[142r]

 Ashley-Combe
 Sunday. 21^st Nov^r ['1841' inserted by later reader]

 Mr Dear M^r De Morgan. [something crossed out]

I said Wed^dy.  At least I
meant to do so.  On Tuesday I have already an
engagement in the morning.  Perhaps you have
written Tuesday by mistake.  But of you cannot
come on Wed^dy, then I must put off my Tuesday's
engagement, that I may see you then.  If it is the
same to you however, I should much prefer Wed^dy.

Can you kindly give me one line tomorrow to
say which it is to be.  I shall get ['it' inserted] in the evening in
S^tJames' Sq^re . Now I proceed to business :
1^stly : You have mistaken my intentions I think about
the formulae of pages 155, 156.  My enclosures 1 & 2
will explain.
2^ndly .  Enclosure 3 contains the demonstration of ''Exercise''

 page 159
3^dly .  Enclosure 4 \( . . . . . . . . . . \) ''Exercise''

 page 158
4^thly : About the Constant in page 141 : I still am
[142v] unsatisfied.  I perfectly understand that ''any value''
consists with everything in page 141.  The principle
is I conceive exactly the same as that by which in
page 149, \(y\) is made \(=a+\sin.x\) instead of \(y=\sin x\) .

I only mean that this result seems inconsistent
with page 116 when it is shown that the Constant
must \(=\frac{w}{2}\) .
5thly : page 161, (line 14 from the top):

 \(\varphi''(x+\theta h,y+k)-\varphi''(x+\theta h,y)=\varphi_1^{('')}(x+\theta h,y+vk).k\) 

  \(v<1\) 
Why is \( v\) introduced at all?
I have as follows :

\( \frac{\varphi''(x+\theta h,y+k)-\varphi''(x+\theta h,y)}{k}=\varphi_1^{('')}(x+\theta h,y)\) 

 if \( k\) diminishes without limit; (\( k\) being \(=\Delta y\) )
or \(\varphi''(x+\theta h,y+k)-\varphi''(x+\theta h,y)=\varphi_1^{('')}(x+\theta h,y)k\) 
But I do not see how \( v\) comes in.
6^thly : I have several remarks to make altogether
on the Article Operation.  I will only now subjoin
two.  I believe on the whole that I understand the
Article very well.
See page 443, at the top, 2^nd Column) :

 \(\varphi^2+2\varphi\psi+\psi^2\), or \((x^2)^2+2(x^3)^2+(x^3)^3\) 
should be it appears to me \(\varphi^2+2\varphi\psi+\psi^2\), or \((x^2)^2+2x^3.x^3+(x^3)^2\)
                                                                                 or \((x^2)^2+2(x^3)^2+(x^3)^2\)
                                                                                          \(=(x^2)^2+3(x^3)^2\) 

[143r] I only allude to \((x^3)^3\), instead of \((x^3)^2\) as I make it.
See page 444, at the bottom, (\) 2^\textup{nd}\) column) :
''Where \(B_0\), \(B_1\), &c are the values of \(fy\) and its
''successive diff-co's [sic] when \(y=0\), &c, &c''
Surely it should be when \(y=1\).
The same as when immediately afterwards, (see page
445, 1^st column, at the top), in developping [sic] \((2+\Delta)^{-1}\varphi x\);
\( B_0\), \(B_1\) &c are the values of \(fy\) & its Co-efficients
when \(y=2\), &c, &c.

I have referred to Numbers of Bernoulli
& to Differences of Nothing; in consequence of
reading this Article Operation.  And find that
I must read that on Series also.

I left off at page 165 of the Calculus; &
suppose that I may now resume it; (when I return
here that is).
I will not trouble you further in this letter.
But I have a formidable list of small matters
down, against I see you.

 Yours most sincerely

 A. A. Lovelace