278 The Laws of Motion of a Cylinder, &c, 
ditions of the Problem, a quantity which will make 
the expreffion : oo fome power of 1+ 4%, whofe 
index is y, a pofitive integer. . 
Prostem If. All things being fuppofed the fame 
as in the laft, it is required to determine the time 
neceffary for compleating the whole operation, on 
the fuppofition that the block rifes from the top of 
the column before the firft firoke, and that the 
velocity with which it afcends both then and after- 
‘wards is uniform, and equal to a given quantity 
b per fecond. 
So.ution. ‘The fum of the fpaces defcribed by 
the block in afcending = x UL Le ret +2zx, 
—_—_—_—)—I1 
eri xxi! == yx 1-fi— 1; but 
== "by Pros. I, therefore the fum — Ry 
t 
rte 
Now as all thefe fpaces are defcribed by the afcend- 
ing block with an uniform motion, we have as b:1 
Cc c E : 5 ° 
fecond :: T= the time fpent in performing 
this part of the, bufinefs, which does not vary with 
y or x, but is made up wholly of conftant quan- 
tities. From the laws of gravity we get the. fol- 
lowing expreffion for the time that paffes while the 
block defcends in free fpace, which is alfo a geo- 
metrical] 
