## Folios 46-47: AAL to ADM

[something written vertically here --- belongs at end of letter so transcribed there]

Ockham Monday. 4^{th} Sep^{r}

Dear M^{r} De Morgan

Will you send on the

enclosed to M^{rs} De Morgan. It

explains the arrangements I have

made in case she comes here,

& also that Lord L & myself

have delayed our own departure

until Sat^{dy} next. Our household

& children however are already

gone.

Now to mathematical business :

I think you have hit the right

nail on the head, altho' my

confused notion of Differentials was**[46v] ** not the __only__ piece of puzzle &

mistiness which constituted the

impediments towards my comprehension

of \(X\frac{du}{dx}+Y\frac{du}{dy}=U\) . The rectifi=

=cation of __this__ however, has I

believe given me the __key__ to the

remaining difficulties. If you

will be kind enough to read

the ['following' crossed out] enclosed observations,

you will be able to judge how

far I __now__ take a just view

of the matter.

I find that when (a long time

ago) I studied Chapter V, I

never gave due importance to

the conclusion

\(\Delta.u=\frac{du}{dx_1}\Delta x_1+\frac{du}{dx_2}\Delta x_2+\frac{du}{dx_3}\Delta x_3+^\text{&c}\)

\(+\left\{(\Delta x)^2,(\Delta x_1\Delta x_2),\text{&c},\text{&c}\right\}\)

deduced at the bottom of page 87,

as the result of pages 86, 87. My**[47r] ** whole attention was given to the

subsequent theorem of page 90,

''__If \(u\) be a function of \(t\) in different__

''__ways &c, &c__'', which I con=

=ceived to be the only object in

view, & that the equation of

page 87 was of no consequence__in itself__, but merely means to

an end. This seems to have been

an egregious blunder, since the

whole theory of __Differentials__

rests on the very part which

I ['comparatively' inserted] neglected, from ['fancying it' inserted] a merely subsidiary

theory. I believe I am not wrong

in this present view of the

matter.

I cannot help here remarking

a circumstance which I ['believe' crossed out] think is

almost invariably true respecting__all__ my difficulties & confusions

in studying. They are without __any__**[47v] ** exception that I can recal [*sic*], from

misapprehension of the __meaning__

of some symbol, or ['of' inserted] some phrase

or definition; & on no occasion

from either any __error in my____reasoning__, or ['from' inserted] any __difficulty__ in

carrying on ['any' crossed out] chains of deductions

correctly, however complicated or

profound or lengthy ['these may be' inserted]. I therefore

have lately begun to ask myself,

whenever I am stopped, whether

I clearly understand __what__ the__subjects__ of the reasoning are; &

to go carefully over every __verbal__

[something crossed out] & __symbolic__ representative of a

thing or an idea, with the

question respecting each, ''now what

''does it mean, & how was it got?

''Am I sure of this, in each instance

''involved in the subject?'' This

may save me much future trouble.

I will send you my remarks __tomorrow__,**[vertical text on 46r] ** as I want to look

over them once more

first; & today I

have had enough of

these subjects.

Yours very truly

A.A.L

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