[68r]

 Ockham Park
      Ripley
       Surrey

 Friday . 17^th Dec^r ['1840' added in pencil by later reader]

 Dear M^r De Morgan.  This
is very mathematical weather.
When one cannot exercise one's
muscles out of doors, one is
peculiarly inclined to exercise
one's brains in-doors.
Accordingly I have been
setting vigorously to work
again, with much satisfaction.

But I am sorry to
say that I am sadly obstinate
[68v] about the Term at which
Convergence begins for the
Series (A) page 231 of Algebra,
and which we thought had 
been made clear by you
on Monday Evening . I must
persist in thinking Convergence
begins at \(\frac{x^{33}}{2.3.4.\ldots 32.33}\),
and I have enclosed my
Demonstration of my view of
the case, & which seems to
me as clear as possible.    

At any rate this will
show you at once where my
blunder is; if I have
blundered, for I can hardly
think I have, so very palpable
[69r] does the proof appear to me.

The other night I had
unluckily been 10 days or
more without thinking about
anything of the kind, and
consequently the ['whole' inserted] thread of the
argument was not present to
me; or I might have
spared you & myself this
trouble now.     
I have thought with much
pleasure of my agreeable
evening on Monday,     
mathematical & educational.

 Yours most truly

 A. A. Lovelace

[69v] [a child's scribbling?]