Of GREATEST ATTRACTION. © 2uF 
blem. This is evident, becaufe the attraction muft vanifh both 
when y = 0, and when x = 0; that is, both when «z is nothing, 
and when it is infinite: This can only happen when. NV 7+ a 
is negative. 
FARTHER, the value of A is always pofitive (as it ought to 
be), 1+ being greater than Vi-+ua’, becaufe it is the {quare- 
root of rh gin-ha. 
Fe Pansies the relation between -A and w will be: beft con- 
ceived, by fuppofing A to be the ordinate of a curve in which 
the abfciffe are reprefented by the fucceflive values of wu. Thus, 
if OP (Fig. 7.) =u, and PM= A, the locus of M is a curve of 
the figure OMM’, which interfects the axis at O, and has the or- 
dinate PM a maximum, when OP = a7 3 beyond PM’ the 
curve has a point M’ of contrary flexure, where it becomes convex 
toward the axis OR, and afterwards approaches OR continually. 
It has alfo another branch mm'n, correfponding to the af- 
firmative values of ¥1 +71’, which has the perpendicular OQ_ 
for an aflymptote; and has the ordinate P’m' a minimum, 
when z= ar After pafling the point where P’m’ is a 
minimum, this branch of the curve recedes continually from 
the axis OR. Befides thefe, there are other two branches of 
the fame curve, on the oppofite fide of OQ, anf{fwering to the 
negative values of w. It is, however, only the firft-mentioned 
of thefe four branches that is connected with the mechanical 
queftion confidered here. 
Vou. VI.—P. II. Dd THE 
