Review of Mr. Blake's Article on the flow of Elastic Fluids. 379 
§ is constant Vx sa and consequently 
vD 
VDS a: DSYP (e) 
VD 
Hence if P be a momentary force which acts upon 6 for a single 
nstant, then will the formula (a), which is identical with (e), 
lepresent correctly the relation between V, D and P, at the orifice. 
gain, if a constant accelerating force P, act continually upon 
abody } during a time ¢, it will give to that body at the end of 
the time ¢ a velocity V and momentum m. And because the ef- 
. (f) 
Also because the momentum of a body is equal to the product of 
the body multiplied by its velocity, we have m= bV. 
And by substituting for m in (f) its value as found in (g) we 
have 6V co tP, or Vc a whence by substituting VDS for 6 and 
a /7p 
reducing and supposing S constant, we have V « . , and there- 
fore, by multiplying both sides by DS, we have 
Jw 
Vis oo (h) 
VD 
Now it is sufficiently obvious that this formula can be iden- 
_ Neal with (a) only when ¢ is equal to unity. Hence if (a) represent 
herally the relation between V and P, on the supposition that 
. 8a constant accelerating force, it follows that the velocity V 
in the formula (h) must have been induced in a unit of time, 
Whatever distance the body may have traversed. Wherefore, in 
t supposition, V must vary as the distance traversed, or as the 
of the discharging vessel when the body is a fluid genera- 
ted at its farther end. But the space traversed by a body in con- 
quence of the action of a constant accelerating force is as the 
Square of the last acquired velocity. Consequently the last ac- 
quired Velocity, or V in the formula (h), must vary as the square 
ot of the space traversed ; and because if the fluid is generated 
at one end of the discharging vessel, and discharged at the other, 
the space it will have to traverse after motion commences and 
*lore it attains the velocity V will be the length of the dischar- 
80g vessel, therefore V in the formula ( h) must vary as the 
“Ware root of the length of the discharging vessel. Now be- 
,  Y Cannot, at the same time, vary both as the length and as 
the Square root of the length of the discharging vessel, therefore 
We cannot restrict ¢ to unity in the formula (h). And conse- 
