ows, to render it into differential calculus:

{78}

"And the whole tells us just this, that David did what he could. He
augmented those elements of his constitution which were (_exceptis
excipiendis_)[164] subject to himself, and the Almighty then augmented his
personal qualities, and his vocational _status_. Otherwise, to throw the
matter into the expression of our notation, the variable e was augmented,
and c x rose proportionally. The law of the variation, according to our
theory, would be thus expressed. The resultant was David the king c e x [c
= r?] (who had been David the shepherd boy), and from the conditions of the
theorem we have

du/de = ce(dx/de) + ex(dc/de)x + cx

which, in the terms of ordinary language, just means, the increase of
David's educational excellence or qualities--his piety, his prayerfulness,
his humility, obedience, etc.--was so great, that when multiplied by his
original talent and position, it produced a product so great as to be equal
in its amount to royalty, honor, wealth, and power, etc.: in short, to all
the attributes of majesty."[165]

The "solution of the family problem" is of high interest. It is to
determine the effect on the family in general from a change [of conduct] in
one of them. The person chosen is one of the maid-servants.

"Let c e x be the father; c_1e_1x_1 the mother, etc. The family then
consists of the maid's master, her mistress, her young master, her young
mistress, and fellow servant. Now the master's calling (or c) is to
exercise his share of control over this servant, and mind the rest of his
business: call this remainder a, and let his calling generally, or all his
affairs, be to his maid-servant as m : y, i.e., y = (mz/c); ... {79} and
this expression will represent his relation to the servant. Consequently,

c e x = (a + mz/c)e x; otherwise (a + mz/c)e x

is the expression for the father when viewed as the girl's master."

I have no objection to repeat so far; but I will not give the formula for
the maid's relation to her young master; for I am not quite sure that all
young masters are to be trusted with it. Suffice it that the son will be
affected directly as his influence over her, and inversely as his
vocational power: if then he should have some influence and no vocational
power, the effect on him would be infinite. This is dismal to think of.
Further, the formula brings out that if one servant improve, the other must
deteriorate, and _vice