## Folios 40-41: ADM to AALAL

**[40r] ** My dear Lady Lovelace

There is a misprint

in page 83, I find, line 6 from

the bottom. For \(x+w\) read

\( x+1\) . Your result is correct

for an in crement [*sic*] [something crossed out] \(w\) .

**[40r] ** My dear Lady Lovelace

There is a misprint

in page 83, I find, line 6 from

the bottom. For \(x+w\) read

\( x+1\) . Your result is correct

for an in crement [*sic*] [something crossed out] \(w\) .

**[38r] ** My dear Lady Lovelace

I have added a note or two

to your papers.

As to the subject of continuity, it

must be as much as possible your

object now to remember while proving

the things which are true of continuity

to remember that they are not __false__

of ['conti' crossed out?] dis continuous [*sic*] functions, be-

cause true of continuous ones. Thus,

you will afterwards see that

**[37r] ** My dear Lady Lovelace

**[35r] ** My dear Lady Lovelace

We shall be happy to

see you on Monday Evening, and

Lord Lovelace too if he be not

afraid of the algebra

Your points in your letter are

are [should be 'I'] think, clear enough in

your own head. A little addition

however may be made as follows.

**[33r] ** My dear Lady Lovelace

I return the papers about series which

are all right, the old one is as you suppose

With reference to your remarks on the diff^{l} calculus

1. You observe that

**[31r] ** My dear Lady Lovelace

You are right about

the writing down of the

terms:

\(\frac{z}{(2n-2)(2n-3)}\)

is the \(n\) th term divided

by the \((n-1)\) th and the

\( \overline{n+1}\) th divided by the

\( n\) th is \(\frac{z}{2n(2n-1)}\) as you

make it.

**[29r] ** My dear Lady Lovelace

I have made some additional

notes on your papers.

[diagram in original] The meaning of \(\frac{\theta}{\sin\theta}\) is as follows

\(\theta:1\) and \(1:\sin\theta\) compounded

give it in arithmetic

In fact \(\frac{a}{b}\) in arithmetic is another way of writing

\( a:b\) .

In geometry \(AB:AO\) is \(\theta[:]1\)

and \(AO\) or \(OB:BM\) is \(\sin\theta\)

**[27r]** My dear Lady Lovelace

I can soon put you out of your

misery about p. 206.

**[24r] ** My dear Lady Lovelace

I send back your worked question.

The second is right the first wrong in two places

**[20r] ** My dear Lady Lovelace

With regard to the error in Peacock you will see

that you have omitted a sign. It is very common to suppose that

if \(\varphi x\) differentiated gives \(\psi x\), then \(\varphi(-x)\) gives \(\psi(-x)\), but

this should be \(\psi(-x)\times\text{diff.co.}(-x)\) or \(\psi(-x)\times-1\) . Thus

\(y=\varepsilon^x\) \(\frac{dy}{dx}=\varepsilon^x\)