 138 AdvancedCourses 142Associates 188 Major andMinor Courses 142InstructorsandAssistants 138 SpecialClasses, 142Fellows 138 History and Political Science 142

Announcementof Lectures,etc., for 1881—82: Logic, Philosophy,etc., 142Mathematics: PeabodyInstituteLectures 142

MathematicalSeminary, 189 CollegiateInstruction 143AdvancedCourses 189 Synopsisof RecentScientificJournals:Major andMinor Courses 139 AmericanChemicalJournal 144AmericanJournalof Philology 145Physics: Studiesfrom the Biological Laboratory 146LaboratoryWork 189 AmericanJournalof Mathematics 146Lectures 189 Proceedingsof UniversitySocieties:

9Chemistry: ScientificAssociation, 148LaboratoryWork 140 PhilologicalAssociation, 148Lectures 140 Historicaland Political ScienceAssociation 149

Biology: MetaphysicalClub, 149LaboratoryWork 140 MathematicalSeminary 150Lectures 140 Deathof William Hopkins, Secretaryof Boardof Trustees, . 151

Greek,Sanskritand Latin: Brief Announcements 151GreekSeminarium 140 Honors Conferred,June6, 1881 152Greekfor advancedstudents 141Sanskrit,etc., . . . . . . . . 141Latin for advancedstudents 141Greekfor undergraduates 141Latin for undergraduates 141

1~L(EETINGSOp SOCIETIES.Scientific. First Wednesdayof eachmonth,

at 8 P. M. Next meeting,October5.L. B. Fletcher,Secretary.

Philological. First Friday of eachmonth,

at 12 M. Next meeting,October7.

M. Warren,Secretary.

Mietaphysical. SecondTuesdayof eachmonth, at 8 P. M. Next meeting, October

11.

HistoricalandPoliticalScience.ThirdFridayof eachmonth,at 8 P. M. Next meet-ing, October21.

H. B. Adams,Secretary.

Mathematical. Third Wednesdayof eachmonth,at 8 P. M. Next meeting, October 19.

0. H. Mitchell, Secretary.

Naturalists’Field Club. ExcursionseachSaturdayduringtheSpringandAutumn. Regu-

lar meetingsfor the reading and discussionofpapersoncea month.

H. F. Reid,Secretary.

JOHNSHOPKINS

ACADEMIC STAFF, 1881-82.PRESIDENT AND PROFESSORS.

DANIEL C. GILMAN. 81 SaratogaSt. President.A. B, Yale College,1852,andA. NI., 1855; LL. D., HarvardUniversity andSt.John’sCol-

lege,1876; Profeaaorin Yale College, 1863-72;Presidentof the Universily ofCalifor-nia,1872—75.

BASIL L. GILDEESLEEVE. 253 St. Paul St. Greek.A. B., PrincetonCollege, 5849, and A. 85., 1852; Ph. D., University of Gdttinges,1853;

LL. D., Collegeof William and Mary, 1869; Professorof Greekin the University ofVirginia, 1836—76; Professorof Latin in the Universitysf Virginia, 186t-66.

H. NEWELL MARTIN. 221 St. Paul St. Biology.85.B., University of London,1871,andDr. Sc., 1872; A. H., UniversityofCambridge,1874,

and A. M., 1877; Fellow, and late Lectnrer on Natoral History in Christ College,Cambridge;FellowofUniversityCollege,London; 85. D., (Hon.)Universityof Georgia,1881.

CHARLES D. MoltRIs. (Collegiate) 158 N. HowardSt. Latinand Greek.A. B., Lincoln College,Oxford, 1849, A. M., and Fellow of Oriel College, Oxford,1852;

Professorin the University of New York, 1875-78.

IRA REMSEN. 213 St.Paul St. Chemistry.College of theCity of New York; 85.D., Collegeof PhysiciansandSorgeone,N. Y., 1867;

Ph. D., University of G’dttingen, 1870; Professorof Chemistry in Williams College,1872—78,andpreviouslyAssistant in Clemistry in the University of Tilbingon.

HENRY A. ROWLAND. 14 CatliedralSt. Physics.C. E., RensselaerPolytechnicInstitute, 1870; AssistantProfessorin the same,1872-75;

Ph. D., JohnsHopkinsUniversity, 1880.

J. J. SYLVESTER. Mt. VernonHotel. Mathematics.A. 85., Universityof Cambridge;F. H. S., LondonandRdinbnrgh; CorrespondingMember,

InstituteofFrance;Member,Academyof Sciencesin Berlin, Glttingen,Naples,Milan,St. Petersbnrg,etc.; LL. D., University of Dublin, University of Edinburgh; D. C L.,UniversityofOxford; HonoraryFellowof St.John’sCollege,Cambridge; lateProfessorof Mathematicsin the Royal Military Academy,Woolvich; Copley Medalist, Royal

• Society,London, 1880.

A. GRAHAM BELL, Ph. D.‘XV. W. GOODWIN, Ph. D.G. STANLEY HALL, Ph. D.JOHN J. KNOX, A. M.S. P. LANGLEY, Ph. D.SIDNEY LANIER.

GEORGE S. MORRIS A. M.SIMON NEWCOMB, LL. D.CHARLES S. PEIRCE, A. M.LEONCE RABILLON, Bach.bsLett.RICHARD M. VENABLE.

LECTURERS.

‘Washington.Cambridge.Cambridge.Washington.Allegheny.Baltimore.Ann Arbor.Washington.Baltimore.Baltimore.Baltimore.

Phonology.Plato’s Republic.

Psychology.Banking.Physics.

EnglishLiterature.History of Philosophy.

Political Econonsy.Logic.

FrenchLiterature.ConstitutionalLaw.

ASSOCIATES.HERBERT B. ADAMS. 123 ‘XV. MadisonSt. History.

A. B., Amherst College, 1872; Ph. D., University of Heidelberg,1878; Lectnrer on ISis—tory at SmithCollege.

MAURICE BLOOMFIELD. Sanskrit.A. 85., FurmanUniversity, 1877; Ph. D., JohnsHopkinsUniversity, 1879.

HERMAN C. G. BHANDT. 390 Druid Hill AVe. German.A. B., Hamil~n College,1872,andA. 85., 1875; AssistantProfessorof ModernLanguages

in Hamilton College,1874-76.

WILLIAM K. BRooKs. 181 N. CalvertSt. Biology.A. B., Williams College,1870; Ph. D., Hero’ardUniversity, 1873; Directorof the Chesa-

peakeZollogicalLaboratory.

WILLIAM HAND BROWNE. 2 Huntingdon Ave. Librarian.85. D.,Universityof Maryland,1850.

THOMAS CRAIG. Washington,D. C. AppliedMathematics.C. E.,LafayetteCollege,1873; Ph. D., JohnsHopkins University, 1878; of theU. S.Coast

andGeodeticSurvey.

A. MARSHALL ELLIOTT. 142 N. CharlesSt. RomanceLanguages.A. B.,HaverfordCollege,1866,and A. 85., 1878; A. B., HarvardUniversity, 1868.

CHARLES S. HASTINGS. 8 DenmeadSt. Physics.Ph. B., VelsCollege, 1870,andPh. D., 1873; Holderof the“Tyndall Scholarship’~in Paris,

1875.

HARMON N. MORsE. 12 DenmeadSt. Ohemistry.A. B., AmherstCollege,1873; Ph.D., UniversityofOdleingen,1875; Instructorin Chemistry

atAmherstCollege,1875-76.

AUSTIN SCOTT. Washington,D. C. History.A. B., Yale College, 1869; A. 85., University of Michigan, 1870; PIe. D., University of

Leipsic, 1871; late Instructorin History at theUniversityof Michigan.

WILLIAM T. SEDGWICK. 89 Mt. VernonPlace. Biology.Ph. B., Yale College, 1877; Ph. D., JohnsHopkinsUniversity,188L

HENRY SEWALL. 48 MeCulloli St. Biology.S. B., WosloyanUniversity,1876;Ph.D., JohnsHopkinsUniversity,1879.

WILLIAM E. STORY. 41 Franklin St. Mathematics.A. B., harvardUniversity,1871; Ph.D., Universityof Leipsie, 1875; TuterofMathematics

in HarvardUniversity,1875-76.

PHILIP R. UHLER. 218 W. HoffmanSt. Natural HistoryLibrarianof thePeabodyInstitute, andPresidentef the MarylandAcademyofSciences.

MINTON WARREN. 89 Mt. Vernon Place. Latin.A. B., TuftsCollege,1870; Ph.D., Universityof Strassburg,1879.

INSTRUCTORS AND ASSISTANTS.

R. DORSEY COALE. 215 MadisonAVe. Chemistry.Ph. D., JohnshopkinsUniversity,1881.

LAWRENCE B. FLETCHER. 263 N. Howard St. Physics.A. B., Columbia College, 1877, andA. M., 1880; Fellow of Columbia College, 1877-80;

Ph.B,, Jelons HepkinsUniversity, 1881.

FABIAN FRANKLIN. 228 W. LanvaleSt. Mathematics.Ph. B., ColumbianUniversity,1869; Ph.D., JohnsHopkinsUniversity,1880.

PHILIPPE B. MARCOU. 83 Hamilton St. French.A. B., HarvardUniversity, 1876,andA. 85., 1879.

HUGH NEWELL, Maryland Institute. Drawing,Instructorin Drawingin theMaryland Institute.

GEORGE F. NICOLASSEN. 600 W. LombardSt. Greekand Latin.A. B.,University of Virginia,1879,and A. 85., 1880.

EDMUND B. WILsoN. 172 W. Biddle St. Biology.Pb.B., Yale College, 1878; Ph.B., JohnsHopkinsUniversity, 1881,

CHARLES L. WOODWORTH, JR. 205N. HowardSt. Elocution.AmherstCollege.

FELLOWS DY COURTESY.

EDWARD M. HARTWELL. Biology.A. B., AmherstCollege,1873, andA.85., 1576; Ph.D., JchnsHepkinsUniversity,1881.

MITSURU KUHARA. Chemistry.5. B.,University of Tokie,Japan,1877.

ROBERT W. PRENTISS. Mathematics.S. H., RutgersCollege,5878.

HENRY A. SHORT. Greek.A. H., ColumbiaCollege,1880; Fellowof ColumbiaCollege.

GEORGE M. STERNBERG.85.D., CollegeofPhysiciansandSurgeons,N. Y.; surgeon,U. ~. A. Biology.

CHARLES A. VAN VELZER. Mathematics.5. B., Cornell University, 1876.

FELLOWS.WILLIAM .J. ALEXANDER.

A. B., University of London,1876.

JAMES W. BRIGHT.A. B., LafayetteCollege, 1877,andA. 85,1880.

EDWARD S. BURGESS.A. B., Hamilton College,1879.

WILLIAM J. CoMsTocK.Ph. B., Yale College, 1879.

WILLIAM C. DAY.A. B., JohunHopkinsUniversity,1880.

HENRY H. DONALDSON.A. B., Yale College,1879.

WILLIAM P. DURFEE.A. H., University of Michigan,1876.

GEORGE S. ELY.A. H., AmherstCollege,1878.

SPENCERH. FREEMAN.A. B., Universityof Rochester,1873,andA.85., 1878.

J.FRANKLIN JAMESON.A. B., AmherstCollege, 1879.

C. HERSCHEL KOYL.A. B., Victoria University,Ontario,1877.

OSCAR H. MITCHELL.A. B., MariettaCollege,1873, andA. 85., 1878.

BERNARD F. O’CONNOR.Bach.Is Leitres,Universitddo France,1874.

HENRY L. OsBoaN.A. B., WeelsyanUniversity, 1878.

CHASE PALMER.A. B., JohnsHopkinsUniversity,1879.

HERBERT M. PERRY.A. B., HarvardUniversity,1889.

EDWARD H. SPIEKER.A. B., JohnsHopkinsUniversity,1879.

HENRY N. STOKES.S.H., HaverfordCollege, 1878.

MORRISON I. SWIFT.A. B., Williams College,1879.

BENJAMIN W. WELLS.A. B., HarvardUniversity,1877, andPh.B.,1889.

Greek.

TeutonicLanguages.

Greek.

Cheonistry

C1hemistry.

Biology.

Mathematics.

Mathematics.

Physics.

History.

Physics.

Mathematics.

RomanceLanguages.

Biology.

Chemistry.

Mathematics.

Greck.

Biology.

Philosophy.

English.

138 [No. ii.

JULY, 1881.] UN] VEJ?SITYCIPCULAJ?S. 139

ANNOUNCEMENT OF COURSESAND LECTURES FOR 1881-82.The following announcementsare made by the several instructorsin respectto the Lecturesand otherCoursesof Instruction

to be given during the next academicyear.Thesestatementsshould be read in connectionwith the Registerfor 1880—81, to which they are in part supplementary. Ta

this Registerwill be found a full statementof the work performedduring the last academicyear andof the methodsof instruc-tion here pursued. Copiesmay be obtainedon applicationby postal card to the “Johns Hopkins University.”

Studentswho proposeto enterhere in the Autumn are requestedto addresstheir letters of inquiry and application to “ThePresidentof the JohnsHopkins University” rather thnn to any person by name.

MATHEMATICS.I. MathematicalSeminary.

The instructors and more advancedstudentsin Mathematicswill nieetmonthly, asheretofore,underthepresidencyofPROFESSOR

SYLVESTER, as a MathematicalSeminary,for the presentationund discussionof papersor oral communications.

The resultsof specialstudiesupon thefollowing subjects,amongothers,havebeenexaminedand discussedatthemeetingsof theSeminaryduringthe pastthreeacademicyears:

In 1878—79,Newton’srulefor thelimits of roots ofalgebraicequations;theruleofsignsin trigonometry; barycentriccolirdinates;doublepointsof planecurves;thequasi-eve-lute; centralharmonictransformation;specialeasesof Pascal’shexa,,ram;transforma-tionby elliptic codrdinates.

In 1579—fl), a generalizedform of analytical triangle; on vector ratios consideredastrigonometricfunctionsof anbies;on the condition that a lineartotaldifferential equa-tion of the first orderin anynumber of variablesmay admit of a singleprimitive; ageneralization,for n-fold space,of Euler’s equation for polyhedra;a completionof Fer-mat’s theorem;on generalizedformsof trigonometricratios; on volumesand surfacesofn-dimensionalspheres;on trianglesin- and ex-scribableto a beneralcubic curve;on bi-nomial congruences;rotationin four-dimensionalspace;a generalmethodof congru-encesand its applicationto the theoryof cyclotomic functions;completionof Wilson’stheorem,andon thenumberof th residues.

In 1889—81,on the resultantof two congruences;on the multisectionof the roots ofunity; on the prerogativeof a ternarydenominationalsysteriof coinage;on a notationfor totients; on two kinds of k-tb totients; outline of Clebseband Gordan’s methodoffinding thegroundformsof a binaryquantic;a proofof Abel’stheorem;proofthat thereareonly threelinearassociativealgebrasin which division isanunambiguousprocess;adeductionfrom the propertiesof a systemof ibree circles; on v. Gall’s tableof ground-forms for theoctavic; a newproof of Euler’s developmentof the infinite product(1—(I — x

2) (1—z3)...; on Newton’smethodof approximation;upon the similarity betweenp

congruencesandequationsanditssignificance;thecyclotomicfunctions,with respectto aprimemodulusp; on modularfunctions; on thepropertiesof the roots ofz2 = z mod.k;a theoremincluding Fermat’sand Wilson’s theorems;on binomialcongruences,(mod.p f (x)); on a ruleof signsin determinants;a problem in maximaand minima; a geo-metriclocus; on certaincompounddeterminants.

Abstractsof mostof thesepapershavebeengiven in successivenumbersof the Uni-versityCirculars.

II. AdvancedCourses.

1. Theoryof Numbers. Twice weeklyduring thefirst half-year. PROFESSORSYLVESTER.

2. DeterminantsandModernAlgebra. Twiceweeklyduringthe secondhalfyear. PROFESSORSYLVESTER.

3. Quaternions. Threetimesweeklythroughtheyear. DR.STORY.

4. AdvancedTopics of Higher Plane Curves. Three timesweeklyduring the first half.year. DR.’STORY.

5. AdvancedTopics of Solid Geometry. Three times weeklyduring thesecondhalfyear. DR. STORY.

6. Elliptic Functions and Introduction to GeneralTheory ofFunctions. Three times weekly during the first half-year.Dii. CRAIG.

7. AbelianFunctions. Threetimesweeklyduring the secondhalf-year. DR. CRAIG.

8. SphericalHarmonics. Twiceweeklyduring thefirst half-year. DR. CRAIG.

Threetimesweeklyduring9. PartialDifferentialEquations.the secondhalfyear. DR. CRAIG.

10. Calculusof Finite Differences. Threetimesweeklyduringthesecondhalfyear. DR. FRANKLIN.

ii. Calculus of Variations. Twice weeklyduring the firsthalfyear. DR. CRAIG.

12. Mechanicsof Rigid Bodies. Threetimesweeklyduringthefirst halfyear. DR. CRAIG.

13. ElasticityandHydrodynamics.ing the secondhalf-year. DR. CRAIG.

Three times weeklydur-

III. Major andMinor Courses.

14. ConicSections. Threetimesweeklyduring thefirst half-year. DR. STORY.

15. HigherPlaneCurves[ElementaryCourse]. Threetimesweeklyduring the secondhalfyear. DR. STORY.

16. SphericalTrigonometry. Twiceweeklyduring thesecondhalf-year. DR. FRANKLIN.

17. Solid Analytic Geometry [Elementary Course]. Threetimesweeklyduring thefirst halfyear. DR. FRANKLIN.

18. Differential and Integral Calculus. Three times weeklythroughtheyear. DR. FRANKLIN.

19. Total DifferentialEquations. Threetimesweeklyduringthe first halfyear. DR. FRANKLIN.

IV. Logic.The coursesin Logic will be conductedby Ma. C. S. PEIRCE,

andare announcedon page142.

PHYSICS.I. LaboratoryWork.

The PhysicalLaboratory,well equippedwith instruments(espe-cially with referenceto researchesin Heat,Electricity and Mag-netism), is open to advancedstudents,under the direction ofPROFESSORROWLAND, from 9 A. M. to 5 P. M.

The Laboratoryis alsoopento the studentspursuingthemajorcourse in this subject,and,for a weekly exercise,to the classinGeneralPhysics.

II. Lectures.1. PRoFESSoR ROWLAND will lectureon Thermodynamics,on

the TheoryofHeat Conduction,andpossiblyon Sound.2. DR. HASTINGS will conductthe major coursewhich will in-

eludelecturesweeklythroughthe year,iu additionto the work intheLaboratory.

140 JOHNSHOPKINS [No. 11.

3. Du. HASTINGS will give the instruction in GeneralPhysics(including Mechanics,Light, Sound, Heat,Electricity and Mag-netism).* There are daily exercisesthrough theyear,includingtwo lectures, three recitations,and one practical lesson in theLaboratory,(to which a selectnumberof studentsis admitted),weekly.

* To enterthis cla4s,a knowledgeof Trigonometryis essential.

CHEMISTRY.I. Laboratory Work.

The Chemical Laboratory,a new andwell arrangedbuilding,thoroughlyequipped,is open daily from 9 A. M. to 5 P. M. Theworkof theadvancedstudentsis underthedirectionof PROFESSORREMSEN, (who is in the Laboratoryfor consultationduring theregularworking hours),and hewill also,with the coi5perationofDR. H. N. MoRsE andDa. R. D. COALE, direct the generallabo-ratory work.

II. Lectures.1. Lectures in General Chemistrywill be given, four times

weekly during the first half-year,by PROFESSORREMSEN, and twoexaminationson theselectureswill also be held eachweek by DR.COALE. During the secondhalf-year,the lecturesandexamina-tions in GeneralChemistrywill be continuedby DR. MORSE.

2. Lectures on the Chemistryof Carbon Compoundswill begiven by PROFESSORREMSEN,four timesweekly during the secondhalf-year.

3. Lectures on Analytical Chemistrywill be given weeklyby DR. MORSE, throughtheyear.

4. There will be a course in Mineralogy conductedby DR.MORSE. It will consistof work in determinativemineralogyforeight to tenhoursweekly throughthe year; two lectures weeklyduring the first half-year; andone weeklyduringthe secondhalf-year. This course is opento thoseonly who havehadat leastaminor coursein Chemistry.

5. Lecturesonspecialtopicsin Chemistry,foradvancedstudents,by PROFESSORREMSEN. Thefirst of thesecourseswill probablybeon Berthelot’s“L~ssai de M~caniqueChimique.”

BIOLOGY.I. Laboratory Work.

1. TheBiological Laboratory,which containsanunusuallycom-plete collection of physiological instruments,is constantlyopenunder the direction of PROFESSORMARTIN. Opportunities forphysiological and morphological research~re ~PTordedto thosewho maybefound qualifiedto undertakeit, andinstructionis givento advancedstudents,and also to thosewho desirea knowledgeof Biology asintroductoryto thestudyof medicine,or as a branchof a liberal education.

2. TheChesapeakeZoologicalLaboratoryisopenfor thepresentyear,during the warmer months,at Beaufort, N. C., um~der thedirection of DR. W. K. BROoKS. it i~ a stationfor the prosecu-tion of original researchesin respeotto the marine life of theAtlantic sea-board,and advancedstudentsonly arereceived,

II. Lectures.1. PROFESSORMARTIN will give an advancedcourseof lectures

on Animal Physiology,twice weekly during the academicyear.2. Da. BROOKS will lecture from the commencementof the

sessionto the close of April on Humanand ComparativeOste-ology andon the Anatomyof the Mammalia.

3. Dii. SEWALL will meet for lectures or recitations a lessadvancedclassin Animal Physiology,four times weeklythroughthe year.

4. Dii. SEDOWIOK will meetfor lecturesor recitationsa classin GeneralBiology, four times weeklyduring theacademicyear.

5. Instruction in the elementsof Systematicand StructuralBotanywill be given in connectionwith Field Excursions.

GREEK, SANSKRIT AND LATIN.I. The Greek Seminarium, directedby PROFESSORGILDER-

SLEEVE.

Higher instruction in Greek is imparted chiefly through theagencyof the seminarium,in which the studentsare brought intocloser relationswith the professor and encouragedto performmoreindependentwork andengagein moreextendedexperimentsthanwould bepossibleon a systemof mererecitationor thesimplehearingof lectures. The plan of the seminarium,as developedespeciallyin thelastthreeyears,is basedon the continuousstudyof onegreatauthor or onegreatdepartmentof literature. Eachregular memberis requiredto take his turn as interpreter,critic,analyst,and special fields of researchare assignedaccordingtoprogressor bent. It may be addedthat while the seminariumdemandsa largeportion of the student’s time, the requirementsare not so greatasto precludeindependentstudy in otherdirec-tions,andcareis takensoto direct hisprivatereadingthat in theusualperiodof preparationfor thehigherdegreesa comprehensiveknowledgeof GreekLiteratureandGreeklife maybe gained.

Theseminariumconsistsof the Director,Fellows, andScholars,togetherwith such advancedstud~tsas may be found qualifiedto profit by the instructionandexercises.

During the next academicyear,the studyof PLATO and of theliterary formofGreelephilosophywill constitutethechiefoccu-pation of the members.

In connectionwith the seminarium,the Director will interpretthe Symposionof Plato oncea week with conferenceson topicssuggestedby the text.

ProfessorW. W. Goodwin, of Harvard University, will givethreelectureson the Republicof Plato,earlyin February.

The philosophyof Platowill also be takenup in a seriesof lec-turesby ProfessorG. S. Morris in hiscourseon GreekPhilosophy.

It is important that all should be providedin advancewith Ritter andPreller’s Ilistoria phitosophicceexfontium tocis coniexta,with a completePlatonic text and annotatededitions of some of the principal dialoguessuchas Hug’s Symposion,Deusehieand Cron’s,or Sauppe’sProtagoras,Deusehieand Cron’s Gorgias, Wagner’s Phaidon, Thompson’s Plsaidros,alsoRiddell’s Apotogy.

The Workfrom 1878 to 1881.

Theworking of the Greek Seminariurnmaybe illustratedby the fol-lowing summaryof thesubjectstreatedin thelast threeyears.

In 1878—79,theexercisesincludedtheanalysis,exegesisand criticism of selectedtractsof Lucian,andthe prosecutionof researchesintothe languageof Lucian and thelife ofthe secondcentury,sachasLucian’s relation to Herodotns,the Jonismof the Dee Syriaandthe De Asirelogia,the useof theoptativein Lncian Lucian and DiogenesLaertins,traditions as to the oriental origin of Greek philosophy,the worship of the SyrianGeddes~,Lucian’s attitudetoward religion,andLucianasa stndentof art.

JULY, 1881.] UNIVEBSITYCIBOULABS.

In 1879—80,thecentreof work wasAristophanes,and the play selectedfor specialstudywasthe Wesps. Themembersof the seminariumwererequired to presentin turn anexegeticalandcritical commentaryof a portionof this comedy,and this work constituteda regularweeklyexercise. In orderto securea wider knowledbeof the author,cursoryreadingswerealso instituted in the other plays,which were in like mannerassignedto certainstudents,chargedwith the dutyof preparingthe historical introductionandthe analysis. In this way nearlyall the membersweremadeacquaintedwith the bulkof Aristophanes,and someof them followed besidesa courseof studyin thefragmentsof thecomicpoets. Amongthe moreelaboratepapers,whichwerethefruit of this workIn Aristophanes,maybementionedthe following: On the tropologyofAristophanes;onthegenitivecasein Aristophanes;on theinfinitive in Aristophanes;on thedistributionof the chereuteiin the Wbsps.

In 1880—81,theserninariumwas mainlyengagedin thestudy ofthe Attic orators,espe-cial attentionbeingpaid to the developmentof languageand styleand to the antiquecanonsof aestheticcriticism. Thememberswererequiredto furnishin turn exegeticaland critical commentarieson selectportions of theorators,to preparehistoricalintro-ductions,to makeanalysesof speechesand abstractsof rhetoricaltreatises. Parts ofAntiphon, Andokides,Lysias, Isokrates,Isalos, and Demostheneswere studiedin thisway, and someof the minor orations of the four lastnamedwere comparedwith oneanotherin connectionwith theiedicie of Dionysiosof Halikarnassos.Besidesthis gen-eral work, subjectsofspecialstudyin the oratorswereassignedto individual membersoftheseminariem,andasseffort wasmadeto insureapersonalacquaintanceon thepartofallthe studentswith theworks of all theoratorsofthe Attic canon. Introductorylectures,informal examinationsandconferenceswerealsoheldby theDirectorat suitablepointsinthe course. Of the investigationswhich werecarriedon maybenoted:Studieson thenominalperiphrasesfor theverbin AntiphonandThukydides;on thegenuinenessof thefirst Antiphonteanoration;on synonymsin Antiphon; oii the useofthe locativeforma-tions,of mrp~’, andof ~mriin theorators;an elaboratestatisticof certainsyntacticalcharac-teristicsof Andokides;an inquiry into the influenceof technicalrhetoricon the i~uicrem~ofthe Attic drama;specialwork wasalsodonein Isaios,Lykergosand Deinarchos.

II. Greek (for advancedandgraduatestudents).

1. PRorisssoaGILDERSLEEVE will lecture on the History ofGreeleLiterature,weekly, for thefirst threemonths,andthereaftertwice weekly throughtherest of theyear.

2. PROFEssoRGILDERSLEEVEwill alsoconductaseriesof prac-tical exercises(at least twenty) in GreeleProseCompositionandin translatingGreekat dictation.

3. Dii. M. BLOOMFIELD will conducta class in ComparativeGrammar,with especialreferenceto Greek.

III. Sanskrit, etc.

The coursesin Sanskrit and Zend will be conductedby Du.M. BLOOMFIELD andwill include:

1. SanskritGrammar(Whitney’s) andinterpretation.2. Readingof EasyTexts.3. Introduction to theRig-veda.4. AdvancedSanskrit,9akuntala: GrhyasiXtra.5. PracticalIntroductionto Zend.

IV. Latin (for advancedand graduatestudents).

1. Da. WARREN will conduct a Latin Seminariumto meettwice weeklyfor the critical studyof VERGIL. Special attentionwill bepaid to the literaryform, to thedependenceofVergil uponGreekandLatin sources,and to his influenceupon contemporaryand subsequentpoets,as well as upon the prosewriters of thesilver age. Ped~igogicalneedswill be kept constantlyin view,and the seminariumwill be open to advancedundergraduateswho may proposeto becomeLatin teachers,if they shall be foundqualifiedto profit by theexercise.

Studentsareadvisedto providethemselvesin advancewith someeditionof theCommentaryof Servius to Vergil, andwith Kennedy’sannotatededition of Vergil, or Ribbeckscritical edition of thetext in threevolumes.

2. DR. WARREN will beginin Februarya seriesof weekly exer-cises in the interpretationof Latin Inscriptions, especiallythoseof theearlyperiod.

3. DR. WARRENwill also lectureduring the latter half of theyear on certaindistinctive featuresin the SyntaxofEarly Latin.

V. Greek(fort undergraduates).

1. Demosthenes,(Philippic and Olynthiac Orations). FromOctober to February, four hours weekly. PROFEssoR0. D.MORRIS.

2. Sophocles,(Ajax). Lyric Selections. From FebruarytoJune,four hoursweekly. PROFESSORC. D. MoRRIs.

3. Xenophon, (ilellenica, books i—iii). Lysias, (Select Ora-tions). From October to February,four hours weekly. MR.NIcoLAsSEN.

4. Homer, (Odyssey,six books). From February to June,four hoursweekly. MR. NICoLAssEN.

5. In connectionwith eachof the ahovecourses,therewill beweeklyexercisesin GreekProseComposition,andoccasionalprac-tice in readingat sight,andtranslatingGreekat dictation.

6. Towards the close of the year, PROFESSOR GILDERSLEEVEwill conduct an advancedclassof undergraduatesin the WaspsofAristophanes.

‘1. PROFESSORMORRIS will conduct two conferencesweekly,one, in Greekand Latin Metres,with practicalexercisesin versecomposition,if sucharedesired,theother, in Greek History.

Private ]?eading.—Studentshaving the time are encouragedto pursueparallel coursesof privatereadingunderthe directionof the instructor. This will be entirely voluntary, but thosepassingan examination upon suchwork will be able to completemajoror minor coursesin shortertime thanotherwise.

For ex~mp1e, those talcing the coursenumbered1 above may readIsocrates,Phitippus,and Panegyricus,or Plutarch’sLifeof Demosthenes.Those taking the coursenumbered8 mayread Xenophon,Oeconomicusand Agesilaus,or Plato,Apologyand &ito.

VI. Latin (for undergraduates).

1. Cicero, (de NaturaDeorum,book i). Lucretius, (bookv).Catullus,(Selections). From Octoberto February,sevenhoursin two weeks. DR. WARREN.

2. Terence,(Andria, Adelphoe). Plautus (Captivi). FromFebruaryto June,four hoursweekly. DR. WARREN.

3. Quintilian, (book x). Tacitus, (Dialogus de Oratoribus,Agricola, Germania). From October to February, four hoursweekly. PROFESSOR0. D. Moanis.

4. Juvenal, (Select Satires). Martial, (Selections). Pliny,(Select Letters). From Februaryto June,four hoursweekly.PROFESSORC. D. MORRIS.

5. Livy, (booksxxi andxxii, or xxiii and xxiv). From Octo-ber to February,four hoursweekly. MR. NICOLASSEN.

6. Horace, (Select Odes,Satires,Epistles.) From Februaryto June,four hoursweekly. MR. NICOLASSEN.

7. In connectionwith eachof theabovecourses,therewill beweeklyexercisesin Latin ProseComposition,andoccasionalprac-tice in readingat sight, andtranslatingLatin at dictation.

Private Beading.—Studentshaving the time are encouragedto pursueparallelcoursesof privatereadingunder thedirectionof the instructor. This will be entirely voluntary, but thosepassingan examinationupon suchwork will be ableto completemajoror minor coursesin shortertime than otherwise.

For example,thosetaking the coursenumbered1 mayreadCicero, deFinibus book i; deNalura Deorum,booksii andiii, andLucretius, hooks

and ii. Thosetaking thecoursenumbered3 mayread Cicero,de Orss-m~ore,book ii; Tacitus, Annals, books iii and iv, andStietonitis, Life ofTiberius.

141

142 JOHNSIIOPKINS [No. 11.

GERMAN.

The coursesin Germanwill be unde.r the direction of Ma.

BRANDT and will include:

I. AdvancedCourses (introductory to Germanicphilology).

Gothic, (Braune’s GotiseheGraminatik); Old High German,(Hahn’sGrammarandBraune’sReader);Middle High German,(Paul’s small and Weinhold’s large Grammar,reading of the“Minnesino- ~‘)•

II. Major and Minor Courses.

1. Major Course: Middle High German,two hoursweekly onehalf-year; Prose Compositionwith Krause’s Grammatik, onceweeklythroughtheyear; readingof Lessing’sProsa,Luther’s“An denAdel” and the principal plays of Goethe,SchillerandLessing.

2. Minor Course: Readingof Humboldt’s Prosa, Goethe’sG~5tz von Berlichingen, Herrnann and Dorothea, Prosa,etc.;Exercisesandgrammar,onceweekly throughthe year.

ROMANCE LANGUAGES.I. AdvancedCourses.Ma. ELLIOTT will conductthe advancedclasses,which will take

up the studyof the RomanceDialects, Old French, Provenyaland Wallachian.

II. Major andMinor Courses.

1. The major courseclasseswill read,with MR. ELLIOTT, OldFrench, (Aucassinand Nicolete, Suchier’sedition), and Italian,(Dante, Divina Commedia). Hewill alsogive a courseoflectureson French Phonetics.

2. The minor coursewill beconductedby Mr. MAROOII. Theclasswill first read Michelet’s Life of Jeanned’Arc for a fewweeks,andafterwardsother authorswill be takenup.

III. SpecialClasses.

1. A specialhistorical courseon the ModernFren4~hSocialistswill beconductedby Ma. MARcoU. He will also form a conver-sationclass,which will meetthreetimes weekly.

2. M. RABILLON will give coursesof public lectures,in French,andwill meet, in a private class, studentswho wish to perfectthemselvesin the useof oral andwritten French.

HISTORY AND POLITICAL SCIENCE.1. The minor coursein History will be conductedby Da. II.

B. ADAMS. It will include a course in MediaevalHistory, fivehoursweekly during the first half-year, and a course in Inter-national Law andDiplomatic History, five hoursweekly duringthe secondhalf-year.

Candidatesfor this minor coursemust passan examinationin Euro-peanandAmerican History. Freeman’s“ GeneralSketch,”andDoyle’s“United States”will serveto indicatetheamountof knowledgerequired.Au acquaintancewith French and Germanwill beexpectedof graduatestudents,andwill he requiredof undergraduateswho take the courseinInternationalLaw andDiplomatic History.

2. Da. H. B. ADAMS will alsoconduct,duringthefirst half-year,classesin the Sourcesof Early EuropeanHistory, one hourweekly, in Institutional History, one hour weekly, and in ItalianHistory, one hour weekly; during the secondhalf-year,he willconducta classin ComparativeConstitutionalHistory, andgivea course of public lectureson the Developmentof Civil Societyand of Internationalism.

3. Da. AUSTIN SCOTTwill give a courseof public lectureson theDevelopmentof the American Constitution, beginning aboutNovember 1.

4. Mit. R. M. VENABLE will give twelve public lectures onConstitutionalLaw, beginning in January.

LOGIC, PHILOSOPHY, ETC.I. Logic.Mit. PEIRCE will give two courseson Logic:1. An elementarycourseon GeneralLogic, deductive and in-

ductive,including probabilities. This coursewill be designedtoteachthemain principlesuponwhich correctand fruitful reasoningmustproceed;andspecialattentionwill be paid to the discussionof the significanceandvalidity of those logical conceptionsandmaximswhich arecurrentin literatureand in law.

2. A courseupon the methodsof science. A sketchof deduc-tive logic and the theoryof relative termswill leadto a studyofthe methodsof Mathematics. The theory of chancesanderrorswill next be expounded. Lastly, after the developmentof thegeneral doctrine of induction and hypothesis, the methods ofreasoningin several of the physical and moral scienceswill beexaminedin detail.

II. Philosophy,Etc.1. PRoFEssoRG. S. MORRIS will give class lectures, during

the first half-year, on Ethics and on the History of GreekPhilosophy. He will also give a course of public lectures.

2. DR. G. STANLEY HALL will lecture on Psychology.

PEABODY INSTITUTE LECTURES, 1881-82.The following coursesof lectures have beenarrangedby the Trustees of the PeabodyInstitute, to be delivered during the

coming winter:1. Da. EDWARD A. FREEMAN, of Oxford, England. Six lectureson

Otd, Middle and NewEngland, beginning November8.2. PROFESSORW. H. Goonv ‘AR, of the Cooper Union, New ‘York.

Four illustrated lectureson DecorativeArt, beginningNovember29.3. Da. C. S. HAsTINGs, of theJohnsHopkinsUniversity. Threeex-

perimentallectureson ElectricityandMagnetism,beginningDecember13.4. Da. JouN VAN BIRDER, of Baltimore. One lectureon theHuman

Brain and its relationsto Mind, December22.

5. GEORGE M. TOWLE, EsQ.,of Boston. Four lectureson Bismarek,Gambetta,Gladstoneand Beaconsfeld,beginningJanuary10.

6. PRoFEssoRD. CABY EATON, of New Haven. Four illustrated lec-tureson GothicArchitecture,beginningJanuary24.

7. PaoFEssoL~M. C. TYLER, of Cornell University. Four lecturesonthe Pamphleteers,Song-iVriters and Satiristsof the Revolution,beginningFebruary 7.

8. PRoFESSORW. F. APTHOR?,of BostonUniversity. Fourlectureson theGrowthof Music,with musical illustrations,beginning February21.

JIJLY, 1881.] UNIVERSITYCIRCULA115.

COLLEGIATE INSTRUCTION, 1881—82.information as to Graduate Instruction is given in other Circulars.

SPECIAL NOTICE.

Young men who desireto enterthe Johns Hopkins Universityfor collegiateinstruction, either as Matriculates,or as Studentsin branchespreliminary to Medicine, or as Special StudentsinMathematics,Chemistry, Languages,etc.,are requestedto pre-sent themselves,with snch introductions,written or personal,asthey cancommand,at the President’soffice, anymorningbetweenJune 1 nnd June4, inclusive,from 9 to 12 o’clock, whenarrange-mentswill be made for their examination,and information willbe given in respectto classes,terms,lodgings,etc. Thosewhocannot appear in June may presentthemselveson Tuesday,September20.

TIMES OF EXAMINATION.

Thereare two formal examinationsfor matriculation,the firstfrom June 6 to June 9, andthe secondfrom September21 toSeptember24, as follows:

LATIN,GREEK,

GERMAN,Fsu±xcse,

Alienday,June6.

Tuesday,June 7.9—12.8—6.

Wednesday,September21.LATIN,GRE~K,

Thursday, September22.GERMAN,FRENCH,

Wednesday,June8.9—12. ALGEBRA,3—6. GEOMETRY, - - - -

Thursday,June 9.TRIGONOMETRY, - - -

ANALYTIC GEOMETRY, - -

Friday, September23.9—12. ALGEBRA,3—6. GEOMETRY, - - - -

Saturday,September2h.9—12. TRIGONOMETRY, - - -

3—6. ANALYTIC GEOMETRY, - -

9—12.3—6.

9—12.3—6.

9—12.3—6.

9—12.3—6.

Candidatesmay offer some of the subjectsfor matriculationat theJuneexaminations,andtheothersin September.

Studentsresidentin andnear Baltimore areadvisedto presentthemselvesat theexaminationin June,so that if deficientin anystudy theymay preparethemselvesin it for thenext examinationin September. The resultsof thematriculationexaminationwillbe madeknown June10 andSeptember2~, at 12 M.

REQUIREMENTS FOR MATRICULATION.

The specialrequirementsfor matriculationareasfollows:Latin. Grammar,Prosodyand Composition; Ccesar,3 books; Ovid, 2300 verses(300

elegiac); Virgil, .~neid,6 books,and Eclogues;Cicere, 7 orations;Livy,1 book; Ilerace,Odes,2 books.

Greek. Grammar,Prosodyand Composition;Xenephon,Anahasis,4 books;Hamer,Iliad, 4 books; Heredetus,1 book;any onedrama.

Mathematics. Arithmetic, including the Metric system;Algebra, Todbunter, 38chapters;Geemetry,Plane and Selid,Chauvenet;Plane Trigenensetry,Chauvenet,5 chap-ters; Analytic Geemetry,Straight Line andCircle in rectangularcodrdinates,Salmon

(ConicSections)orHowison.Thesubjectsnamed,in both Mathematicsand Languages,merelyindicatethe rangeof

theexamination. Equivalentsare accepted.The accuratereadingat sight of passagespreviouslyunseenmayrenderunnecessary

the examinationin the booksabovespecified.Candidateswhodo notintendto pursuea classicalcoursemayofferGermanand French

insteadof Greek.Theequivalentof a minorcoursein oneof thesesubjectswill beexpected,and a good

elementaryknowledgeof the other.SPECIAL EXAMINATION IN EseGLIsse.—Allcandidatesfor admissionwill beexpectedto

satisfythe authoritiesthat,in addition to the studies.in Mathematicsand Languagesrequiredfor admission,they havebeenwell trainedin the ordinaryEnglishbranches,including the useoftheEnglish language,GeographyandUnitedStatesHistory.

SPECIALEXAMINATION IN NATURAL SCIENCE—Eachcandidatefor admissionis expec-tedto offer for exasninationin somebranchof Natural Science. PhysicalGeographyisrecommendedas within the reach of all. An elementaryacquaintancewith Botany,ZoOlogy,or NaturalPhilosophyisalsodesirable.

COLLEGIATE COURSES.

Coursesof study arearrangedfor collegiatestudentsin Mathematics,Physics,Chemis-try andBiology; in Greek,Latin, French,Germanand English;andin History, PoliticalEconomy,etc. It isnotsupposedthatanystudentcanfollow aD thesecourses,buteveryoneis requiredto selectsuch a combination aswill secureto him a liberal education,foundedupon studiesin severalbranchesof literature and science. As a rule, eachstudentwill, havethreecoursesin progresssimultaneouslywith dyeweekly exercisesineach.

Thefollowing combinationsaresuggested(but notprescribedexclusively)asan aidtostudentsin the selectionof their coursesfor theBachelor’sDegree:

1. CLASSICAL, in whichGreekandLatin arethe mainsubjects,anda ModernLanguage,onePhilosophicalandosseScientificcoursesubordinate;2. MATHEMATICAL, with Math-ematicsand Physicsasmainsubjects,and in additionaModernLan~uage,Chemistry,andone Philosophicalcourse; 3. SCIENTIFIC, in which markedproficiencyin Mathematics,and in either Chemistry,Physicsor Biology is required,and in addition oneScientificcourse,onePhilosophical,and one in Language; 4. LITERARY, in which the Romanceand Teutonic Langua~esare takenasthe main subjects,and Latin and anyothertwocourses,oneofwhich must beScientific, assubordinate;5. PRELIMINARY TO MEDICINE,in which the principal studies are Biology and Chemistry, and in additionPhysics,aModern Language,and one Philosophicalcourse; 6. PRELIMINARY TO THEOLOGY, inwhich GreekandHebrewarethe principal subjects,andonePhilosophicalandtwo Scien-tific coursessubordinate;7. PRELIMINARY TO LAW, in whichmarkedproficiencyin His-tory and Philosophyis required,andin additiona ModernLanguage,and two Scientificcourses;S. PRELIMINARY TO BusINEss.

SPECIAL COURSE PRELIMINARY TO MEDICINE.Thiscourseis framedto meetthewantsof thosewho intendat a laterday to beginthe

study of Medicine.

The requirementsfor entranceby non-matriculatedstudentsto the course areasfollows:

English. Candidateswill be examinedin the wholeof Lounsbury’sHistory of theEnglish Language,andwill be required to satisfythe examiner,by meansof a writtencomposition,of their ability to expressthemselvesin correctandidiomatic English,pro-perlyspelled,punctuated,anddividedintoparagraphs.

Elementary Mathematics. Arithmetic; Algebra; threebooksof Euclid, or anequivalentamountofGeometry;PlaneTrigonometry,andthe useof Logarithms.

The examinationin Algebra will beconfinedto thefollowing: definitionsandexplana-tions of algebraicalsignsandterms;addilion;subtraction,multiplication anddivisionofalgebraicalquantities; ratio, proportionand variation; simpleequationsinvolving notmore thantwo unknownquantities.

Latin. Translationof passagesfrom the first four booksof Ceesar,Dc Bells Gallice,andofthesixth book of the.Aineid ; theelementsof Latin Grammar,especiallyAccidence.

Candidateswho obtain permissionat leastafortnight previously, will bepermitted tooffer themselvesfor examinationin equivalentportionsof otherLatin classicsthanthosepresentedabove.

Physical Geography. Guyot’s Physical Geographyand Huxley’s Physiographyarerecommendedastextbooks.

French asacl German. In addition to the abovesubjucts,candidates may offerthemselvesfor examinationin FrenchandGerman;thosewhopasswill beexcusedfromattendanceupontheinstruction in tisoselanguagesduring the subsequentcourseofstudy.

The examinationin Frenchand Germanwill test the candidate’sknowledgeof theelementsof the Grammarof thoselanguages,and his ability to translateat sight easypassagesfrom proseauthors.

Drawing. Someknowledge of Drawing is very desirable; studentswho arepro-ficientin this subjectmayomit it fromthesubsequentcourse.

Thosewho wish to follow this courseshouldindicatetheir intentionto do so beforetheexaminationbe,,ins.

A circular giving the detailsof thecoursemay beobtainedon application.

SPECIAL STUDENTS.In exceptionalcases,young men of collegiate age, who can satisfya committeecon-

slating of the President and two of the chiefinstructorsthat they are sufficientlyadvancedin characterand attainmentsto beallowed theprivilege,and thatthereissomegood reasonwhy theyshould notoffer themselvesfor matriculation,maybe admittedtocertainclasses.

CHARGES FOR TUITION.The chargefor tuition sseIghtydollars peryear. A depositof ten dollars is required

fromeachstudent. Theress anaddltsonslfee for material,etc., in the Laboratories.

SC HOLA RSH I PS.A limited numberof freescholarshipsare awardedto young men from Maryland,

the District of Columbia,VirginiaandNorthCarolina.

Instructionswill beresumedfor thenextacademicyearon Tuesday,September27, 1881.

143

Baltimore, May 15, 1881.

JOII3~SffOPKINS [No. 11.

SYNOPSISOF THE RECENT SCIENTIFIC JOURNALSPublished here.

American Chemical Journal. Editedby PROFESSORIREMSEN. Vol. 1ff. No. 1. March, 1881.

Article 1.—Revisionof the Atomic Weight of Aluminum.By J. W. MALLET, F. R. S.

This is the first half of an exhaustiveaccountof the author’s workon the subject mentioned. After a brief statementregardingearlierexperimentsundertakenby Berzelius, Sir Humphrey Davy, Thomson,Dumas, Tissier and others, for the purposeof determiningthe atomicweight of aluminum,a largenumber of ingenious and careful newex-perimentsaredescribed. Thevaluesnow adoptedby differentwriters onchemical subjectsvary between27.26and27.5. The mean resultof thenew experimentsis 27.02. Threemethodswereused.

1 st. Ainmonium alum was ignited with great precautionsand theamountof aluminum oxide,thus formed, wasdetermined.

2d. Theamountof silver requiredto precipitatethe brominefrom purealuminumbromidewas determined.

3d. A knownweightof aluminumwasallowedto acton a concentratedsolutionof sodiumhydrateandtheamountof hydrogenevolvedcarefullymeasured;andin someother experiments,involving the same reaction,the hydrogen,insteadof being measured,was passedover cupric oxideand thewater,thusformed, weighed.

The resultto which the author is led is 27.019-4- .003, or 27.02. Thisbeingsonear an integer leadsto a discussionof the bearingof the finalresultupon “Prout’s law.” Theauthorthinks that “not only is Prout’slaw not as yet absolutelyoverturned,but that a heavyand apparentlyincreasingweight of probability in its favor,or in favor of somemodi-fication of it, existsand demandsconsidere,~tion.”

Article 11.—NewPhenetolDerivatives. By E. J. IfALLOCK.A descriptionof n few new substitution-productspreparedaccordingto

well known methods.

Article 111. Preliminary Notice ofa NewVegetableColor-ing Matter. By S. P. SADTLER andW. L. ROWLAND.

Thecoloringmatterwasextractedfrom “a variety of wood,calledBeth-a-bctrra, which had beenrecentlyimportedfrom thewestcoastof Africa.”The new substanceconsistsof microscopicplates madeup of a seriesoffiat prisms,joined laterally. It has the formula 028112905,orpossibly(J

22 H2304,and appearsto be related.tochrysophanicacid andthechrysa-robin which Liebermannand Seidlerfoundto be thechief constituentofgunpowder.

Article 1 V.—ConcerningPhthalimide. By M. KULIARA.On treating phthalicacid with phosphoruspentachlorideit is converted

into a chloridewhich when treatedwith aqueousammoniais convertedback,for themost part, into phthalic acid. Under somecircumstances,however, the natureof which could not be determined,a substanceisformedwhich hasthesamecompositionasphthalimide,but differs from

it markedlyin its properties. It is probably06114{ ~~NH) } 0. When

thechlorideof phtbalicacid is treatedwith ammoniagas,it is convertedinto phthalimide. The experimentsdescribedin this paper make thecommonlyacceptedformula of phthalimideappearprobable.

Article V.—Researcheson the SubstitutedBenzyl Com-pounds:—SubstitutedBenzaldehydes.By 0. L. JACKSON andJ.F. WHIT1~.

The substancesdescribedare parachlorhenzaldehyde,parabrombenzal-

dehyde,paraiodbenzaldehydeandmetabrombenzaldehyde.

Article VI.—On .Furfurol and certain of its Derivatives.By H. B. HILL.

On examining “the working of a new processfor the manufactureofaceticacid by the dry distillation of wood at a low and carefully regu-lated temperature,”the author noticed that, in the rectification of thecrude wood spirit, a yellowish oil passedover with the vaporof waterafter themorevolatile portions had beendistilled off. An examinationof this oil showed that it containeda largeamount of furfurol whichcould be isolatedin a pure statewith little trouble. Startingwith thefurfurol thusobtained,the author hastakenup a carefulstudyof a num-ber of its derivatives, particularlyof mucrobromic acid. In this paperthepreparationof theacid and that of its saltsis first described;then theactionof phosphoruspentabromide,acetylchlorideandof bromine.

Article VII.—Chlorobromideof Lead. By M. W. ILLs.

Among thefurnaceproductsfound by theauthorat theGrant Smelt-ing Co. works, is a peculiar substancewhich analyses prove to be achiorabromideof lead, Pb (BrOl). It occursin several forms, as forexample,in pure white,delicate,dendritic plates,not unlike crystalsoflead chloride; in long acicular needles;in semi-fuseddistorted needleshavinga slightly yellowish tint, and alsoin entirely fused warty masses.Thecorrespondingsilversalt was madeandwasfoundto resemblecloselyBreithaupt’smegabromiteandRichter’sembolite.

Article VIII.—Allcalimetrywith Phenol Phthaleinas Indi~cator. By II. B. WARDER.

The experimentsof the author, as well as thoseof Luck, show thatphenol phthalein may be used to distinguish between alkalinity andcausticity.

Brief Reviewofthemostimportantchangesin the IndustrialApplicationsofChemistrywithin the lastfewyears,(continued.)By J. W. MALLET.

The specialsubjectstreatedin this reportare:1. Art~/lcial Production of Heat for Domestic Purposes. 2. Artsficial

Production of Light: a. Gandles; b. Liquid illuminantsfor burning inLamps; c. Illuminating gas. 3. Appendix to Production of Heat andLight.—Matches.

Reporton Analytical Chemistry. By H. N. MORSE.

Recentimprovementsin analyticalmethodsas applied to thefollowingsubstancesare discussed:Oxygen; Ozone; Water; Hydrogenperoxide;Halogens; Nitrogen; Arsenic; Carbon.

Notes: The Densityof Iodine Vapor, by Crafts and Meier; Ozone,byHautefeuilleand Chappuis;Nitr~/lcation, by Hautefecille and Chappuis;Picene,by C. Graebeand J. Walter.

RecentPublicationsRelating to Ohesnistry.

Vol. III. No. 2. May, 1881.

Article 1.—Revisionof the Atomic Weight of Aluminum.By J. W. MALLET, F. R. S.

Conclusion of the paper of which the first half appearedin the lastnumber. Thegeneralresultsof thewholepaperweresummedup in theabstractof No. 1 (above).

Article If.—On Furfurol and certain of its Derivatives.By H. B. HILL.

Continuationof thepaperof thesametitle in the precedingnumber.In this instalmentthe subjectsdiscussedare: thedibrommaleic acid ofKekuld; mucobromic acids with oxidixing agents; decompositionofmucobromicacid by heat; and theactionof bariumhydrateon theacid.

Article 111.—On the Diiodbromacrylic and Chlorbrom-acrylic Acids. By C. F. MABERY and RACRAEL LLOYD.

An accountof someof thederivativesof theacidsmentioned.

Article IV.—On Microlite from AmeliaCo., Virginia. ByF. P. DUNNINGTON.

The mineral describedis found in crystalsvarying in dimensionsfrom.one-tenthto three-quartersof an inch, andin largercrystallinemassesofwhich onewas obtainedweighing eight pounds. An analysiswas made

which led to theformula 8 (Ca2Ta2O5)+ NbOF3. It is essent~Lm(0aW03) ially a

calcium tantalate.

Article V.—On the Conductof Finely DividedIron towardsNitrogen. By IRA REMSEN.

In examiningcertain carbon compoundsaccording to the usualmethodfor the detectionof nitrogen, the question arosewhetherif sulphur ispresentin addition to the nitrogen, the latter can bedetected. Certaincompoundsknown not to contain nitrogenwere treatedwith purefinelydivided iron and sodium, and a precipitate afterward obtained whichindicatedthe presenceof a cyanide. Oncarryin0theexperimentsfurtherit was found that when iron by hydrogenand certain non-nitrogenous

144

1JiYIVEI?SJTYCJROULAIi?S.

organicsubstancesare heatedtogetherwith metallicsodium in anatmo-sphereof nitrogen, a cyanide is readily formed. The nitrogen is thusabsorbedand convertedinto thecyanidemuchmore readily than in thecaseof anyother reactionasyet known.

Brief Reviewof the mostimportantchangesin theIndustrialApplication.sofChemistrywithin the lastfewyears,(concluded).By J. W. MALLET.

The subjectstreatedare: 1. Materials employedin Washing:a. Soap,b. AccessoryMaterials usedin Washing. 2. Appendix to Washing: a.Peifumes. 3. Materials for Writing, Printing, etc.: a. Paper; b. Inkc. Mucilage; d. Artists’ pigments.

RecentProgressin Agricultural Science. By II. P. ARMSBY.

Thesubjecttaken up in this report is the respirationofplants.

Notes: AsbestosStopperfor C’ombuslion Tubes,by J. FlemingWhite;Actionof Ozoneon Germs containedin the Air, by E. Chappuis; Qurn-quivalenceofBoron, by Michaclisand Becker;Evaporationwithout Fusion,by Lothar Meyer; On theAbsorptionof SolarRaysby AtmosphericOzone,by W. N. Hartley; On Chrbo. ytartronic Acid and theStructuralFormulaof Benzene,by L. Barth; On the Conduct qf Palladium, RhodiumandPlatinum towardsIlluminating Gas,by Th. Wilm; On theAtomic Weightof Platinum,by K. Seubert.

RecentPublicationsrelating to Chemistry.

Contentsof Vol. III, No. 3. June, 1881.

Article 1.—Onthe Depositionof Copperon Iron in a Mag-netic Field, by IRA REMSEN.

Article 11.—Determinationof Chromium in Chrome IronOre, by II. N. MORSE and W. C. DAY.

Article 111.—OnFurfurol and certain of its Derivatives,(concluded,)by II. B. LuLL.

Article IV.—Dinitroparadibrombenzolsand their Deriva-tives,by W. D. SCHOONMAKERand J. A. VAN MATER.

Article V.—Onthe Molecular WeightofHydrojluoric Acid,by J. W. MALLET.

Article VI.—SomeDouble and Triple OxalatescontainiNgChromium,by F. W. CLARKE.

Article VIL—The Titration of Tartaric, Malic and CitricAcids with PotassiumPermanganate,communicatedby F. W.CLARKE.

Article VIIJ.—RelationbetweenTemperatureand the Rateof ChemicalAction, by R. B. WARDER.

Article IX.— Oxidation of $ulphaminemetatoluicAcid inAllealine and in Acid Solution, by R. D. COALE and IRAREMSEN.

Article X. — Concerning lilesitylenic Sulphinide, by IRAREMSEN and P. H. BROUN.

Also Reports,Reviewsand Notes, by R. II. CHITTENDEN,H. N. MORSE, R. B. WARDER andJ. W. MALLET.

American Journal of Philology. Edited by PRO-

FESSOR GILDERSLEEYE. Vol. II, No. 5, 1881.

Article I. Verrius Flaccus, (Secondpaper). By HENRYNETTLESHIP.

The main question raised in this paper is whether the philologicalwriters of thefirst five centuriesof theChristianera havepreservedfrag-mentsotherthanthosewhich havesurvived in theepitomesof FestusandPaulus. The work of Verriuswas the first great encyclopwdiaalpha-betically arrangedthat was known in Roman literature and thereisevidenceenoughthat it was largelyconsultedby the scholarsand anti-quariansof thefirst and secondcenturies—soby Quintilian, by Pliny theElder, by Velius Longus. Aulus Gellius studiedVerrius Flaccusa greatdealand in connectionwith this part of his subject,ProfessorNettleshipexaminesthe relation of Nonius to Verrius Flaccus, and comesto the

145

conclusionthat the numerouscoincidencesaredue to the fact that bothwriters used thesameauthorities. Nonius who has beenconsideredthegreatestfool in theworld of scholarsdoesnot, afterall, seemto fall muchbelow thestandardof an African of thethird centuryA. D. In anycase,t~e important matter is to ascertainwhatwere the sourcesfrom whichNonius drewthe materialsfor his lucubrations. The theorywhich findsmost favor among recent scholars is that Nonius copied largely fromGellius, and that the non-Geilianpart of his book is patch-workmadeupout of commentaries;but ProfessorNettleship’saim is to makeit proba-ble that Nonius did not borrow from Gellius at all, and that thereisnothing to showthat hehad ever read Gellius. They simply drewfromthe same sourcesas did also Julius Romanus and Lutatius Catulus.Severalof the noteson Vergil in Macrobiusare ultimately derived fromVerrius Flaccus,a factwhich shows that Verrius was oneof the earlie~tscholarswho contributed anything to the interpretation of Vergil. Attheclose of his articleProfessorNettleshipsubjbinsa specimenof recon-struction of partsof thefirst two lettersof the De VerborumSignificatufrom notesin writers later thanVerrius.

Article IL A StudyofBentley’sEnglish. By hENRY E.SHEPHERD.

Bentley’sEn~lish falls for themost part, accordingto ProfessorShep-herd, within a periodof change,a period that is distinguishedby theexpansionof simple,conciseEnglish prose and the completedecadenceof theponderous,complicatedsyntaxof the formerage. A morevigor-ous, nervous,energeticEnglish thanBentley’shasrarelybeenproduced~and ProfessorShepherdin illustration of the peculiarities of Bentley’sdiction hasselectedprincipally from theDissertationof Phalaris,1. Ex-pressionsthat have becomeobsoletein the literary form of thelanguage,thoughstill currentin familiar speech. 2. Wordsthat areoften regardedin our day as of recentintroduction into the vocabulary. 3. Wordsorexpressionsfrequently stigmatizedas “Americanisms,”thou~h in manyinstancessurvivorsof olderandreputableusage. 4. Wordsandphrasesemployed with a peculiar significance, sometimesarchaic, sometimesapparentlyimpressedupon them by Bentley.

Article III. On the ConsonantDeclensionin Old Norse,(First paper). By S. PRIMER.

The article openswith an exposition of thetwo prevalenttheoriesoforiginal consonantstems or original vowel stems advancedin explana-tion of the consonantdeclension in Germanic. The stems are thendivided into four groups: 1, theu- and i- (relatively -a- and-n-) stems;2, thenamesof relationship; 3, the presentpartciples; 4, the I- stems,andGroupI carefully consideredand comparedwith thesamewords inthe sisterlanguages... The vital questionbetweenthese two conflictingtheoriesis theumlaut, i. e. whetherit wascausedby thea of theending-asor whether it is due to the fact that these stemswere onceu- and istems. In order to get at the truth of the matter it was necessarytoexaminehistorically theinner developmentof theu- and i- stemsin OldNorse, Old English and Old Frise. The first partof the investigationbreaksoff in the midst of this examinationwhich will becontinuedinthesecondpart.

Article II~. On theEnclitic Ne in Early Latin. By MIN-TON WARREN.

The aim of thewriter is set forth in the opening paragraph,viz: toshow that the enchiticne in early Latin was not confined to questions,and to establishaprobability in favor of the existenceof two particlesn~ distinct in origin andsignification. Fourteenpassagesfrom Plautus,Terenceand Ennius are then discussedin which ne is foundin theMSS.wherethesenseeither dQes not requireor doesnot admit of an interro-gation. In eight of thesepassagesmostof theeditorshaveremovedne,e.g., in Adelph,770, Pun si meus......... The writer proceedsto showthat Prisciandistinctly recognizesan affirmative n~, for which he hasbeenundeservedlyridiculed by Hand. The evidenceof old glossescol-lected by thewriter in Paris,St. Gall andBerneis then adduced,andtheinterpretationof ni by enim,ergo,vero, usqueand etiasn shown to restupongoodgrammaticaltradition. Theexistenceof a negativen~ in suchexpressionsasdixin = nonnedixi is distinctly admitted,but for theneinegone,tune,etc.,anaffirmative origin is claimed. Supportedby thecloserelationsof this n~ to enim and nempeand by the compoundnemutin aglossof Festus,the writer positsapre-Plautinenemas theoriginal formof n~. Finally two possible instancesof survival of the form nim arecited, Trin., 922, andMere.,767.

The Reviewsand Book Notices containarticles on Dellbriick’s Grund-lagendergriechisehenSyntax,Enthoven’sDissertation on theIon of Eu-ripides, Timayenis’History of Greece, Paul’s MittelhochdeutscheGram-matikandWeinhold’sKleine mitlelhochdeutscheGrammatik,Carpenter’sGrundrissderneuislded’ischenGrammatik,Ward’sEnglishPoets,M allery ‘sCollection of Gesture-signsand Signalsof the North American Indians,PrattandLeafs Storyof Achilles,Hart’sSyllabusofAnglo-SaxonLitera-ture,andGummere’sAnglo-SaxonMetaphor.

JULY, 1881.]

JOHNSHOPKINS

Reportsare given of K6lbing’s EngliseheStudien, .Journal Asiatique,RheinischesMuseum,Phitologus,Neuc JahrbiicherfdrPhilologie u. Pueda-gogik, Archivfitr mittel- und neugriechisehePhilologie.

List of RecentPublications.

No. 6 (beingthesecondnumberof Vol. II) of the AMERICAN JOURNALOF PHILOLOGY will contain:

The first article of PRoFESSoRSHORT’S series on the Revisionof theNewTestament,(a preliminary statementas to theconditionof theGreekandof the Englishtext.)

Theconclusionof Da. PRIMER’S essayon theGonsonantDeclensioninOld Norse.

An unpublished Icelandic poem, (Fable of the Fox,) edited by DR.W. H. CARPENT. R.

A statisticof the useof Mie in Old French, by MR. B. F. O’CONNOR.Notesby DR. S. GARNER, PROFESSOR M. W. HTJMPHREYS, MR. A. D.

SAVAGE, andPROFESSOR STIEPITERD.

Reviews,BookNotices RecentPublications.

Studiesfrom theBiologiea~Laboratory. Editedby PROFEssoR MARTIN. Vol. II. No. 1.

Article 1.—AContributionto theStudyofInducedKeratitis.By WILLIAM COUNCILMAN, M.D. With one coloredplate.

(Reprintedfrom theJournalof Physiology. Vol. III, No. 1.)Theauthor givestheresultof an extendedseriesof histological obser-

vationsmadeon inflamed corneasandshowsthat in theprimary destruc-tive processesthe “wanderingcells” foundin the lymph channelsplaythemain part; while in thesubsequentregenerationit is thepropercor-nealcorpuscleswhich arethe activeelements. Theselatter multiply bydivision aroundthezonewheretheinflammationhasdestroyedthecorneaandbuild up thenew tissue.

Article IL—Somefurther Observationson Heat Dyspncea.By CHRISTIAN SIHLER, M.D., Pa.D.

(Reprintedfromthe Journalof Physiology. Vol. III, No. 1.)In this paperthe author gives an accountof further experimentson

this subject,(seeStudies from theBiological Laboratory,Vol. I, No. 2).He shewsthat the hurried respirationswhich result from exposureto awarm temperaturearenot mainly, if atall, dueto a direct actionof warmblood on therespiratorycentre,ashasbeenmaintainedby Goldsteinandverygenerallyaccepted,but are dueto astimulationof peripheralsensorynerves,either by the warm air acting on the skin, or the warm bloodflowing throughvariousorgans.

Article 111.—TheInfluence of Quinine upon the ReflexExcitability of the Spinal Cord. By W. T. SEDGWICK, Ph. D.

(ReprintedfromtheJournalof Physiology. Vol. III, No. 1.)

Theexperiments,madeon frogs,wereundertakenwith thespecialviewof settlinghow quinineactsin depressingthereflex excitability; whetherby exciting the so-called“centresof Setschenow’ (whoseexistencehadbeen made doubtful by the work of various experimenters,though stillperhapsgenerallyaccepted,)or in some other manner. The conclusionarrivedat is that no support of Setschenow’stheorycan bedrawn fromtheactionof quinine,which exerts its influenceby stimulating sensoryfibres, chiefly in thevagi,andis thereforecomparablein its action to thewell known reflex depressinginfluence of powerful stimulation of anafferentnerve.

Article IV.—TheEarly Developmentof the Wolffian Bodyin Amblystomapunctatum. By S. F. CLARKE, Ph. D. Withthreeplates.

The conclusionsarrivedatare that the methodof developmentof theurino-genital systemin this form is quite different from that in alliedgenera,but in many respectsresemblesthat occurring in the Elasmo-branchFishes, thoughdifferingfrom it in others.

Article V.—Noteson the FormationofDentineand OsseousTissue. By CHRISTIAN SIHLER, M. D., Ph.D. With onecoloredplate.

The paperdealswith a numberof points of detail on these subjects,concerningwhich thereare importantdifferencesamongprominenthis-tologists, and endeavors,by theuseof new methodsof working, to deter-mine which view is themorecorrectin eachcase. The resultsarrived atdo not readily admit of statementin a brief abstract.

Article VI.—The First Zoca in Porcellana. By W. K.BROOKS, Ph. D., and E. B. WILSON, Ph.D. With two plates.

This paperis basedon the study of the eggsof a femaleof Porcellanaocellata,obtained at the Marine Station of the University last season.Theeggswerekept aliveuntil theyhatched,andthen the larvncarefullywatched and their successivestagesof developmentstudied. The formand numberof theappendagespresentmanypointsof greatmorphologi-cal interest.

Article VII.—The Study of iluman AnatomyHistoricallyand Legally Considered. By E. M. IIARTWELIJ, Pa. D.

This article is basedon paperspublished by the authorin theJournalof theAmericanSocial ScienceAtsociation,theBostonMedical andSur-gical Journal,and the Brooklyn Annals of Anatomy and Surgery,butin its presentform containsmuch new matter. It givesageneralaccountof the history of the studyof human anatomyand of legislative enact-mentswith respectto it; andin moredetail treatsof thesametopicswithreferenceto theUnitedStates.

Article VIIL—On the RhythmicNature of Segmentation.By W. K. BROOKS, Ph. D. With one plate.

Theauthor callsattentionto thefact that thesegmentationof an ovumis not a coutinuousprocess,but long periods of rest alternate,in manycases,with brief periods of activity, during which greatmorphologicalchangesoccur. He describesin detail theprocessasobservedin theovumof anosseousfish, and suggeststhat theexplanationof this intermittenceis to be sought in the expenditureof energy taking place during eachepoch of cell division, which necessitatesa time of rest, during whichassimilationsmay occur,before furtheractivity canbemanifested.

Article IX.—ANewMethodofStudyingtheMammalianHeart.By II. NEWELL MARTIN, M. D., D. Sc., M. A. With one plate.

The authordescribesin detaila methodof physiologicallyisolating themammalianheart from all of the remainderof the body but the lungs,andkeeping it alive for severalhours under conditionspermitting of areadyobservationof theinfluenceupon it of varying temperatures,vary-ing arterialpressures,differentdrugs,etc.,etc. Themammalianheartcanthusbestudiedalmostasthoroughlyasthe frog’s hearthashithertobeen.

Article X.—The Processesoccurring during the SecretoryActivity of the Pepsin-FormingGlandsof the Frog. By II.SEWALL, Ph. D.

The authorconcludesthat a large amountof secretionmaybe causedto appearin thestomachof thefrog without a correspondinghistologicalchangein thecesophagealglands. This secretionis broughtaboutby theinjection of certain food materials under the skin. The microscopicchangeswhich the pepsin-formingglandsundergoin natural digestionmaybe startedby the absorptionof fluid from the rectum alone. Thedisappearanceof granulesfrom thepepsinglandsin digestionis probablystartedby local stimulationof thealimentarycanal; the regenerationofthe granules dependingupon the presenceof new building material intheblood itself.

American Journal of Mathematics. Editor inChief, PROFESSOR SYLVESTER; Associate Editor in Charge,DR. STORY. Vol. IlL Nos. 3, 4, 1880.

Article 1.—AMethodof Developingthe Perturbative Func-tion ofPlanetaryMotion. By SIMON NEWCOMB.

“The objectof thepresentpaperis to exhibit a methodof effectingthedevelopmentin powersof the eccentricities,which seenisto me to offersomefeaturesof interest,and possibly to contain thegermof someprin-ciple which I havenot fully grasped,andwhich mayadmit of wider andmore important applications. I refer especiallyto the expressionof thecoefficient of eachpowerof theeccentricity in termsof thecoefficientsoflower powers,and to the expressionof the coefficient of each term in-volviug theperihehiaof two planetsasthesymbolic productof coefficientsinvolving theperihelion of oneonly Onegreatpractical advantageof the processis that it is reducedto a uniform operation of algebraicmultiplication,which canbeexecutedby an unskilledcomputer,andcanbecarriedto anyextentwithout repeatingthepreviousprocesses.”

Article 11.—OnDe Morgan’s Extensionof the AlgebraicProcesses. By MISS CHRISTINE LADD.

An investigationof the propertiesof the processeswhich result fromthe extensionin both directionsof the addition and multiplication pro-

146 [No. 11.

UNI VEJ?SITY CIBOULAPS.

cessesin a sensein which multiplication is an extensionof addition. Then-tb processis denotedby +~ordinary addition is —j--, and ordinarymulti-

eplicatiion is+. The n-tb processis introduced throu

1,h the logarithmic

process,thus:log. ab=log. a-f-log. b,i. e. log (at b) ==log. a~log. 6,

andin generallog L b~ log a± log 6,(ar) 14-1

from which follows

and

theformerof which gives the extensionto all positive valuesof n, andthe latter to all negativevaluesof n.

The inversesof theseprocessesarealsotreated,and a numberof curiousresultsobtained.

Article 111.—Onthe Motion of a Perfect IncompressibleFluid whenno SolidBodies are Present. By H. A. ROWLAND.

Article If—On CertainPossibleCasesofSteadyMotioninan IncompressibleViscousFluid. By THOMAS CRAIG.

A classof fluid motionsis studiedfor which thequantityv2u.dx+ v2v. dif + v2w. dz

canbeanexactdifferential. It is shownthat for sucha casethevelocitiesu, v, w andthecomponentsof rotation~, ii, ~ satisfytheequations

dP dl’ dPup+vy+wi=O,

dl’ dP dl’yand that consequentlythestream lines andvortex lines form a networkon thesurfacesP = coast. It is then one of the conditions,under theabove assumption.for steadymotion in a viscous fluid that there shallexist in the fluid aninfinite systemof surfacesP = coast,eachof whichis coveredby anetworkof stream lines andvortex lines. Of coursethisonly refersto thepart of thefluid moving subjectto thecondition

v2u. d. + v2v. dy±v2w. dz d~b.A particular caseis studied,viz, themotionof an ellipsoid in a fluid.

The resistanceis computedfor this caseandalsofor thecaseof a movingsphereby meansof a new form for the ‘Dissipativity.’ Thevaluesof thevarious constantswhich enterinto the problemof themoving ellipsoidaregivenin termsof elliptic functions.

Article V.— On Binomjal Congruences: comprising anExtensionof Fermat’sand Wilson’s Theorems,and a Theoremofwhichboth are SpecialCases. By 0. 11 MITCHELL.

In the first section,the numberof numbersless than k containingsand no prime factorof k not found in s is definedas the s-toiient of k,wherek~albu . . . q1 and s=a b. . . . t, and it is designatedby i-

8(k).Any given one of these numberswhose enunserationmakes up thes-totientof ic is called ans-totiLiveof k, and is denotedby AT8. Unity isincludedamongthevalueswhich s canhave.

In the secondsection, x2 —~ x mod. k is shown to have2~ roots, one

belongingto eachof the2~ classesof the totitives of k, i beingthenum-ber of theunequalprimefactorsof k. Theseroots arecalled the repeientsof k, andanygivenoneis designatedby R

8. Certainrelationsareprovedto exist amongtheserepetents,of which the mostfundamentalare

R, R8’ R88~ mod. k,I?8+R,’~It881+J4 mod.k,j4’+ l4~ J?~7 mod. k,

wheres is prime to ~I, ands denotestheproduct of all theunequalprimefactorsof k exceptthosecontainedin s.

in sectionthree,generalformsof Fermat’sandWilson’s theoremsaregiven,viz:

x8(k) R’ mod. kand II, (k) .4- 14 mod. k, where ll~ (k) denotesthe productof all thes-totitivesof k. When s 1, thesebecometheordinary theorems,viz:

xT(k)~~h1mod k,ll~ (k) = ± 1 mod.k.

In thesucceedingsectionsother fundamentaltheoremsin power resi-duesare so generalizedasto apply to all numbers,whether prime to themodulusor not. A generalexpressionis given for the numberof rootsof x~—DOmod.. k, andfor thewholenumberof the nth-powerresi-duesof themodulusk.

In the last sectiona theoremis givenwhich includesboth Fermat’sand Wilson’s asspecialcases, if k= a~6~...t~... q~, 3 = a6... t, a =

atbI... lx, and A = anydivisor of r1 (-~), this theoremis

147

mod. k;

kexceptwhen = a power of a prime number, doublesucha power,

or —4 and is at the same time an odd number,in which casestheS

right handmemberis (— R,)Q+ 1 where Q = thenumberof powerresi-k

duesmod. —.

a/ A /

AT8 is any root of .X8~D, mod.k,// A /1

X8 is anyroot of AT, D8 mod. k,&c., &c. For A = 1, this becomestheWilsonian theoremgivenabove.

For A = r1 (Li.), it becomesthe Fermatiantheoremgivenabove.

Article VI.—Linlcagesfor x”’. By F. T. FREELAND. Witha plate.

“By thefollowing method of combining reciprocators(a Peaucelliercell with a modulusone) and bisectors(a pantographwith equalarms) alinkagefor Xm maybeobtained,mbeinganypositive or negativeintegeror fraction.”

Article VII.—The Strophoids. By W. W. JOHNSON.

A deductionof tile equationandsomeof thegeometricalpropertiesof“the locus of the intersectionof two straight lines which rotate uni-formly about two fixed points in a plane.”

Article VIII. —Onthe Ratio betweenSectorand Triangle inthe Orbit of a CelestialBody. By ORMOND STONE.

“This ratio maybeexpressedby theformula

1 rr’sin(v’—v) sin2~

wherethe massof thebody is neglected,r andr1 are the radii vectores,

v andvt the correspondingtrue anomalies,p the semi-parameter,and rtheproductof theinterveningtime and theconstantof thesolarsystem.”

Then, approximately,

For a closerapproximation

2~r

(rr’)T (r+r/)w

I I,e cos 7/

2i-2 2i/rr’ 1where i~—, cosy= cos—(v’—v).

(r+r’)3 r+r’ 2“This formula includes termsof the same order as thoseincludedin

Hansen’smethod, and,if employedin connectionwith a tablegiving thelogarithmsof theratiosbetweensinesandarcs,is rathermoreconvenient.”

Article IX.— Centre of Gravity of Surfaceand Solid ofRevolution. By E. W. HYDE.

The quaternionformulae for the centre of gravity of a surfaceandsolid of revolutionare

2,5

P=J~je’Sr~i— e~r Vrj’52 TVq5’ Vr~b. dl

-- (a% — l~Yi)f TV~b’Ve~b. dl

and

— i9if S. ~‘Vnp. dl

respectively,wherep = ~s(I) = i~ is the equationof thegeneratingcurve

(planeor tortuous)and 9~ — ~ is the anglethroughwhich it revolves.

Article X.—Ona Point in the Theoryof Vulgar Fractions.By J. J. SYLVESTER.

The reciprocal of an integer maybe called a simple fraction. Anyproperfraction may be developedin one way only as a sum of simplefractionseachof which hastheleastpossibledenominator. Sucha deter-minatedevelopmentmaybe called a soriies. The presentpaperhasforits objectthedeductionof somepropertiesof the successivedenominatorsor elements of a sorites,and the actual developmentis illustrated bynumericalexamples.

JULY, 1881.]

JOHNShOPKINS

ArticleXI.—Onan hnrnediateGeneralizationofLocal Theo-remsin which the GeneratingPoint Dividesa VariableLinearSegmentin a ConstantRatio. By SAMUEL ROBERTS.

“If two curveshave aoneto onecorrespondence,and if thepoints ona particular straight line of onecorrespondto pointson astraight line oftheother,thecurvesareof thesameorder anddeficiency.”

“A curvemaybedeterminedasthelocus of a point, which divides ina constantratio a terminatedstraightline variablein length andpositionand a family of curvesrelatedto oneanotheris obtainedby changingtheratio.”

“If similar triangles,uniformly directedwith respectto thegeneratingsegments,besuperposedthereon,eachhavingfor base the correspondingsegment,the generallocus of the vertex,say thevertex-curve,is of thesameorder and thesamedeficiencyasthecorrespondingratio-curve.”

Someinterestingresultsof this theoremaregiven.

Article XII-~-~-On the &pansion of ~(x + h). By A. W.WHITOOM.

Theobjectof this article is to obtaina developmentfor theargumentof theremainderin Taylor’s theorem,

Article XIII .—Onthe Theory of RationalDerivation on aCubic Curve. By W. E. STORY.

This is a modification and extensionof ProfessorSylvester’stheory,first given in this Journal,Vol. III, pages58—88, 184—189. The notationhas been so modified as to correspondto theusualrepresentationof thepointsof a cubic by meansof a singleparameter,the connectionof whichrepresentationwith the theoryof total derivationis established.

A number of “totitive” problemsare solved,and in a note arecon-tainedsuggestionsfor a generalnotation for “totients.” A list of themoreimportantwritings on thesubjectis appended.

Article XIJT.—InstantaneousProof of a Theoremof La-grange on the Divisors of the Form Ax2 + By2+ Cz2, witha postscript on the Divisors of the Functionswhich illultisectthe Primitive Rootsof Unity. By J. J. SYLVESTER.

In this noteis givenashort proof that thecongruenceAx2+By~ + 0z2~0 (mod.p)

is soluble for everyprimemodulusp.

PROCEEDINGS OF UNIVERSITY SOCIETIES.Abstracts of the J~[ore Important Papers Read at Recent ]VLeetings.

Scientific Association

.

April Meeting.

A Study of Blood Pressure in the Coronary Arteries of theMammalian Heart, by H. N. MARTIN and W. T. SEDGWICK.

An abstractof this paper is given in University Circular No. 10,page 127.

On a New Methodof Studying the Mammalian Heart, by H.N. MARTIN.

This paperis printed in the Studiesfrom the Biological Laboratory,Vol. II, No. 1. An abstractis alsogivenin UniversityCircular No. 10,page127.

SomeElectromagneticExperimentswith Nickel, by E. H. HALL.

May Meeting.

On the Fixing of Nitrogen by Soils, by W. A. NOYES.In thespring of 1880, someexperimentswereundertakenin connection

with ProfessorMierrick, atIowa College,to determinethe effect of vary-ing conditionsof light, heat and moisture on the amount of nitrogenfixed by soils. Ten specimensof a soil, previously analysedfor totalnitrogenand nitric acid, were subjectedto variousconditions for fifty-sevendays,and again analysed. All specimensgainedin total nitrogen;onlythosein direct sunlightgainedin nitric acid. Thegreatestgainwasin asoil in diffused light, wateredand stirreddaily. Both wateringandstirring increasedthegainof total nitrogen. Thevery surprising resultwasobtainedthat a sampleof thesoil in a closedfruit jar, exposedto dif-fusedlight gained23 per cent.,the greatestgain being only 25 per cent.

Note on the Physiologyof the Turtle; by E. M. HAUTWELL.

This papergave an accountof someinvestigationsinto the functionsof the spinal nerve trunks of the Pseudemysrugosa,or Slider Terrapin,as it is commonly called; the structureof its spinal ganglia; and theanatomyof its sympatheticnervous system. Inasmuch as the spinalnervetrunks are separatefrom each other,insteadof united,as in mostVertebrates,it had been suggestedthat the ventral and dorsal trunksmight bepurely motor and sensoryin their functions. It was found onexperimentthat electricalstimulation of thecentralendsof divided dor-sal and ventral trunks alike gave rise to reflex movementsin animalsrenderedinsensibleby annestheticsor by cutting the spinal cord justbelow themedullaoblongata. Stimulationof the peripheralendsof thesenervescausedmovementsin musclesto which theventral trunks weredistributed. No movementsresultingfrom theexcitationof theperiphe-ral ends of dorsal trunks had been observed. It was concludedthattheventral trunks containsensoryandmotor fibres; and that thedorsaltrunks are probablysensoryand not mixed in function. Attention was

called to thefact that the spinal gangliacontain fibres from both dorsalandventral roots. Various peculiarities in the structureand arrange-ment of the sympatheticgangliawere noted. It was statedthat experi-ment had shown that a branch of the middle cervical ganglion of thesympatheticactedasanacceleratornerveof theheart.

On the Action of Nitrogenon PureIron, by IRA REMSEN.This paperis printed in the American ChemicalJournal,Vol. III,

No 2. An abstract is givenon page 144 of this Circular.

JuneMeeting.

On the Deposition of Copperon Iron in a MagneticField, byIRA REMSEN.

This paper is printed in the American Chemical Journal, Vol. III,No. 8.

On aModificationof Fechner’sPsycho-physicalLaw in its Appli-cationto Vision, by C. S. HASTINGS.

Philological Association

.

April Meeting.

On an Affirmative Enclitic ne in Early Latin, by M. WARREN.This paperis printed in the American Journalof Philology, No. 5.

An abstractis given on page.145 of this Circular.

On theAblaut in English, by B. W. WELLS of Boston.This paperattemptedto showthat the tendencyof Old EnglishStrong

¶,Terbsto becomeweak in later periods of thelanguagewastheresultoffixed principlesand duechiefly to theinfluenceof consonantsin thestemauslaut~also that the strong forms,wherethey remained,were for themost part regularlyand phoneticallydevelopedfrom the corresponding0. E. forms,exceptionsbeingcausedalmost solelyby adesire for distinct-nessandsimplicity in theablaut.

On anAlleged Fact in the Life of Euripides,by C. D. MORRTS.Attention was called to a statementwhich is found in the notes of

several commentatorson Eurip. Hipp. 612, (4 y2i~a bu6poX, 4 in~

av6yorog)and thebiographiesof thepoet,that hewas formally accusedofimpiety beforetheAtheniancourtson the groundthat by the abovelinehe had given encouragementto perjury. The authority quotedfor thisstatementis apassagein Aristotle’s Rhetoric(iii. 16, 8). On examination,however,it appearsthat this passageaffords no support to theinference

148 [No. 11.

UNIVEI?SITYCIiWULAI?S.

derivedfrom it. Aristotle, in that chapter,is engagedin pointing outand illustrating various ways in which an orator may get~rid of anunfavorableimpressionor prejudice (6ta~o2o~)which exists or is excitedagainsthim: andhequotes,asoneexample,the reply of Euripideswhenthefactthat hehad written theabove line wasallegedagainsthim by hisopponentin a lawsuit. But it is expresslystatedthat thesuitin questionwasoneinvolving anexchangeof properties,technicallycalledavridoat~,in which theoathsof the parties,as to the characterandextentof theirpossessions,were an essentialfeature,and it was of the utmostmomentthat no antecedentdiscreditshouldattach to the word of eitherof them.The fact that theverb Kar?/yopeivis employedto expresstheattackmadeonEuripidesby hisantagonistdoesnot atall imply that this matterwasmadethebasisof aformalaccusation;because,asl3remisays,in comparingtheuseof Karyyopeh’and~ former meansgenerally‘convicije oppro-briis atqueetiamccdumniisatiquemadoriri.’

May Meeting.

The Akkadian andits Influence on SemiticLanguages,by REv.FRANCIS BROWN, of the Union Theological Seminary,New York.

The Akkadian, spokenby thepre-Serniticinhabitantsof Babylonia,isan agglutinativelanguagein anadvancedstageof development. On thebasis of Haupt’s “Akkadischeund Su~nerischeKeilsehrifttexte” it is easyto show that the Sumerianis a dialect of the Akkadian, and it is theAkkadian whose traces are most numerousin the Semitic languages.The Assyrianshows them most clearly. The adoption,from the Akka-dian, of the cuneiformcharactersaffected theAssyrian phonology,par-ticularly in causingthealmosttotal disappearanceof weakletters. Atephinitial, andin afew cases,theconsonantwaiv, were probablystill heard.The quiescents,asyodh andwaw,sometimesmodifiedtheadjacentvowel,andthushada secondaryrepresentationto the eye. North-Semiticpho-nology,however,was not materiallyaffectedby the Akkadian, since thecontactwas too short. TheSemiticvocabularyborrowedmuch from theAkkadian ;—the accompanyingchanges—consonantaland vocalic—arewithin tolerablywell defined limits. Akkadian influencewas felt (to aless degree)in Assyrian morphology,and in style, while its various de-greesin other dialectsmay be expectedto throw light on the history ofSemiticmigrations.

A Defenceof “Is Being Done,” by G. II. STOCKBRIDGE.

The chief objectionurged against this phraseologyis that it does notaccordwith the geniusof the English tongue. The history of its risedoesnot favor the objection. It seemsto have been a normal growth.Moreover,an analysisof the phraseindicates its conformity to Englishusage. The auxiliary to be is equivalentboth to theGermansein (to be)and theGermanwerden (to become). The houseis beingbuilt, then,cor-respondsexactly to Das Haus wird gebaut, and means, the house isbecomingbuilt, is in processof completion as a structure. Again, thealternativelocution,is doingor is buildeng,restsfor its justificationon thesame groundsas the idiom in questien. Side by side with the activeverbal noun, therehas alwaysexistedacorrespondingpassive,and so ifis doing beregardedas derivedfrom is in doing or is a doing, is beingdonemay claim its origin from is in beingdoneor is a beingdone.

A Review of Guillemard’s Hebraisms in the New Testament,by J. M. CROSS.

Historicat and Political ScienceAssociation.

March Meeting.

The Influence of GeographicalPosition upon Ideas of theFuture World, by ALLAN MARQUAND.

Assumingthat beliefs respectinga future world vary with the geo-graphical position of the country in which they arise, many of thesebeliefswere examinedwith referenceto their content of natural sceneryand climate, it was ascertained(1) that amonginland peoplesarefoundsuchbeliefs as that of happyhuntinggrounds,Elysian fields,andgardens; as also reachingheavenby climbing a tree, following a trail,ascendinga mountainor crossinga river. Among sea-faringpeoplesanddwellersby greatlakesarefoundconceptionsof happyor enchantedislands,reachedby a ferry over the waters. (2) In northern latitudes,thehappycountry is depictedasonewhereperpetualsummerreigns; theabodeof miseryis in the midst of ice andsnow. In middle latitudes,both heatandcold contribute elementsof future torment. In southernlatitudes,future happinessis frequentlyconceivedasin a coolerclimate,beneaththeshadeof trees,while themiserableareto suffer from extremeheat. Fire in the abodeof tormentappearsto be an Oriental and com-parativelymodernbelief. (3) Valleys,plains, andmountainshave alsoaddedspecialcharactersto theideaof thefuture world.

Origin andDevelopmentof the Municipal Governmentof NewAmsterdam,by J. F. JAMESON.

Theobject of this paperwasto tracethehistory of the governmentofManhattanundertheDutch,andto showhow closelytheearliermunicipalarrangementsandtheprovisionsof thecharter finally grantedfollowed theinstitutionsthenexistingin the citiesof the Netherlands. The develop-ment of the Dutch municipal institutions from the earliest timesto theearlypart of the eighteenthcenturywasbriefly described. At thelatterperiod, the chiefmunicipal officers were a schout(at once sheriff andpresidentof the court), two or four burgomasters,or administrativeofficers, andfive, seven,or nine schepens,or associatejudges. The prin-cipal legislative body was the old council or senateof ex-magistrates.These either appointedthe magistratesdirectly, or nominateda doublelist, from which the governor-generalof the provincechose them. Inthe details,therewasthegreatestvariety in thedifferenttowns,andthesepeculiaritieswerelong retained,throughthe conservatismof the Dutch.Thecity governmentshadalreadybecomeverypowerful andoligarchical.Municipal taxeswere underthe entirecontrolof themagistracy.

The origin and characterof the Dutch West India Companyweredescribed,and its charter was discussedat length. Important inaccu-raciesin the translation given by O’Callaghanin his History of NewNetherlandwere pointed out, and were shownto have beencopied byOCallaghanfrom the translationin Hazard. These errors,followed byall subsequentwriters, havegiven rise to an incorrect viewof thedelin-quenciesof theCompany. During theadministrationsof May, Verhuist,Minuit andVanTwiller, undertheAmsterdamChamberof theCompany,no tracesof self-governmentare found. The CompanyappointedtheDirector-General,and the Director-Generalwas the government. Theofficers assistinghim were as much provincial as municipal. In Kieft’stime, the Eight Men, and,in thefirst yearof Stuyvesant,the NineMen,representativesof the commonalty,were infrequently and unwillinglyconsulted. But the able and energetic remonstrancesandappealsfor amunicipalgovernment,addressedby the Nine Men to theStates-General,were at last effective. In 1652, the city of New Amsterdamwas incor-porated. But Stuyvesant,interpreting the charter in the narrowestmanner,for a long time withheld from the burgomastersand sehepenstheright of electing theschout,the right of co-optation,andthecontrolof the municipal excise. The magistracygained full powers of self-governmentonly sevenmonthsbeforethecaptureby theEnglish in 1664.

The city governmentestablishedby thecharter wasmodelledon thoseof theNetherlands,thoughof coursesimpler. The officers borethesametitles anddischargednearlythesameduties. The mannerof their elec-tion, thejudicial andfinancialarrangements,werethesame. Everythinggoesto disprovethetheory,apparentlyadoptedevenby Bancroft(II, 306),that the free governmentsof New Netherlandarosefrom imitationofthoseof New England. On the contrary, theDutch burghersfollowed,to use their own words, “the laudablegovernmentsof theFatherland.”

MayMeeting.

The CurrencyQuestionin theUnited States,by P. B. MARCOU.

Immigration,by STEWART B. LINTHICUM.

Metaphysical Club

.

March Meeting.

J. G. Ficlite’s “Scienceof Knowledge,” by M. I. SWIFT.

Fichte developedthe Idealism latent in Kant. His purposewas toshowthat we have knowledgeof absolutereality, and that this is to befoundin the natureof knowledgeitself. By knowledgehemeanspureself-contemplatingactivity; it returnsupon itself andis itself its ownobject. This is the nature of pure Being, or Universal Spirit. For ascienceof knowledgetheremustbe foundanunconditionedand all-inclu-sive first principle of knowledge. “I am I,” or “Ego=Ego,”is sucha principle. The affirmation ‘I am’is at the basis of all other actsofknowledge.

Fichte developsthe activity of an absolutelyunconditionedEgo, andby this his Idealism is explained. The world, in itself considered,isnothing: it finds its being in an absoluteknowledge, or self, which isGod. In this Being thereis no duality, no antagonismof matter andspirit, for theyare one,namelypure activity. This is not the commonempty conceptionof spirit. Fichte’s Idealism does not annihilate theexternalworld. Regardedas existing absolutely,for itself, theworld isinexplicable; viewed as activity, or spirit, it becomesintelligible. Ourknowledgeof Being ~vasgained originally wholly from ourselves;weknow ourselvesas Being. But we know ourselvesas ac~vity, asspirit;we cannot thereforepredicate true Being of any thing but Spirit. We

JULY, 1881.] 149

JOhNShOPKINS

read in the externalworld the formsof our own knowledge,and fromthis we know that the world can only exist as the expressionof a spiritlike our own. It thencorrespondscompletelyto Being as we know it inourselves. Matter, in itself, regardedas Being, is meaningless. Thewarrantof thecertaintyof our knowledgeis that, whenviewed asabove,it explainswhat is otherwiseincomprehensible. In this knowledgeweknow God.

Hickok’s View of Philosophy,by F. E. STEBBINS.

Reason,asessentiallyself-activity, is the universaloneinvolvedin thetotality of being. A completepsychologicalanalysisrestsin theattain-ment of this unmade,self~evident,self-sdpportingultimate. Thestarting-point and terminationof speculationand likewise the dialecticalprocessrevealingits universal implication are disclosedin this principle asself.knowing andself-determining. Reason,in distinction from all abstractmethods, integrates,deals in concretewholes. Its immediate insightinto anyexperiencereadstherewhatwas conditional for it. It is notadeductionfrom experiencebut an induction from without and so pro-ductiveof wholly new knowledge. This activity seesin anyconstructionthat an intelligent constructingactivity must have been asa prior. Itseesin a constructingactivity that itselfmusthave been,asoverlooking,determiningand authoritativelycontrolling. In placeand periodit seesspaceand time as conditional for limitation; in force, the condition forbodiesin their placesandperiodsin spaceandtime; in life, the conditionfor anexperiencein organicfacts;that thecondition for humanexperiencein a world of forcesand lives and living men is a PersonalCreator,who,assourceof the universalenergyconstituting force and life is prior to,and hasa being irrespectiveof spaceand time; that the experieiiceofmankindin a common spaceandtime could not be exceptas eachtookhis placesand periods from the same forces and lives which filled thecommon spaceand time. And not alone does the Reasonoversee theactivities of distinguishing and defining and connecting; it thoroughlyknowsitself andseesin itself all reasonabletruth. In this insight, itse(fis revealedas ultimatestandardin the spheresof art, scienceandmorals.As its own object finite reasonknowsthat theAbsolute reasonmustbe,and alsothat it mustbe independentsourceand ruler of the totality ofbeing. Thus in all experience,as symbol, Reasonknows the meaningbeforeput into it—the conditionswithout which theexperiencecouldnotbe; the conditions with which the experiencemust be if it is, and theccnditionswhich evincea proposedend assufficient reason. Thesecon-ditionsarenot assumptionsor pre-suppositionstakenbecauseneededandwhich shownothing for their validity, but legitimatepre-requisitestakenbecauseknownd priori to bein orderthat experiencemay be.

April Meeting.

On RelationsbetweenSensations,by C. S. PEIRCE.

Hegel’sPhilosophicalPropaedeutic,by B. C. BURT.This was “discovered”among Hegel’smanuscriptsin 1838,by Karl

Rosenkranz,and edited by him in 1840. It was written for Hegel’sclasseswhile hewas rector of the Gymnasium at ~uremberg. It is arelatively popular exposition,in outline,of themain body of his thought.It is divided into threecourses,only the first havingbeenentirelywrittenout by Hegel. This course,—OnRights,Moralsand Religion—waspre-paredwith greatcare and possessesan interestmore thanhistoric. Theother coursesare not to be overlooked. Translationsare given in theJournalof SpeculativePhilosophy,Vols. III and LW.

On the Relationof’ Induetio~to Hypothesis,by E. W. DAVIS.

an ~ induction }The probability of j hypothesis is increasedor diminished, in

general,by increasingor diminishingthenumberof {~ } com-

pared.Since the order of reasoningin induction is case,result, rule, and in

hypothesisprecisely the reverse, rule, result, case;it follows that whatinduction

appearsas ~ hypothesis when time is reckoned positively, becomeshypothesis)induction ~- if we conceive time to be reckoned negatively.

StraightLines andParallels,by J. B. PETERSON.

May Meeting.

Logical Machines,by ALLAN MARQUAND.Cnnynghame’sSyllogistic Cylinder, Stanhope’sDemonstratorand the

machinesof Jevonsand of Venn were described. Logical cards wereoffered asa substitutefor the Logical Slate or Stamp. Diagramswereexhibited for afour-term machineresemblingthat of Jevonsin having

thirty-two rods raisedor loweredby sixteenkeys. It differs in requiring.only threeoperationsinsteadof five, in having a sliding face with slitsso arr’ n ~d as to exhibit a complete analysisof the combinations,indispensingwith springs and levers, and in other particularsof minorimportance.

A marked improvementwas made upon the machine of Mr. Yenn.In place of circles, ellipses, etc., rectangles are used to representthe “compartments”of the universe. A squarewire frame work withawire dividing it into two parts,if allowedto fall on a squaresurfaceofthesamesize,will divide it into two compartments,distinguishedasAand a. A similar frame work falling at right angles to the first willdivide eachof these,giving the four compartmentsAB, AS,aB, aS. A3d and 4th charactereachrequire frameworks with two dividing wires;a 5th and 6th characterrequire four such wires; in general,countingcharactersby couples,eachof thenth couplewill require a frameworkwith 2” —‘ dividing wires. On thisprinciplemachinesfor anynumberoflogical terms may be constructedmuch moreeasily than hasyet beensupposed.

The ExternalWorld, by J. B. PETERSON.Berkeleyand his followers denythat we haveanyknowledgeexceptof

thephenomenaof ourown minds,andmaihtain that our belief in aworldexternalto ourselvesis an illusion. But this theoryis liable to two objec-tions, either oneof which is fatal to it. In the first place,it belies thetestimonyof consciousness,which affirms that material objectsare notwithin themind but without it. Secondly,it contradictsitself, since itassumesthehumanbody and its sense-organsasexternalrealities.

The questionwhetherthereis a world externalto ourselvesis one thatoughtneverto havebeenraised; but the questionwhat we know of thatworld and how we know it, is one of the highest importance,and theknowledgeis probablygiven us in thefirst instance,in the consciousnessof our own limitation.

On the Validity of Indnction,by B. I. GILMAN.

In this paperthreetheoriesof the subjectwere referredto and criti-cized,viz: that founded on Laplace’sprinciple of inverseprobabilities;thatof Mill, foundedupon theLaw of Causation;and that of Mr. Peirce,foundedupon the material view of probabilities and the theory of theadaptationof mind to theuniverse.

Mathematical Seminary

.

April Meeting.

On the Multisectionof the Rootsof Unity, by J. J. SYLVESTER.

If p be a prime number,e a divisor of p — 1, and the e periodsintowhichthe primitive pth rootsof unity may bedistributedarethe rootsof~ ±B ~ , I call this lastwritten function (sayE), thee-periodfunction to p. Every divisor of suchfunction, it is well known,if notpitself or ane”’-power residueof p, mustbe a divisor of the discriminantof B.

Every divisor q of the discriminant is necessarilya divisor of B butmayor maynot be,accordingto circumstances,ane’

5-powerresidueto p;if it is not, then q may be called anexceptionaldivisor of the period-function.

When e = 2 the discriminant is p itself so that (as is well known)thereareno exceptionalfactorsto the two-periodfunction. Whene= 3,it maybe shown that every factor of the discriminant is necessarilyacubic residueof p.

This may be proved by the Law of Reciprocity for cubic residues,although obtainedin quite a differentmanner. It followsthat thethree-periodfunction hasno exceptionaldivisor.

Whene= 4 it is betterto distinguishbetweenthe two casesof p = 8i±1 andp Si + 5.

In theformercase2 is not necessarilya biquadraticbut maybeonlya quadraticresidueof p, althougha divisor of the 4-periodfunction.,andconsequently2 may be an exceptionaldivisor. When p = Si±5, if~=f2 ±4y2, every divisor of y is necessarilya divisor of the functioninasmuchasy is containedin the discriminant,but whilst divisors of ~‘ ofthe form 4i + 1 are biquadratic,thoseof the form 4i — i will be onlyquadraticandnot biquadraticresiduesof p. The resultsfor e= 4 sofarasyet statedmay be proved by the law of reciprocity for biquadraticresidues.

But whenp = 8i + 5, or in otherwords, whenp =f2 + 4y2 wherey is3p2+f2odd, it maybeshownthat is alsothat factor of thediscrimifiant

16which isrepresentedby(m~—y

1) (~~—ri~) (~2—r3) (77iiZe), ~ ~

- y2, ?1~ being the 4 periods taken in natural order),and it is capableofproof that everydivisor of this chainof productscannotbut bea biquad-

150 [No. 11.

UNIVERSITYCIRCULAPS.

ratic residueto p,* or in other words,every divisor of J2±4~2 is a4

biquadraticresidueof f2 -i-- 4y2 when this last quantity is a pPimenum-ber. This theorem,deducedfrom the methodapplied to thedivisorsofperiod-functions,does not appearto he referableto uny known theoremconcerningbiquadraticresidues. ProfessorSylvester finally statedthathehad underconsiderationthe questionof the existenceor otherwiseofexceptionalfactorsto the e-periodfunction in thegeneralcaseof e beinga primenumber.

A Rule of Signs in Determinants,by II. M. PERRY.

Any m columnsof a determinantmaybesubstitutedwithout changingtheir order for the m first columns, (the columns they replace beingsimply advanced)by

m(m—1

)

2inversions. ~Jis thesumof theindicesof the columns.

A similar formula holds for the rows,and the total numberof inver-sionsrequiredto bring anyminor to theupper left handcorneris

~i + ~j— 2m— m(m— I).The first two termsonly affectthesign, and the expandeddeterminant

A maybewrittenA = ~ (—1 )~(i +1) MM1,

M andM’ are complementaryminors. ~(i +3) is thesumof theindices

in eitherminor, since

Whenthe rowsretain their order(m(?n~l) ÷~~)MAT’,

A==~2(—1)wherem is theorder of the minor in thefirst rows.

In applying theaboveformula it is only necessaryto countthenumberof odd indicesin oneminor. The sameformula is applicablein alternatenumbers.

Notes,by F. FRANKLIN.1). On Newton’s method of approximation. Suppose the equation

f (x) = 0 has one and only one root comprisedbetweena and b; thenFourier’sconditionsthat Newton’s methodof approximationshould leadto this root are that neitherf/ (x) nor f” (x) should vanish betweena andb. It is easilyshown, however,that the first condition is super-fluous it is sufficient thatf” (x) should not vanishin the interval. It

* For supposeq, a prime-numberdivisor of the “chain-product,”to be nota biquad-ratic residueofp; then if q isa quadratic residueof p, it may be shownthat q mustbealsoa divisorof (m~ — ‘l2)~ ~ — ~ and thereforeof py2,which is impossiblebecausey isprime tof andp, andif qisanon-quadraticresidueofp it maybeshownthatall fourrootsof thecongruence,which expressesthatthe 4-periodfunctioncontainsp mustbeequal tooneanother,whichadmitsof easydisproof. Henceq cannotbutbea biquadraticresidueof p.

Death of William Hopkins, Secretaryof theBoard of Trustees.

“William Hopkins,a retired merchantand a first cousinof the lateJohnsHopkins,died in this city todayin his 67th year. He was a sonof Gerard T. Hopkins, and a member of the societyof Friends. ** *Mr. Hopkins was long a memberof the firm of T. W. & G. Hopkins.His sterling integrity andsound judgment,which he neverallowedanyimproperinfluenceto warp,securedhim the confidenceand respectof theentire businesscommunity,and his opinion on mattersof businesswasoftensoughtfor. He wasa trusteeof theJohnsHopkinsUniversity andtheJohnsHopkinsHospital,and adirector in theFarmersandPlanters’BankandtheMaryland Fire InsuranceCompany.”

The Sun,Baltimore, May 28, 1881.

MIxUTE ADOPTED AT A MEETIKG OF THE BOARD OF TRUsTEEs.

At a meetingof the Board of Trustees,June 6, 1881, the followingminutewaspresentedand adopted:

That the Presidentof the Board•be requestedto communicateto the brothersandsistersof Mr. William Hopkins, late the Secretaryof the Board,an expressionof therespectwhich his former colleaguesentertainfor his upright and honorablecharacterandhis faithful attentionto the detiesof a Trusteein this University, and alsoof theirsympathywith thefamily in this bereavement.

151

is alsovery easily seen that a superior limit to theerror after the first1 F”

approximationis + — (b— a)2,where a is that oneof thequan-— 2f’(a)

tities a, b from which theapproximntion hasto start,and ~ thearith-metically greatestvalue which f/f (x) assumes,as x passesfrom a to b.This limit is moreaccuratethan theonegivenin Serret’sGoursdAtyibreSupdrieu’reandthereobtainedby along andratherdifficult process.

2). On a determinantexpressionfor the numberof terms in a zero-dioyonat determinant,etc.

3). On thelengthof a continuedfraction, etc.

On a Notation for Totients,by W. E. STORY.[See “Note on Totients” appendedto an article “On the theoryof

rational derivation on a cubic curve” in the fourth numberof VolumeIll of the Amer. Jour.of Math.]

The lflrst) totientof n to the condition K is thenumberof integers,notgreaterthann, which satisfythecondition K. Thek-th totientof n to theconditionK is thenumberof setsof h numbers,neithergreaterthann, whichsatisfythecondition K. The first and k-th totientsof n to thecondition K

are representedby T[K] and T[K]C respectively.

[K] is a numbersatisfyingthecondition K[i] “ “ not satisfyingthecondition K,[K]” is a setof ,7c numberseachsatisfyingthe condition K,[k]k “ “ ‘‘ neither 0 0

“ C’ “ some ~ ‘‘ ‘‘

CC “ not all “ “ “

[ic.x]is a numbersatisfyingboth theconditionsK and x~[K,x] “ “ “ oneor otherof theconditionsK and,r,An denotessome(any)factor of n,

n in a set of k numbersdenotessome(any) factorof n common to allthe numbersof theset,

C denotes“contains as a factor,” C denotes“does not containas afactor.” Thesesymbolsare to be followed by thenumberscontainedornot contained.

Severalapplicationsof this notation were given. The numberof setsof k numbers,neithergreaterthann, all containingsomecommon divisorof a satisfyingthecondition K, but not all containinganyonedivisor of nsatisfying the conditionx (different permutationsof k numberscountingas different sets),is

U~j

m[C (~‘i.K). 0 (~x) ‘P1 1 / 1 \ / 1 \/ 1\

= It ~ \ 7/k d’V~/k d”kJol’~ I.

where6, 6’, 6”, . . . are the leastdivisors of n satisfying-thecondition K,and di, di’, di”, . . . arethe leastdivisors of a satisfyingthecondition x.By a setof leastdivisors is meant a set of divisorsno oneof which is amultiple of anyother.

BRIEF ANNOUNCEMENTS.BenjaminC. Burt, Fellow in Philosophy,hasbeenappointedAssistant

Professorof English andRhetoricin the University of Michigan.

Edwin H. Hall, Ph. D., late Fellow, and Assistant in the PhysicalLaboratoryhere,has beenappointedInstructor in Physicsat HarvardUniversity.

Mr. SidneyLanier, Lectureron English Literature, will give readingsin thelessfamiliar Playsof Shakespeare,earlyin thenextacademicyear.

At a meetingof The Physical Society of London, May 14, 1881, acommunicationfrom PROFESSOR ROWLAND and Dn. E. L. NIcHoLs onElectric Absorptionin Crystalswasreadby ProfessorFoster.

According to thetheoryof Clausius,Maxwell, and others,thereshouldbe no electric absorptionin the caseof perfectlyhomogeneoussubstances.ProfessorRowlandtestedthis deductionin thecaseof glass—whichis notquite homogeneous—quartzand calcite. This was done by placing thematerial as the dielectric in a condenserformed of two amalgamatedcopper plates. The condenserwas chargedby six Leydenjars,and theabsorptionmeasuredby aquadrantelectrometer. The resultswerethatquartzhad about one-ninth the absorptivepowerof glass, and calcitenoneat all, a factwhich makesit useful for the constructionof standardcondensers.—TheElectrician, London,May 21, 1881.

JULY, 1881.]

JOHNSHOPKINS UNIVERSITYCIII CULAPS.

HONORS,Publicly Announced June 6, 1881.Fellows.

The appointmentsof Fellows and Fellows by Courtesywere

announcedas given on page 138.

Doctors of Philosophy.

The degreeof Doctor of Philosophywas conferredupon thefollowing persons:

1. Louis BEvIEa, of Marbletown, N. Y., A. B., Rutgers Col-lege, 1878. His principal study has been Greek, the sub-sidiary, Sanskrit, (in which he was examinedby ProfessorC.R. Lanman,now of Harvard University), and Latin. He sub-mitted a thesis “On the Genuinenessof the First Antiphontean

2. R. DORSEY COALE, of Baltimore. His principal studyhasbeenChemistry,the subordinate,Physics. His thesis,“On Sul-phamine- and Sulphoisophthalic Acids,” has been printed, inmodified form, in the American Chemical Journal, (vol. iii,no. 3.)

3. EDWARD A. FAY, of Washington,D. C., A. B., Universityof Michigan, 1862, and A. M., 1865. His principal study hasbeen the RomanceLanguages, (including Old French, Pro.ven9al, Italian, Spanish, Portuguese,Wallachian, and LowLatin,) the subordinate Latin. His thesis, “On the Condi-tional Relations in the RomanceLanguages,”wassubmittedtoProfcssor Austin Stickney, of New York, formerly of TrinityCollege, Hartford.

4. LAWRENCE B. FLETCHER, of Marlboro, N. Y., A. B.,ColumbiaCollege, 1877, andA. M., 1880; (Fellow of ColumbiaCollege, 1877—80.) His principal stndy hasbeenPhysics, thesubordinateChemistry. He submitteda thesis “On the Deter-mination of the Mechanical Equivalentof Heat by ElectricalMeans,” which was referred to ProfessorJohn Trowbridge ofHarvard University,andwill shortly be printed.

5. SAMUEL GARNER, of Annapolis, A. B., St. Johns College,1871. His principal study has beenthe RomanceLanguages(including Old French, Italian, Spanish,Portuguese,Proven~al,Wallachianand Low Latin,) thesubordinate,German. He sub-mitted a thesison “The Gerundial Constructionin theRomanceLanguages,”which was examined by ProfessorF. Steugel, ofColumbiaCollege.

6. EDwARD M. HARTWELL, of Littleton, Mass.,A. B., AmherstCollege, 1873, and A. M., 1876. His principal study has beenAnimal Physiology,the subordinate,Animal Histology andAni-mal Morphology, lie submitteda thesis,“Notes on somepointsin theAnatomy and Physiologyof the Slider Terrapin,(Psen.demysrugosa),” which will be printed in a forthcoming numberof theStudiesfrona theBiological Laboratory.

7. WILLIAM T. SEDOWICK, of Farmington,Conn., Ph.B., YaleCollege, 1877. his principalstudyhasbeenAnimal Physiology,thesubordinate,Animal Morphology and Vegetable Physiology.His thesis,on “The Influenceof Quinine on the Reflex Excita-bility of theSpinal Cord,” hasbeenprinted in The Journal ofPhysiology, (vol. iii, no. 1).

8. CHRISTIAN SIRLER, of Cleveland,Ohio, ConcordiaCollege,1866; M. D., Universityof Michigan, 1871. His principal studywasAnimal Physiology,thesubordinateAnimal Morphology andChemistry. his thesis on “The Formationof BoneandTooth”wassubmittedto Dr. GeorgeA. Otis, of theU. S. Surgeon-Gen-eral’s Office, Washington.*

9. EDMUND B. WILSON, of Geneva,Ill., Ph. B., Yale College,1878. His principal studyhasbeenAnimal Morphology,thesub-ordinateAnimal Histology,andAnimal Physiology. His thesis,on“The Origin and Significance of the Metamorphosisof Actino-trocha,”has beenprinted in the Q~tarlerly Journal of Micros-copical Science,(April, 1881).

Bachelors of Arts.

The degreeof Bachelorof Arts was conferredon thefollowingpersons:

1. WILLIAM W. BADEN, of Baltimore, whoreceivedhis previoustrainingat StenartHall, and hasfinishedmajor coursesin GreekandLatin, andminorcoursesin Chemistry, German,andFrench.

2. HENRYJ.BoWDoIN, of Baltimore,aformer stndent~ofMr. H.W. Luckett, who has finished major coursesin GermanandHis-tory, andminor coursesin Latin, French,andPhysics.

3. JOHN W. BROWN, of Govanstown,who pursuedhis prelimi-nary studies under Mr. G. G. Carey, and has finished majorcoursesin MathematicsandPhysics,am~d minor coursesin Latin,French,and German.

4. DAVID T. DAY, of Baltimore,who pursuedhis preliminarystudiesunderMr. W. S. Marston,andhas finishedmajor coursesin Chemistry,andGerman,andminor coursesin French,Physics,andEnglish.

5. WILLIAM H. HOWELL, of Baltimore,who receivedhis pre-vioustraining at theCity College,andhas finishedmajor coursesin Biology andChemistry,andminor conrsesin Physics,German,and Philosophy.

6. JoHN JOHNSON, of Owings Mills, a former student of theMeDonoghSchool,whohasfinishedmajorcoursesin GermanandHistory, andminor coursesin French,English, andPhysics.

7. JAMES E. KEELER, of Mayport, Florida, who receivedhisprevious training at the La Salle (Ill.) High School, and hasfollowed major coursesin PhysicsandGerman,andminor coursesin Mathematics,French, and Chemistry, and has also pursuedstudiesin Astronomy.

8. EDWIN G. RICHARDSON, of Baltimore, who receivedhisprevioustraining at the PembrokeSchool,and pursuedstudiesin Greek and Latin as major subjects,and in History, German,andFrenchas minor subjects.*

9. ADONIRAM J. ROBINSON, of Baltimore, a former student ofthe City College, who hasfollowed major coursesin History andPhilosophy,and minor coursesin Physics,French,and German.

10. HENRY ROLANDO, of Baltimore, who receivedhis previoustraining at the City College,and has finished major coursesinBiology andChemistry,andminor coursesin Physics,French,andGerman.

11. LEE SALE, of Louisville, Ky., a former studentof thoLouisville High School, who has finished major courses inLatin and Greek, and minor coursesin History, German,andPhysics.*

12. MACTIER WARFIELD, of Baltimore, who receivedhis pre-vious training at theUry House School,Penn.,and has finishedmajor coursesin Biology and Chemistry, and minor coursesinPhysics,French,andGerman.

* ThethreedegreesthusmarkedwereconferredFebruary22,1881.

Graduate Scholarships.

GraduateScholarships,for thecomingyear,havebeenconferredupon thefollowing: *

1. WILLIAM H. HOWELL, of Ba1tin~re,A. B.,”JohnsHopkinsUniversity, 1881. Biology.

2. WILLIAM D. MACCLINTOCK, of Millersburg, Ky., A. B.,KentuckyWesleyanCollege, 1878. English.

3. CHALMERS C. NORWOOD,of Fort Valley, Ga.,A. B., David-son College, 1878. Mathematics.

4. WILLIAM A. NOYES, of Grinnell, Iowa, A. B., Iowa College,1879. Chemistry.

Honorable ]Jlention.Honorablementionis madeof GUSTAV BISSING, of Baltimore,for

superiorattainmentsshownin his examinationsin Mathematics.

* Six graduatescholarships,eachyieldingtwo hundredand fifty dollars,in additiontotuition, will be awarded,at the openingof thenext academicyear,on termssimilartothe Fellowships.

152 [No. 11.