[119r]

 Ockham.
Monday Morning
          16^th  ['July' crossed out] Aug^st 
                         ['1841' added by later reader]

 Dear M^r De Morgan.  I send you today, 1^stly:
a paper in which I have proved the Theorem
\( \int fx\frac{dx}{dt}dt=\int fx.dx\) (of pages 102, 103), backward{s.
That is I have assumed \(\int fx.dx\), & deduced
from it that when \(x=\psi t\), then \(\int fx.dx=\int fx\frac{dx}{dt}dt\);
whereas in the book \(\int fx\frac{dx}{dt}dt\) was assumed,
& the process was exactly reversed.
I do not send this as having any advantage
over the other proof.  Merely because it happened
accidentally to strike me, & I wrote it down;
& I now ['may' crossed out] enclose it for inspection, to see that I
have correctly deduced each step.
2^ndly : I enclose you my Second Paper on ['the' inserted] Accelerating
Force subject.  This one is the explanation of

 \(S=\int v.dt\) 

Tomorrow I hope to send you the one on \(t=\int\frac{ds}{v}\) .
[119v] I hope I am not plaguing you very much.
I am anxious to read up to a certain point
before moving to Devonshire.

Believe me

 Yours most truly

 A. A. Lovelace