210 Of the SOLIDS 
cease 9) Beg tSe mcg ssepr eels 
THEREFORE (2 2) @+y)? =a—y Paror 
(2a—y) (*+y)* =22°—y’. 
As this. equation is homogeneous, if we make 4 =u, or 
@ 
y=ux, both w and y may be exterminated.. For we have by 
fubftituting ux for y, (2e—ua) (x +1n° x)* = 24" — v2", 
or (2 a°—ua’) (10°)? = 2a*—wu' x’, and dividing by 2’, 
(2—z):(1 40)? = 2—ux°; whence fquarimg both fides, 
(44—4u+) (I+) = 4—40' +44. 
From this, by multiplying and reducing, we get 4u°— 9 u 
Soe or fT; and u= SE NEY. 
2. THE two values of w in this formula create an ambiguity 
which cannot be removed without fome farther inveftigation. 
If A be the attraction of the cylinder, then A = 22 (w+ y — 
Vx +"), into which expreffion, if we introduce w, and exter- 
minate both w and y, by help of the equations 7 x y* = m3, and- 
Tft+u—VYi+u 
ee 
uz 
2 
Y =u, we get A= 2.03 m 
v 
NotTwiITHSTANDING the radical fign in this formula, there 
is but one value of A, correfponding to each value of uw, as the. 
pofitive root of W1 —u? is not applicable to the phyfical pro- 
blem. 
