## Folios 157-158: AAL to ADM

**[157r] ** East Horsely Park

Ripley

Surrey

Dear M^{r} De Morgan

In consequence of

y^{r} kind reply to my

former note, Lord L

think I had better

send you the paper,

(which has been put

into type, tho' not

published).

## Folios 154-155: AAL to ADM

## 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

## Folio 175: ADM to AAL

**[175r] ** [in De Morgan's hand] This complete differential of \(\varphi\), as

it is called namely

\(\frac{d\varphi}{dx}.dx+\frac{d\varphi}{dy}.dy+\frac{d\varphi}{dz}.dz\)

is a perfectly distinct thing from

\(\frac{d\varphi}{dx}+\frac{d\varphi}{dy}+\frac{d\varphi}{dz}\)

and also from \(\frac{d^3\varphi}{dx\,dy\,dz}\)

Read again page 86 when \(x\) is changed

to of 87

page 198--199 & the

references

## Folios 168-170: ADM to AAL

**[168v] ** [In De Morgan's hand] When an equation involves only two

variables, it is easy enough to write all

differential equations so as to contain nothing

but differential coefficients; thus

\( y=\log x\frac{dy}{dx}=\frac{1}{x}\)

## Folio 45: ADM to AAL

**[45] **[in ADM's hand]

\(\int_a^{a'}f\,ds\)

\(\int_a^{a'}\varphi s.ds\) \(\varphi s\) meaning \(f\)

\(\int f\,ds\)

\(\int\frac{dv}{dt}.ds\)

\(\int\frac{dv.ds}{dt}\)

Negative & Impossible Qu. \(\int dv.frac{ds}{dt}\)

Operation \(\int dv.v\)

Relation \(\int v\,dv\) [diagram in original]

\( v^2=2\int_a^{a'}f\,ds+C\) \(dy/dx\)

\( V^2=0+C\)

\( v^2-V^2=2\int_a^{a'}f\,ds\)

## Folios 50-52: AAL to ADM

S^{t} James' Sq^{re}

Saturday Morning

Dear M^{r} De Morgan. I

hope you have not by

this time come to the

conclusion that I have

drowned the Differential

Calculus at least (if not

myself with it also) in

the Seine or the Channel.

## Folios 58-60: AAL to ADM

[CH] I think this is in fact a letter to *Mrs *De Morgan. The

reference in the letter to *Mr. *De Morgan is pretty clear

evidence for this. As for the salutation, the 'r' of what

appears to be 'Mr' curls back on itself very slightly, in a

way that is suggestive of AAL's way of writing 'Mrs'.

Compare what we find here with, for example, her 'Mr'

in Box 170, fol. 54r, and the 'Mrs' in Box 171, fol. 5r.

Other points to mention, although these are by no means