[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
conclusive, are that the letter is much chattier than her
usual letters to ADM, and that the letter ends 'Yours most
sincerely', which, based on a glance through the letters from
Box 171, was AAL's usual way of ending letters to Mrs.
De Morgan --- her standard sign-off to Mr. De Morgan
seems to have been 'Yours most truly'.]

[58r]

 S^t James' Square
       6 o'clock
       Sunday Evening

 My Dear M^r De Morgan

I am very sorry
indeed at the extremely
dispiriting account you
give of yourselves; & also
I am much disappointed
at losing the pleasure
of spending this evening
with you. I was
out when your note arrived,
[58v] but I hear from the
servants that it came
just after half past four
o'clock.
Can I, (as far as you
at present foresee), spend
next Sunday Evening
with you?  I hope so,
for I believe it will
be my last ['Sunday' inserted] previous to
going to Paris; & I
have no week-day evening
disengaged to offer.

[59r] Another of the little
mathematical epochs, that
are so interesting to me,
has arrived; I mean
another Chapter of the
Differential Calculus is
just satisfactorily completed;
& I have a whole bundle
of papers to submit to
M^r De Morgan upon it,
& one or two questions
to ask on some trifling
points in it that are
not perfectly clear.  But
[59v] as it is not of a nature
that immediately presses,
all this may I think
wait till I can come
to you. Meantime I
shall begin Chapter VI,
on Integration &c.

I have since I 
saw you had such a
wonderful quantity of
occupations of various
sorts to get thro', that
I feel a little surprised
how I have managed to
[60r] ['got thro'' crossed out] accomplish, even this much
of the mathematics.
However I do not think
anything will ever manage
to oust the latter.  Indeed
the last fortnight is
rather a convincing
proof that nothing can.

I have been out
either to the Opera,
German Opera, or
somewhere or other, every
night.  I have had
music-lessons every morning,
[60v] & practised my Harp too
for an hour or two; &
I have been on horseback
nearly every day also.  I
might add many sundries
& et-ceteras to this list.

I must however maintain
that the Differential
Calculus is king of the
company; & may it
ever be so !

Believe me

 Yours most sincerely

 A. Ada Lovelace