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Jevons, Bentham and De MorganAuthor(s): R. D. Collison BlackReviewed work(s):Source: Economica, New Series, Vol. 39, No. 154 (May, 1972), pp. 119-134Published by: Blackwell Publishingon behalf of The London School of Economics and Political Science

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2/17

1972]

Jevons, Bentham and De Morgan'

By

R. D.

COLLISON LACK

I

I

should like to begin by

expressingmy thanks to the

Provost and

ProfessorialBoardof University

College,and particularlyo Professor

MarianBowleyof the Department

f PoliticalEconomy, or

the honour

which

heyhavedone me in inviting

me to address ou today.

To lecture

at UniversityCollege,London, would be an honour and a privilegeat

any time-but

to

be askedto

deliver he JevonsCentenaryLecture s a

privilege f a veryspecialkind.Specialprivileges arrywiththem

special

responsibilities nd I am very

sensibleof the particular esponsibility

whichrestson

me, charged s

I

am with

the

task of fitly

commemorating

the centenaryof Jevons's

greatestachievement n Economics n the

College

n

whichhe was proudto profess hat subject.William

Stanley

Jevonshas long beenrecognizedas one of the most original

hinkers

who have contributed

o

the

development

f economicscience,and the

Theory of Political Economy

whichhe published ust a hundredyears

ago

has

equally

been

recognized

s

a

landmark

n

the development

f

the

subject.

Over

the

last half century

t

has therefore

attracted he atten-

tion

of

some of the

most distinguished

conomists

o

that

it is

now not

easy

to

say somethingwhich

s at once

true

and freshabout

the

book or

its author.Nevertheless shall hope to be able

to convinceyou that

there

s still

something

o be learntabout

t

todayby looking

at it froma

specificallyUniversity

Collegeviewpoint.

I can best do this,I think, by beginningrom anoutlineof the life of

Jevons.

n

doing

so there s a

specialdifficulty

which

s

perhaps

best met

by recognizing

t

frankly.

I

cannot

and do

not

pretend

to

know as

much about

the life

and work

of Jevons as do some

members

of

this

audience;

no

doubt there are

many

others

in

it

to

whom the main

outlines

of Jevons'scareerare

familiar,

but

there

are

probably

others

again

to whom

they

are not.

Since a

knowledge

of the

main

facts

of

Jevons's

career

s essential

o an

understanding

f

my

theme,

I

hope

those

to

whom

they

are

already

amiliarwill

bear

with

me

while

I

sketch

themin for the benefitof thoseto whomtheyarenot.2

The life

of William

Stanley

Jevonscould

be characterized

n a

sentence

as

short,

varied

and full of

achievement.

evons

was born

in

1835,

the

ninth

child of Thomas

Jevons,

a

Liverpool

ron

merchant;

his

mother

was

the

eldest

daughter

of

William

Roscoe,

a

Liverpool

banker

who

established

high reputation

s

historianand

art

collector.Jevonswas

1

The Jevons

Centenary

Lecture delivered

at University College,

London,

November

3,

1971.

2

For fuller

details

see

Rosamond

Konekamp,

"WilliamStanley

Jevons

(1835-

1882),SomeBiographicalNotes", ManchesterSchoolvol. XXX (1962),pp.251-73.

119


3/17

120

ECONOMICA

[MAY

thus

brought

up

in that circle

of well-to-do

non-conformists

who

contributed

as

much

to

the

intellectual

life

as to the economic

develop-

ment of the north of England in the early Victorian period through their

remarkable

combination

of business

and cultural

interests.

The interest

which these people

had

in

education

is well known,

and

in this company

it

is

hardly

necessary

to stress that University College,

London,

was founded largely

in

response

to the demand

of

middle-class

non-conformists

for

the

higher

education

for their children which

they

were prevented

from obtaining

at Oxford

and Cambridge.

Jevons

himself

was

educated

in

Liverpool

until

the

age

of

15, partly

at

the

Mechanics

Institute

School

whose headmaster

was W.

B.

Hodgson,

later to become the holder of the Chair of Political Economy at the

University

of

Edinburgh.

In 1850

Jevons entered

University College

School,

spending

one

year

as

a

pupil

and

a

further

two as

a

student

at

University College.

In 1853he had decided

to leave

College

and

go

into

business

in

Liverpool,

partly

at least

in

consequence

of the

recurrent

financial

difficulties

which

had

plagued

his

family

since his

father's firm

had

become

bankrupt

as

a

result

of the

railway

crisis of 1847. In

June

1853,

largely through

the

good

offices

of Thomas

Graham,

then the

Professor

of

Chemistry

at

University College,

the

seventeen-year-old

Jevons

was

offered

the

post

of

Assayer

to

the

newly

formed

branch

of

the

Royal

Mint

at

Sydney.

He did

not in fact

leave for

Sydney

until

June 1854,

because

of

delays

in

completing

the

new

Mint

Buildings.

In

the interval

he

had trained

with Graham as

an

Assayer

and taken

a

further diploma

course

on the

subject

in

Paris.

Jevons

remained

in

Australia

until

early

in

1859.

During

most of this

period,

apart

from

his

professional

work in

Chemistry

at

the

Mint, his

interest was

mainly

in the field of the natural sciences such

as

Botany,

and especially Meteorology, but he was also a keen observer of the

rapidly changing

social

scene

in the

Australia of

his

time. The

interest in

social

subjects-particularly

the social life of

towns-which he

had

already

shown

during

his

early years

in

London

seems

to

have

grown

strongly

after

he had been

living

in

Sydney

for

a

year

or

two.

In

1856

and

1857

he

was

supplementing

his

reading

of

Mayhew's

Great

World

of

London

with such

standard

economic works as those of

Adam

Smith

and

John

Stuart Mill and

with

lesser-known

works like

Lardner's

Railway Economy. By

the

beginning

of

1858 Jevons

seems

to have

come

firmlyto the decision to devote his career to the study of social science.

He

wrote

to

his

sister

at this time: "There

are

plenty

of

people engaged

with

physical science,

and

practical

science and the arts

may

be left

to

look after

themselves,

but

thoroughly

to

understand the

principles of

society appears

to

me

now

the most

cogent

business."1

I

W. S.

Jevons to Henrietta

Jevons,

Letters

and Journal

of

W.

Stanley

Jevons,

1886, p.

101

(hereafter

LJ). Jevons recordeddetails

of his

reading

in diaries which

he kept

in

Australia,

but unfortunately

he did not continue this

practice

after

his

return to London.

Relevant

extracts

from

these

diaries

are

included in

the

forth-

coming edition of the Papersand Correspondencef W. S. Jevons, sponsored by

the

Royal Economic

Society.


4/17

1972] JEVONS,

BENTHAM

AND DE

MORGAN

121

Soon after,

Jevons

made

the

decision

to

give up his lucrative post

at the

Sydney

Mint and return to

London,

his

first

objective being to equip

himself for his new career by completing his degree at

University

College. Not unnaturally,

the

decision came as a shock to his

relatives,

for

Jevons's

father had died

without restoring the family

fortunes, and

he and his brothers and sisters had to fend for themselves in the

world.

Nevertheless,

Jevons was convinced that

the

decision was for him

a right

and

necessary

one and he did not

lack the courage to go through

with it.

Resuming

his studies at

University College

in the

autumn of 1859 he

remained in London until 1863, gaining his BA degree in October

1860

and

his

MA

(with

Gold

Medal)

in

June 1862.

This was the period when Jevons "struck out the true theory of

economy"

and suffered the "sad

reverse"

of

being placed fourth instead

of

first in

the

College

examinations

in

Political

Economy because of

what

he

described as

a

"difference

of

opinion

.

.. perfectly allowable"

between himself and

the

Professor,

Jacob

Waley.

Much

has

been written of late about

the

"professionalization"

of

the

study

of

economics,

and

certainly

this had not

proceeded

far in

England

in the

early 1860s,

so that

the path

to

advancement

for a

bright

young

man interested

in

social science was not so clearly marked then

as

it

is

now. After toying with the idea of earning his living by journalism or

other

forms of

writing,

Jevons

fell in

with a

suggestion

made

by

his

cousin Harry

Roscoe that he

should

come to the then

recently-formed

Owens

College, Manchester,

as

a tutor-the

only

tutor in the

College

and

one

who was therefore

expected

to

offer tuition

on

any subject

which

students

could take there. Jevons

did all

that could

be

expected

of

a

struggling young academic,

and

more;

the

work

on The

Coal

Question,

which

he

began

in

1864

and

published

in

1865,

earned him

a national

reputation in a remarkably short space of time-which was probably

not

without

effect in

securing

his

appointment

to the

Chair

of

Logic,

Mental

and

Moral

Philosophy

and Political

Economy

at

Owens

College

in

1866.

It was

in

Manchester

that much of

Jevons's best

creative

work was

done

and

in

the

following

ten

years

his

reputation

rose

from

being

a

national

to an

international one. He became

influential

in

the work of

the

London

(now Royal)

Statistical

Society, gave

evidence before

many

select

committees and

royal

commissions

on

monetary

and other

questions, and was consulted by Robert Lowe, the Chancellor of the

Exchequer,

on

matters

of economic

policy.

His

work

on

logic

and his

pioneering development

of a

logical machine,

ancestor

of

the

modern

computer,

led to

his

election to

Fellowship

of

the

Royal Society

in

1872.2

But the strain

of

combining

all

these activities with

the

heavy

1

LJ, p. 154.

2

See

Jevons,

"On the Mechanical Performance

of Logical

Inference",Philo-

sophical

Transactionisf

the

Royal

Society,

vol.

160

(1870),

pp. 497-518. Jevons's

election to Fellowship is recordedin Proceedingsof the Royal Society, vol. XX

(1872),

p. 198.


5/17

122

ECONOMICA

[MIAY

teaching programme

which

included

much

evening

lecturing

told on

Jevons's

health.

This,

combined

with

the desire to have access

to the

London libraries and the

London circles

in which

he was now a res-

pected authority, led Jevons to decide to return to University College,

this time

as Professor of Political

Economy, a post which he held

from

1876 until

1880.

The

duties

of the

professorship

in those

days

were light; only

one class

was involved,

which met once a week. Indeed, the appointment

carried

less

reward

and less

prestige

than others

which Jevons might

have

taken

-at

Edinburgh

for

example.

But he was anxious

to have a

post

which

would enable him

to

devote

most of his

time to his writing and

the

prospect of a return to his old College was also attractive to him. In

1880,

however,

he

regretfully

decided

that his

strength

was

not

equal

to

a combination

of

teaching

and

writing,

and that

the

many

works which

he wished

to

complete

must have

his

whole attention;

he

therefore

resigned

the

Chair.

Unhappily,

little

time

was

left to

him for the

completion

of

the

projects

which

he had

planned,

especially

the

grand

project

of a

comprehensive

treatise

on

the

principles

of economics.

When his

active

career as an

academic

economist

and

logician

had

lasted

no more

than

twenty years,

he lost his

life

in a drowning accident

in August 1882.

This is no

more than

a

bald

sketch

of a

fascinating life;

but

it should

make clear

that

in that life

University

College, London, was

a

recurrent

motif.

It

would

be

interesting

and

worthwhile

to

expand

on that

theme;

but

in

this lecture

I

wish

to

deal only with a special aspect

of

it-to

consider

two major

intellectual

influences

in

the

development

of

that

economic thought

which

is

especially

typified

in

Jevons's

Theory of

Political

Economy

of 1871. These

intellectual

influences are particularly

connected

with

the history

of

University

College, London, and

I

think

it can be argued that

they came to bear

on Jevons through his connec-

tion with

University

College.

It has

often

been

said

that the Theory of

Political Economy

marks

a

watershed

in

the development

of economic

thought

mainly

because

of

two outstanding characteristics

in

it-its

introduction into economics

of

psychological

hedonism

on the one

hand,

and of mathematical

and

quantitative

techniques

on the other.

The first of

these,

it

seems to

me,

can be

directly traced

to

the utilitarian

philosophy

of

Jeremy

Bentham

and the second to

the mathematical

logic of Augustus De Morgan.

II

It

has long

been a

commonplace

of text-books

in the history of econo-

mic

thought to say

that the

"simple

hedonism" of Bentham

was the

basis of

Jevons's

essentially

subjectivetheory of value.

Like all

stereo-

typed statements,

this is

a half-truth

which merely

skates over the

surface

of

the relationship between

the

thought of

Bentham and

that

of Jevons.


6/17

1972] JEVONS,

BENTHAMAND

DE

MORGAN

123

The

fact is

that, as

one

recent writer

has

pungently said, "When

the

concept

of

utility entered economic theory

many

men of

substance

in

the

field were

believing

utilitarians.

Long

before the notion came under

final attack from Sir John Hicks and Sir Roy Allen in the thirties, the

intellectual temper of the times had changed so that

you

could

hardly

have

found a

utilitarian under

a

flat stone."'- It

is

not

surprising then,

with

so

many

economists

trying,

as

Dennis

Robertson

put it,

"to

remove the offending odour

of

utility"2 to find that

modern

commentat-

ors

have

been

disposed

to

minimize

the extent of Jevons's Utilitarianism.

Ross

Robertson,

for

example,

has said that

"one has

the

feeling

as he

reads Chapter

II

of the Theory, the chapter

on

pleasures

and

pains, that

Jevons

is

simply going through

the motions of

citing

an

unquestioned

authority

before

proceeding

to an

altogether

different

kind an

analysis

".3

To

my

mind

this illustrates

an

understandable,

but

regrettable,

vice of

the intellectual historian-that

of

trying

to

explain

the

thinking

of his

subject,

not

in

relation

to the

thought

of the

subject's

own

time,

but in

relation to the ideas of the present time.

In

the Theory of Political Economy Jevons does

in

fact

say

"I

have no

hesitation

in

accepting the Utilitarian theory of morals" ;4

and

to gloss

over

this

does,

I

think,

lead to a fundamental

misconception

of the

natureof the work. If, as I shall try to show, Bentham's ideas permeated

Jevons's Theory inescapably,

then it

is worth while

to

ask, first, how

Jevons

came

under their influence.

A considerable

part

of the

process

of

Jevons's intellectual

develop-

ment

can be

reconstructed

from the

letters

and

diaries which he

wrote

during

his

early life.

In his first

two years as

a

student

at

University

College (1851-53) although

he "had

several

rather

learned discussions

with

Harry [Roscoe]

about

moral

philosophy"5

he

does

not

appear

to

have studied the

subject formally

at

all.

During

his

latter years

in

Australia, when he was beginning to read political economy, he does

not seem to have paid much attention to

philosophy,

and

none at

all

to Bentham.

On his return

to London

and

to

University College

in

the

session of

1859-60

Jevons

did, however,

enrol

in

the

course

on

Philosophy

of

Mind

and

Logic given by John Hoppus-which included

a

section on the hist-

ory

of

philosophy, taking

in

Bentham.6 It seems

unlikely

that

Jevons

would

have derived a

whole new

direction in his

thinking

from

Hoppus,

1

V. C. Walsh, Introduction to ContemporaryMicroeconomics,New York,

1970, p. 24. Of recent years,

there has been a revival of interest in utilitarianism

among philosphers;

cf.

J. Narveson, Morality and Utility,Baltimore, 1967.

2

D. H. Robertson,

Lectureson EconomicPrinciples,vol. 1, 1957,

p. 86.

3

Ross M. Robertson,

"Jevons and his Precursors",

Econometrica, vol. 19

(1951), p. 233.

4 Theoryof Political

Economy(hereafterTPE),

4th

ed., p. 23.

5LJ, p.

23.

6

Calendar

of UniversityCollege

London

for

the session

1859-60, pp.

18-19.

Jevons'senrolment

n the

class is

recorded

n

the

Professor's

Fees

Books, 1859-60.

I

am indebted to Mrs. J.

Percival,

Archivist

of University College, London, for

assistance

n

locating

this

information,

and other details

relating

to De

Morgan's

classesandJevons'sattendanceat them.


7/17

124

ECONOMICA [MAY

whose

lectures

were

notoriously

dull

and

ill-attended.' On

the

other

hand,

in

1860

Jevons

did

go

to "Mr. Martineau's

mental

philosophy

class in

Manchester New

College,

which

is close at

hand in

University

Hall

".2

Now

Martineau was a considerable

philosopher

whose

long

and

deep study

of ethics

had

led

him

to

a

sophisticated

understanding

of

Utilitarianism,

and it seems much more

likely

that

his teaching

would have stimulated Jevons

and

increased

his interest

n

Benthamism.3

There

are various indications from

Jevons's

correspondence

at

this

time that

he

felt

a

growing

interest

in

philosophical

questions,

and

moral

philosophy

in

particular.4

In

the

circumstances it would have

been

surprising

f

Jevons

had not

been

influenced towards

Utilitarianism,

for

apart from the generalacceptabilityof the doctrineat the time therewere

special

factors which would

naturally

have drawn him in that

direction.

Apart

from the obvious and

natural

attraction of the

great

name

of

Bentham

for

any University

College

man,

there

was

also

the

fact

that

Jevons, like

James

Martineau,

was

a

Unitarian. There had

long existed

a

connection

between

Unitarianism in

theology

and

Utilitarianism

in

philosophy and, as has been

remarked by Professor

Mineka, "Unitar-

ians and

Utilitarians

came

largely

from

the same levels of

society, the

'1H. Hale Bellot,

University College, London, 1826-1926, p.

111: "Afterhis first

or second lecture he seldom had

a

pupil;

because, burying

his

face

in his

manu-

script,

he

mumbled so

that

only

an acute

ear could catch

much

of

what he

said,

and

those

who

caught

something

called

it

rot."

(Quoted

from a

manuscript

by

J.

B.

Benson.)

I

LJ, p. 155.

3The

implication

of this view is

that Jevons must

initially

have

become

acquain-

ted with

Bentham's ideas

through

Hoppus's

course, or

the

reading

prescribed

for

it, combined

this

with

his

notions

of

a

mathematical

theory

of

economy, and

subsequently

extended

his

knowledge

and

understanding

of

Utilitarianism

hrough

his

contacts

with

Martineau's

hinking.

For,

according

o

Jevons's

diary

rom

3rd

to

5th February,

1860, he "was

almost entirely

engaged

in

commencing

a

work on

Pol. Econ.... Value to be establishedon the basis of labour and the problems

of

rent,

wages,

interest,

etc. to

be

solved

as mathematical

functions

. .

.". On

February19,

1860 there

is

the

entry:

"At

home

all

day

and

working

chiefly at

Economy,

arriving

as I

suppose

at

a

true

comprehension

of

Value,

regarding

which I

have

lately

very

much blundered."

This,

as Professor

La

Nauze

has

suggested, pinpoints

the

discovery

of

the

utility approach

by

Jevons.

(La

Nauze,

"The

Conception

of Jevons's

Utility

Theory", Economica, vol. XX

(1953), pp.

356-8.)

It was

not

until

October or November

1860 that Jevons

began

to

attend

Martin-

eau's mental

philosophy

lectures,

but

this

does

not

prove

that

Martineau's

eaching

played

no part

in the working

out of Jevons's

ideas, for the

original

manuscript

of the

Brief

Accolnt

of

a

General

Mathematical

Theory of

Political

Economy is

dated "London September27, 1862". Martineau would

certainly have

appealed

to Jevons as one

who,

in

his

own

words,

"carried

nto [moral

and

metaphysical

speculations]

a store of

exclusively

scientific

conceptions,

rendered

amiliar

in

the

elementarystudy

of

mathematics,

mechanics and

chemistry"-Types of

Ethical

Theory,

1885,

Preface,

p.

viii.

Apart

from

the

more

generalpoints

made in

the

text

above,

it

is

interesting

to

note

that the

Brief

Account

contains

one

passage

which

seems

to echo

Martineau as

well

as

Bentham-paragraph

2,

which

begins

with

a

reference to "the

great

springs

of

human

action".

In

1847

Richard

Holt

Hutton,

another

student

of

Martineau

and

later

a

relative of Jevons

by

marriage,

had urged Martineau o

draw

up

"a

graduated

able

of the

springs of

action", and

this

subsequently

became

an

important

part

of

his

lecture

course. Cf. J.

Estlin

Carpenter,

James Martineau,

1906, p. 298.

4

Cf.

LJ, pp.

149,

155-60.


8/17

1972]

JEVONS,

BENTHAM

AND DE

MORGAN 125

enterprising,

successful

middle class",

and

shared

inclinations towards

humanitarianism

and

a

faith

in

science.1

This,

as

we

have

seen,

was the

social background

in which

Jevons

had

been reared and

his return to

University College

had

brought

him back

into

it.

Certainly,

however utilitarian philosophy

may

have entered into

Jevons's

thinking,

it

remained

a

part

of

it for the rest of

his

life

and was

much

more

than

just

a

peg

on which

to

hang

the

particular

type of

subjective

analysis

of demand

with

which his Theory

of

Political

Economy

has

come to be

specially

associated.

That his thinking moved

towards

what

Martineau called

"Hedonist

Evolution"

is clear

from the

article

on Mill's Utilitarianism

which

Jevonswrote

for

the Contemporary

Reviewin 1879.2That it remainedfirmlyin the tradition of Bentham is

clear

from

the last book

he

completed

on an economic

subject,

The

State

in Relation

to

Labour,

when

we find

the

statement

that "it

may

be

fearlessly

said

that

no social

transformation

would

be

too

great

to

be

commended

and

attempted

if

only

it could

be

clearly

shown

to

lead

to

the greaterhappiness

of the

community".3

Now,

as

this

quotation

brings

out,

Benthamism was very

much a

social

philosophy;

yet

the

Theory

of

Political

Economy,

with which

we

are

here

primarily

concerned,

deals

very

little

with

social

questions.

How then does Bentham come into it? Clearly it is not the "greatest

happiness

principle",

but the

"principle

of

utility"

which matters

in

the

Theory.

Indeed

that

work

not

only

starts

out

from,

but

revolves

around,

the

theory

of

pleasure

and

pain.4

Lookiing

back

upon this,

later economists

have been

able to

point

out

the

drawbacks

from

which

it suffers

very clearly,

and indeed

they

are

undeniable-it

is

difficult

to evade Marshall's

indictment

that

"Jevons'

great

error was

that of

applying

to

utility

propositions

that

are

only

true

of price".5I shall returnto this point in a moment, but let me suggest

that

if instead

of

looking

back

with the benefit

of

hindsight

we

try

to

put

ourselves

in Jevons's

place

and look

forward,

as

he must

have done

when

first

developing

his

theory (in

1860-62),

the matter

appears

in

a

different

ight.

Already

in 1858 Jevons

had seized

hold of the idea that

"economy,

scientifically

speaking,

is

in fact a sort of

vague

mathematics

which

calculates

the causes

and effects

of man's

industry,

and shows

how

it

may

best

be

applied".6

By

June

1860

he had

"struck

out

... the

true

Theory

of

Economy

...

entirely

mathematical

in

principle

.

.

.".7

His approach,then, was that of a pure scientist; but as a distinguished

I

F. E.

Mineka,

The Dissidence

of Dissent,

Chapel

Hill,

N.C., 1944, p.

146.

2

W.

S.

Jevons,

"John

Stuart

Mill's

Philosophy

Tested;

IV-Utilitarianism",

Contemporary

Review,

vol. XXXVI,

(1879),

pp.

521-38.

3

W.

S.

Jevons,

The State in Relation

to

Labour,

1882,3rd

ed.,

p.

12.

4

I

have

argued

this

point

more

fully

in

my

Introduction

to the Pelican

Classics

edition

of

the

Theoryof

Political

Economy,1970, pp.

15-20.

5

Marshall

to

J.

N. Keynes,

November

26,

1889;

Principles of

Economnics,

th

ed.,

vol. II, p.

260.

6

LJ, p. 101.

7

LJ,

p. 151.


9/17

126

ECONOMICA

[MAY

philosopher of science, F. S. C.

Northrop, has pointed

out, the subject

matter of

economics, as Jevons and his successors came

to conceive it,

is not objective n the senseeither of the immediately nspected sense

data or the verified, nferred

common-sense objects

.. The question

then

ariseshow

a

deductive

heoryreferring

o such a

subject

mattercan

be empirically erified.... It

might be supposedthat

the verification s

like

that

of

naturalscience,except for the minor difference hat natural

science

appeals to empirical

data given through

the

senses,

whereas

economic

science uses empirical data

given

introspectively....

But

upon

this basis one would

expect

a

different cience

of

economics

for

each

individual.It is clear that

economic

science does not conceive

of

itself

in

this way. It claims

for its theory the same

validity

for

every-

body thatnaturalscienceclaimsfor its laws and verifiedpropositions.

But

how, by appeal to

introspectionrather

than to the

senses,

can one

get

any

criterion

for public validity?1

Now it seems to me

that this

is just the problem which

Jevons,

as

a

young scientist

trying to reason

out "the true Theory of Economy",

must have

encountered-and must have

realized that Bentham

could

provide

an

answer of

satisfying symmetry through the

"principle

of

utility".

Here we must come back to the criticism of Marshall and other later

writers.

Jevons,

in

the

opening pages

of

the

Theory,

says

with

all

the

emphasis

italics

can

give, "our

science

must be

mathematical, simply

because it

deals with quantities".2

In seeking to ground

that

science on

pleasuresand pains which not

only notoriously defy

quantification but

also

differ in

quality was

not

the

scientist being

unscientific,

the

logician

illogical?

Once

again, instead of

trying

to

answer

on our

terms,

let

us

see what answer

Jevons

himself gave-for

he

did

not

overlook

or

evade

these

questions.

First, on the question of higher and lower pleasures, Jevons argued

that

"my

present purpose

is

accomplished

in

pointing

out

this

hierarchy

of

feeling,

and

assigning

a

proper

place

to the

pleasures

and

pains with

which

the

economist deals. It

is

the

lowest

rank

of

feelings

which

we

here

treat".3

So much

is stated

in the

Theory;

but

in

his

critique

of

J. S. Mill's

philosophy

Jevons went

further and indicated

that

the

question

of different

grades

of

pleasure

could

be

logically handled-by

a

strict

adherence to

Bentham's

ideas:

"Nor is it to be

supposed,

that

Bentham, in making his analysis of the coinditions of pleasure, over-

looked the

difference

of

high

and

low;

he

did

not

overlook

it

at

all-he

analysed

it.

A

pleasure

to be

high

must have

the

marks of

intensity,

length, certainty,

fruitfulness

and

purity,

or of some

of

these

at

least;

and

when we

take

Altruism

into

account,

the

feelings

must

be of

wide

extent-that

is,

fruitful

of

pleasure

and

devoid

of

evil to

great

numbers

'

F. S. C.

Northrop, The

Logic of

the

Sciences

and

the

Humanities,

1959

printing,

pp.

240-41.

2 TPE, 4th ed.,

p.

3.

3

TPE,4th ed., pp. 26-7.


10/17

1972]

JEVONS, BENTHAM

AND DE MORGAN

127

of

people"; and so, he

argued,

"Mill proposed to give

'geniality'

to

the

Utilitarian

philosophy by

throwing into

confusion what it was

the

very

merit

of

Bentham to

have distinguished

and

arrangedscientifically.

We must hold to the dry old Jeremy, if we are to have any chance of

progress

in

Ethics".'

If by holding to

the dry old

Jeremy

pleasures and pains can all

be

brought

to

a

common

denominator, there

still

remains

the question

in what

units is

it

to

be expressed? To this,

in the first

edition of the

Theory,

Jevons

frankly answered, "Greatly

though I

admire the clear

and

precise notions

of Bentham, I know not

where his

numerical data

are to

be found".2

His

mode of

escape

from

this difficulty was similar

to Marshall's "measuringrod of money"-"A unit of pleasure or of

pain

is difficult even to

conceive;

but

it

is

the amount of

these

feelings

which is

continually

prompting

us

to

buying

and

selling,

borrowing

and

lending,

labouring and resting,

producing

and consuming; and it

is

from the

quantitative

effects

of the

feelings

that

we must

estimate

their

comparative

amounts"'.

Nevertheless,

in

framing

the

rest

of

his

analysis

in terms of

utility

and disutility he

undoubtedly gave

grounds for

Marshall's

criticism4

and

proofs

of

his

allegiance

to Bentham.

III

If, as

seems

undeniable to me, the

influence

of

Bentham in the

creation of the

Theory of Political

Economy

was

considerable and

pervasive,

the

passages

which

I

have

previously quoted

to the effect

that "our

science

must

be mathematical"

reflect

an

influence on

Jevons

which was

earlier and more

profound-that

of

Augustus

De

Morgan.

De Morgan became the first Professor of Mathematics in University

College,

London,

in

1828,

at

the

early age

of

twenty-two.

He

has

been

described

by

its official

historian as

"the

outstanding figure

in

the

first

quarter-century

of the

life

of

the

college",

and

by

the

great chemist

Sir

Henry

Enfield

Roscoe-the

same

Harry

Roscoe

who was

a

cousin

of

Jevons-as "one of the

profoundest

and

subtlest

thinkers of

the

nineteenth

century".

In the fabric

of De

Morgan's

life the

Unitarian thread

again figures

prominently.

He left

Cambridge because of his

objections

to

the

relig-

ious

tests-just

as had

his father-in-law, William

Frend,

himself

a

Second

Wrangler

who

was

deprived

of

his

tutorship

at

Jesus

College.

Frend

was

an

associate

of

many

of the

leading political

and intellectual

figures

of the

early

nineteenth

century,

wrote for

the

Unitarian

Monthly

Repository,

and

was identified with the

earliest

schemes to

set

up

a

1

Contemporary eviewvol. XXXVI, 1879, p. 533.

2

TPE, 1st ed., p. 12.

This passage

does

not appear

in

later editions.

3

TPE, 4th ed., p. 11.

4

Quotedabove, p. 125, n. 5.

5

Bellot, op. cit., pp.

80-81.


11/17

128

ECONOMICA

[MAY

University

in London free of

all

religious

tests.1

Forty

years

later

it

was

on this

very

issue that De

Morgan resigned

his Chair at

University

College.

In

refusing

to

appoint

James Martineau to

the

Chair

of

Mental

Philosophy in 1866 because he was a Unitarian minister, the College

had, as De

Morgan

saw

it,

betrayed

the

basic

principle

on

which

it

was

founded,

and

he refused

to

have

any

further

connection with

it.2

During

the

thirty

and

more

years

of

his

connection with

University

College,

De

Morgan

made a

substantial

contribution

to

mathematical

knowledge,

but he was also

particularly

interested

in

the

relations

between mathematics and

logic.

Although

he

was

less

successful

here

than his better remembered

contemporary

George

Boole,

he

did

valu-

able work

in

this field. De

Morgan

also

found time

for

an immense

amount

of

semi-popular

writing

on

scientific

subjects,

as well

as

much

public

work,

in

support

of

decimal

coinage

and

on

insurance

matters.3

Nevertheless

it

was

as

a

teacher

rather than a

writer that De

Morgan

enjoyed

his

greatest

success and

reputation.

His own mind

was so

agile

and

so

profound

that

he set a

high

standard for

his

students;

but it

is

clear

from the

testimony

of

many

of

them that

he

possessed

a

rare

gift-

the

capacity

to

convey

to

those

who are

not

naturally

mathematicians

something

of the

significance

of

the

subject,

its

power

and

elegance.4

There is ample evidence of the influencewhich De Morgan had upon

Jevons-it

amounted

almost

to a

fascination.

At the time

of

his matric-

ulation in

1852, Jevons's

main

interests

were in

chemistry and

botany,

but he attended De

Morgan's

"Higher Junior"

classes

and

"Lower

Senior"

Classes.5

By

his

own

testimony

he

found

this

"interesting

though rather

hard";

he

kept up

diligently with

the

class

work

and

formed

the

intention "to

have

all

De

Morgan's

books".6

It

may

seem

that there

is

nothing

very

remarkable in all

this, but

the

effect which

it

had

on

Jevons

comes out

clearly

in

a

letter he

wrote to

his sisterfrom Australia five years later:

For my own

part

I

have never

had the

courage to

open

the many

mathematical ooks I

brought

with

me; but what

do you

think I

would

I

See

Frida

Knight,

University

Rebel,

the

Life of William

Frend,

1757-1841,

1971;

Mineka, op.

cit.,

pp.

148-50;

S. E. De

Morgan,

Memoir

of AuglustusDe

Morgani,

1882, pp.

19-24.

2

Bellot, op.

cit., pp.

339-43;

De

Morgan,

op.

cit., pp.

336-61.

3

De

Morgan,

op.

cit.;

and see also

the

article

"De

Morgan,

Augustus"

which

Jevons

wrote

for

the

Encyclopaedia

Britannica,

11th

ed.,

vol.

VIII,

pp. 8-10.

4

One

historian

of

mathematics

has described

De

Morgan as

"displaying

unusualgiftsas a teacher and scatteringhis energiesrecklessly.His Trigonometry

and Double

Algebra

1849)

contained

certain eatures

of

quaternions,

but

he

did not

follow this

or

any other

theory

to the

conclusion

that

seemed

within his

reach....

His

contributions

to

the

theory

of

probability

still

rank

as

among

the best

in

English and the same

may

be

said

for

his

contributions to

logic....

Had

he

been

able

to confine himself

to one

line,

he

might

have been a

much

greater

though a

less

interestingman." D.

E.

Smith,

History

of

Mathematics,1951

ed.,

vol.

I, p.

462.

5

Shortly

after

this

lecture

was

delivered the

original

manuscript

of

Jevons's

notes

on these

lectures

was quite

unexpectedly

discovered in

the

Library

of the

University

of

Glasgow.

Hence

it

has

become

possible

to fill

in

more of

the

details

of the

mathematical

teaching

which

Jevons

received

from

De

Morgan. See

Appendix,

below.

6

LJ, pp. 22-3. For the seventeen-year-old evons, the intentionmay have been


12/17

1972]

JEVONS,

BENTHAMAND

DE MORGAN

129

do if I

had

opportunityever

again?

Attend

College

and De

Morgan's

mathematical

ectures

The

utility of

mathematics s

one of the

most

incomprehensiblehings

about it;

but though I

was

never

bright or

successful in his class, in spite of workinghard, I feel the greatest

benefitfrom

it.1

That there

was

the

greatest

benefit

to

be derived

from

mathematics

by any scientist

was

emphasized

to

Jevons

by

his

cousin

Harry

(Sir

Henry

Enfield)

Roscoe who,

finding

chemistry

to involve

more

mathe-

matics

as

it

advanced,

wished

that he

had

paid

more attention

as

a

student to De

Morgan's

teaching.2

Now

I have

pointed out that

already

in

1858-59 Jevons

had

begun to

feel for those "generalprinciples or laws" which he felt must underlie

the

workings of

society and

to

see them in

terms

of "a

vague sort

of

mathematics". So,

defending

his

decision

to return to

England,

he

wrote to

Harry Roscoe:

"I

wish

especially

to

become

a

good

mathe-

matician,

without which

nothing,

I

am

convinced,

can

be

thoroughly

done. Most of

my

theories

proceed

upon

a

kind of

mathematical

basis,

but I

exceedingly regret

being

unable to

follow

them out

beyond

general

arguments. 3

So the

wish

of

1857 became the fact

of

1860.

"I find

the

classes

at

college a little dull", Jevons wrote to his brotherHerbert, "the charmis

rubbed off

a few

things; but then one learns more and more

to

adore

De

Morgan

as an

unfathomable

fund

of

mathematics".4What

material

did Jevons

draw from

this

unfathomable fund

to

use in

building

his

Theory of Political

Economy?

Perhaps only

some

things

which

lay

near

enough

to the

surface,

in the

shape

of

the elements of

calculus,

it

may

seem.5

more laudable than practical, for De Morgan's text-books are reputed to have

been

"a

mine

of information for the teacher and entirely hopeless for the pupil".

Smith, op. cit.,

vol.

I, p.

462.

1

W.

S. Jevons to

Henrietta Jevons,

June

17, 1857, LJ, pp. 88-9.

2

H. E. Roscoe to W. S. Jevons, February 21, 1854:

"I

mean to go hard at

mathematicswhen I am in Paris.... Nothing can be done without mathematics&

I

hope

to make

up for not attending to

De

Morgan as

I

ought to have done-fool

that

I

was."

3

W.

S.

Jevons to H. E. Roscoe, January,

1859,

LJ, pp. 118-19.

4

W. S. Sevons to Herbert

Sevons,

January27, 1860,

LJ,

p.

150.

5

Therewere other parts of Jevons's work in which other elements drawn from

De

Morgan's "unfathomable und" were important. Perhaps the most notable is

Jevons'suse of probability heory in his interpretationof scientificmethod. Cf. W.

Mays, "Jevons's Conception of Scientific Method",

The

ManchesterSchool, vol.

XXX (1962), p. 226; E. A. Madden, "W. S. Jevonson Induction and

Probability",

in

Blake, Ducasse and Madden,

Theories

of Scientific Method, 1960, p. 247.

In discussion

after

the

delivery

of

this

lecture,

Sir

John

Hicks

drew

my attention

to the

passage

in

Edgeworth'sMathematicalPsychics, 1881, p. 7,

where

he

argues

that the

"implied equatability

of

time-intensity

units"

of

utility

"resembles the

equation

to each other of

undistinguishable

vents or

cases,

which

constitutes

the

first principle of the mathematicalcalculus of belief".

Sir John

suggested that

De

Morgan's

references o

probability

in his lectures

might similarly

have

prompted

Jevons to

think

of utility as a concept susceptible to mathematical treatment,

if

not to

direct

measurement.

I am much indebtedto SirJohnfor this stimulatingsuggestion,whichcertainly


13/17

130

ECONOMICA

[MAY

It is easy

to be

slighting

about

Jevons's mathematics,

as Marshall

was1;

Jevons

himself had no illusions

about his talents

in that

field:

"I am,

of

course,

better

up

to De

Morgan'sbrain-rackings his session",

he wrote in Michaelmas term 1860, "and shall devote much time to

mathematics, yet,

from

having

no

natural talent for

figures

or

quick

memory,

have

no

hope

of

becoming

a

practical

mathematician.

Besides,

it is somewhat

late

in

the

day

at

twenty-six

to learn mathematics, with

which you

will succeed

from the first or never.

"2

But De Morgan

himself drew

a

distinction between

the

analysis

of

the

necessary

Laws

of

Thought,

and the

analysis

of

the

necessary

Matter of

Thought.3

It

was surely

in

the

field of the

laws

of

thought

that Jevons

learnt most from him.

Building

on

the foundations

laid

by

De

Morgan

and Boole,

Jevons

went

on to build

up

his own

system

of

logic,

and contended that

"it

may

be

inferred,

not that

logic

is a

part

of mathematics .

.

.

but

that the

mathematics

are

rather

derivatives of

logic".4

This

statement, which

is

wholly

in the

spirit

of De

Morgan's

work, may serve

to

put the Theory

of

Political

Economy

into its true

perspective

as

a

work

in

mathematical

economics.

The

matter

of

thought

in

it was

not

highly mathematical,

but its whole

structure

was

built up

in

accordance

with a concept

of

scienceas governed by laws of thought whichcould, where quantitiesare

involved,

be

expressed

in

a

mathematical form5;

and

that approach

was

surely

based

on the hard

training

which Jevons

had

received

in

De

Morgan's

classroom.

IV

A commemoration of

a

great work

always runs the risk

of being

either

adulatory

or

patronizing.

On the one hand there is the danger of

seeming to suggest that its author had correctly anticipated everything

derivessupportfrom a passage

n

chapterI

of TPE (lst ed., pp. 9-1

0;

4th ed., p. 8):

"Previous o the

time

of Pascal, who

would have thought of measuringdoubtand

belief? Who could have conceived that the

investigation

of

petty games of chance

would have

led to the

creation

of

perhaps

he

most sublime

branch

of

mathematical

science-the

theory

of

probabilities

?" With the recent

discovery of Jevons's notes

on De

Morgan's

lectures

(see Appendix)

it is now

possible

to

say definitely that

De

Morgan

had

introducedhim

to

elementaryprobabilityconcepts

in his

"Higher

Junior"

class of

1852-53,

and that

Jevons

was

again working on

the

subject, in

moredetail,

n

1860-61,

in

connection with De

Morgan's ectures.Hence, although

the

original manuscript

of the

Brief

Account

contains no direct referenceto these

concepts, it is certainly possible that they played a part in the conception of

Jevons'sutility theory along with what he himself

describedas the "most luminous

and philosophical

view of

existing and possible

systems of symbolic calculus"

which

he found

in

De

Morgan's teaching

and

writing.

1

"They [Cournot

and von

Thtunen]handled

their

mathematics gracefully:

he

seemed

like

David

in

Saul's armour." A. C.

Pigou (ed.), Memorials of Alfred

Marshall,p.

99.

2

W.

S. Jevons to Herbert Jevons,

November 28, 1860,

LJ,

p. 155.

3

M.

J.

M. Hill,

"Some

account of

the

holders of the Chair of Pure Mathe-

matics . .

.", MSS

in

University CollegeLibrary,quoted in Bellot, op. cit., p. 81.

"

W.

S. Jevons to Thomas

Jevons, August

30, 1863, LJ, p.

191.

5

This emerges very clearly in Jevons's statement at the conclusion of TPE,

4th

ed.,

p. 267:

"The

problem

of economics

may,

as it

seems to

me,

be stated

thus:


14/17

1972] JEVONS,

BENTHAMAND DE MORGAN

131

which

is known about

the

subject

today,

on the

other

that of

pointing

out that we have learned so much since that it seems

hard

to

conceive

how or why

the pioneer originally made

so

many blunders.

I have tried to avoid both these traps by seeking not to make a fresh

evaluation

of

the

Theory of

Political

Economy,

but rather to think

back

into the

structure which Jevons was trying to

build in it

and to

show

where he obtained the chief materials which he used

in

doing

so.

Those

materialswere

peculiarlyconnected with

University College,

but the

work

which

Jevons

chiselled out

of

them

was

peculiarly

his

own.

Whatever

may

have been its

strengths and weaknesses, we come back

to

the fact

which

has brought

us together here today-the

Theory of Political Economy

was a landmark in the development of modern economics, and Jevons

made

it. He was one of many

worthy

students who read Bentham

and profited

from De Morgan's lectures; but, as Foxwell

reminded

Keynes, "the

only point

about Jevons was that

he

was

a

genius".1

Queen's

University,Belfast.

APPENDIX

Oni evons'smathematical tudiesat UniversityCollege,London.

The comments

which

I

made n this lectureon theinfluenceof De

Morgan

on

Jevonswerebased on evidencedrawn rom

Jevons'spersonal ournal

and

correspondence,

and

the

Calendars

of

University College, London, in

addition to the

other printedsources given

in

the

text

above. By

a

remark-

able coincidence,

a

considerable

quantity

of

new

manuscript

evidence be-

came

available only

a

few weeks

after the lecture

had

been

delivered.

Mr. R. P.

Sturges, who

is

acting

as Research Assistant on

the

project

for

compiling

a Guide

to

ArchiveSources

n the

History

of Economic

Thought,

has beentravellingall over the BritishIsles in the searchfor suchmaterial.

In

the course

of

a

trip to Scotland

in

late November, 1971,

he

discovered

in

the Libraryof the Universityof

Glasgow, the following three

tems:

(1)

Manuscript notebook with

title-page: "Lectures

on

Mathematics

delivered

n

University College,London, by

ProfessorA.

De

Morgan.

Session 1852-3. W. S. Jevons"

(Ms.

Gen.

483).

(2)

Manuscriptnotebook with title on

spine: "MathematicalTracts, De

Morgan"(Ms.

Gen.

485).

(3) Manuscript notebook with

title-page: "NOTES,

and

EXTRACTS,

concerningLECTURES on the PURE MATHEMATICS,delivered n

University

College, London, by

Augustus

De

Morgan,

Professor etc.

Session

1860-61".

On

facing page:

"W. S.

Jevons, University

College."

(Ms. Gen.

484).

Given, a certain population, with various needs

and

powers

of

production, in

possession of certain lands and other sources of material: required, the mode of

employing their labour which will

maximize

the utility

of the

produce".

This clearly foreshadows the modern presentation of the same problem in

terms of "constrained maximization", and brings out sharply the real character

of Jevons's break

with the classical

tradition.

1 J. M. Keynes, Essays in Biography,1951 ed., p. 307.


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132

ECONOMICA

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I

have since had

an

opportunity

o examine

hese

manuscripts,

nd

have no

doubt that

all

three

are

in

the

handwriting

of

Jevons.

According

to

the

records

of

Glasgow

UniversityLibrary,

he

notebooks were

bequeathed

by

George AlexanderGibson,who was Professorof Mathematics n Glasgow

University rom

1909

to

1927

and

died

in

1930;

there

is

no

evidence as to

how

the notebooks came into his

possession.

With the

aid

of these

notebooks

t is

possible

to

put

some flesh

on

the

bare

bones

of

the outline

of

Jevons's mathematicalstudies

previously known.

The syllabus

of De

Morgan's

Mathematics

ectures altered but

little

over

theperiod

of

Jevons's irst

and secondattendances

at

them,

and

ran

typically

as

follows:

The Lower Division of the Junior Class is intended for those Pupils who

possess

very

little

previous acquirement.

The

Subjects

read

are,

the

First

Four

Books of

Euclid;

Arithmetic,

and

the Arithmetical

Theory

of

Propor-

tion;

the Sixth Book of

Euclid;

Solid

Geometry; Algebra,

arithmetically

considered,

as

far

as

equations

of the

first and second

degrees.

The

Higher

Division of the Junior Class is intended

for

those

whose

previous

reading

will

enable them to

begin

the

Fifth Book of

Euclid.

The

Subjects

read

are,

the

Fifth

and Sixth Books of

Euclid;

Solid

Geometry;

a

Review of the

Principles

and

Operations

of

Arithmetic;

Algebra;

Plane

Trigonometry;and,

if

time

permit,

the

Conic Sections

geometrically.

The Lower Division of the Senior Class will

comprehend

those

who have

(either

in the

College

or

elsewhere) passed through

the

Subjects

of

the

precedingClass. The Subjectshere read are, SphericalTrigonometry; Conic

Sections;

applications

of

Algebra

to

Geometry; higher

parts

of

Algebra;

Differential and

Integral

Calculus.

The

subjects

read in the

Higher

Division

will

consist of

Developments

of

the

Differential and

Integral Calculus,

to

prepare

he Student

for

the

higherapplications

of

Mathematics o

Physics.

(Calendar

of

UniversityCollege,

Lonidon, 853-54, pp.

7-8).

The Professors Fees

Books of the

College

record

that

Jevons

was en-

rolled for

De

Morgan's

classes in 1851-52

and

1852-53,

and

again

in

1859-60 and

1860-61;

but

as one fee

could

cover several

classes

this does

not establish which class or division of a class he attended in each year.

These details,

which could

previously only

be inferred

from

references in

Letters and

Journal,

can

now be confirmed

precisely

from

the

notebooks.

Thus the

first

notebook

(MS.

Gen.

483)

makes clear

that

Jevons had

attended

only

De

Morgan's

"Lower Junior" class in

1851-52,

before his

matriculation

into

University

College.

The

first

seventeen

pages of the

notebook

contain

undated

notes on the

subjects

of this

class,

but

the

note-

book

is,

in accordance with

its

title-page, mainly

devoted

to the

lectures of

1852-53.

It

makes clear

that

Jevons attended both

the

"Higher

Junior"

and

"Lower

Senior" classes

during

that

academic

year. Apparently he had al-

ready developed

his

lifelong passion

for

economizing

paper-for

he

made

one

notebook suffice for both

classes,

first

filling

the

right

hand

leaves

from

front to

back,

then

turning

the book

upside

down to fill

the

facing leaves in

the

opposite

direction-a

system

which

does

not

make

the

notes

easy to

follow.

The

second notebook

is

clearly

the one which

Jevons used for

what

he

described as

"the

long

job

of

copying

out De

Morgan's

tracts".'

These

were

tracts which

De

Morgan prepared

on

various

aspects

of

mathematics

1

LJ,

p. 23.


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134

ECONOMICA [MAY

The same interest

n the logic and philosophy

of mathematicsmanifests

itself in the "Higher Junior"

and

"Lower

Senior" courses,

but Jevons's

comment

of October

31, 1852,

seems

hardly surprising:

"We have

just

finishedwhatwe areto do at presentof doublealgebraand series,whichI

think rather

interesting,

hough

hard".' It

must

have

been a

considerable

effort

to

keep up

with the work of

the two classes at the same

time,

but

Jevons appears

o have done

it

conscientiously,

n

spite

of the fact that his

main interestat this time

was in chemistry,and by the

end of the

academic

year

he

had

got

a

good

grounding

in

the

theory

of

equations

and the

differential alculus.Certainly he

result

of

his

work

was

not

discreditable,

although

Jevons's own account of

it was

modest enough:

"Mathematics

was a

much harder

affair,

of

course.

Some time

before

the examination

I

formed some desperateresolutionsas to the place I would get, and I did

work

up

a

little.

I

tried very

hard

in

the

examination,

but spent too much

time on the hard

ones,

and came out fourth".2

When Jevonsreturned

o

UniversityCollege

in

1859,

he must have found

this earlierexperienceof

"Lower Senior" mathematicsvaluable. Neverthe-

less

it must

again have been

a

considerableeffort for

him to deal with the

two Senior Courses simultaneously,

especially

in

view

of the fact that he

was also

taking

courses in Greek, Latin and German,after a six-yearbreak

from

academicwork.3 So naturallyhe would have been

"better up to De

Morgan'sbrainrackings"

when, after taking his BA degree,he re-attended

the "Higher Senior" class in the following academic year

4

and this

probablyaccountsfor the

more eclectic approachof the

1860-61 notebook.

Integration

Rule of

Derivation by Arbogast's

Bernouilli'stheorem

method

General

formula

of

Reduction Curves of Pursuit

Integration of

rational and integral

Cauchy'sTheorem

functions

Method

of

Parameters

Differential

equations

Systems

of

Equations

Homogeneous

functions

Partial

Differential Equations

Convertible

Operations

Curves, Lines, AnglesSingular Points TrigonometricalFunctions

Infinities

Asymptotes-

Infinity

of

Functions

Problems

on

Lines

and

Planes

Discontinuity

Paraboloid

Singular

Values

Factorial Integrals

Method of

Quadratures

1

LJ, p.

23.

2LJ, p.

36.

3Ibid., p.

148.

4

Ibid., p. 155.

Black Jevons, Bentham and the Morgan

Documents

Transcript of Black Jevons, Bentham and the Morgan