‘The Laws of Mation of a Cylinder, &ce. ~ 285 
is'as the fquare ‘of the ‘velocity and furface con- 
jointly, we —have, as per: frsprexK cul: 
a = the variable part of the 
c 
-retarding force; and the whole tetarding force — 
13 . 2She + 
— 
; Eee C= 4 & 
sheet an: 4 ith its hone rapen sac rpares 
2 sp fx + 2 fF EXT putting h =e—b, 
25h CT ind ca } 
Let =r, re t, and by reduction we have 
rititz x pte Xo! Hop ea ae 
Now becaufe x and v begin together, put x — 
Av +Bv? 4 Dvi+Ept + Kv® + &e. where 
the figns and values of A, B, D, E, K, &c. will be 
determined by the refolution of a fubfequent equa- 
tion, thn: = vxX%:A+2Bv+ 3Dwv+4Ev3 
+ 5Kvu* + &c. and fubftituting -for the values 
of x and + in the Equation ry #442 x p4x 
he D lee CU, uv, we get rAd titpic.. Ape 
—OscABt atph tid x vticr RE GIpe 
—4tcB43tpD+3tAB Xx vic —v. From 
this expreffion, the values of the co-efficients A, B, 
Oo D; ES k, 
