The Laws of Motion of a Cylinder, &e. 277 
after the fecond ftroke. And this quantity being 
added to x x 1-++# gives x x 1 +t, for the dif- 
tance of the required point from the top of the 
pillar after the fecond ftroke. By proceeding in this 
manner we find the fucceffive values of the heights 
defcended through yf the block before each fucceed- 
me. ftroke’ to: ube = «7, zat zx Ith. 
xxI nr x continued to x x 1 ree the and thofe of 
the {paces penetrated by each ftroke ih fucceffion, 
Ba De Se Ox KT, FO STE Mt yy POE te Cee. 
continued to txy 1 +t? ". Now it is evident that 
each rank of quantities exhibited above, conftitutes 
a geometrical progreffion, but the fum of the latter, 
which is the fum of the fpaces penetrated by all 
y y 
rn G acai es ey ene Pig cased a 
the flrokes erecia anh eae +t—x—c 
c 
> ited 0 ap Fe 
per queftion, and x == 
1+t—r1 
c 
% Cc 
Coroxrary I. When y==1,x==1+t—1 oat Nh 
q* b OT ee ee 
Cor. II, Since x = y rt+27 = 
I + pl qT, 
+x | ; 
a, hence it appears that x cannot be affumed 
at pleafure, but muft be, according to the con- 
ditions 
