[5r] My dear Lady Lovelace

I should be as able as willing to see 
you in town on Friday, but have first heard that
M^r Frend is not so well as he has been, and am
going to Highgate to day to see how he is.
In consequence, having various matters to complete
definitively by the 16th instant, I shall 
find it impossible to go to town again
this week.

 With regard to the second chapter, pray 
remember that you are not supposed to 
know, or to want to know, what 
differentiation is, but only that there 
is a process of that name, which is 
to be learnt by rule for the present,
[5v] as an exercise in algebraical work.

 With regard to the logarithms, in the
first place, Bourdon is too long.  If you
will look at the chapter in my algebra,
you will find it shorter.

In the equation
\(a^b=c\)
\(b\) is called the logarithm of \(c\) to the
base \(a\) .  This is the meaning of the 
term.  But for convenience the 
series \(1+1+\frac{1}{2}+\frac{1}{2\times 3}+\frac{1}{2\times 3\times 4}+\)\&c ad inf
or \(2.7182818\cdots\) (called \(\varepsilon\) ) is the base always
used in theory; while when assistance
in calculation is the object, 10 is
always the base; thus if

\(\varepsilon^x=y\)    \(x\) is the logarithm of \(y\)

[6r] Thus \(a=\log b\) 
is by definition
synonymous with \(b=\varepsilon^a\)  \(\varepsilon\) being \(2.7182818\cdots\) 

I remain

Yours very truly

 ADeMorgan

3 Grotes' Place, Blackheath

 Wednesday M^g