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Folios 46-47: AAL to ADM

[46r]

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

Ockham Monday. 4th Sepr

Dear Mr De Morgan

Will you send on the
enclosed to Mrs 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 Satdy 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

About this document

Date of authorship: 

4 Sept 1841

Holding institution: 

Bodleian Library, Oxford, UK

Collection: 

Dep. Lovelace Byron

Shelfmark: 
Box 170