suspended from two points. 417 
initial values of x and y, and the velocities of projection in directions 
' of those axes. The general expressions of the velocities are 2 mr =, 
which by means of the equations (B) become 
dx 
_  G=— a sine (at+e) 
4 (C) 
= =— ab sine (dt+c’) 
If we therefore suppose the value of x, y at the commencement of the 
motion to be ¢, e’, we shall from the equations (B) have e=) cosine c, 
e’=/' cosine c’; and if the velocities in directions a, y, be at that time 
v, and v’, the equations (C) will become v=—ad sine c, and v’=—a’b 
sine ¢. From these we deduce 
VV 
b=,/ee+ oA 
, fo vy! 
b =e d Ba re 
(D) 
v 
Tang. ore? 
Tang. « ¢e ae 
which determine the constant quantities. 
The commencement of the time ¢ being arbitrary, we may, by 
taking it at that point of any revolution where y=0', reduce the con- 
stant c’ too. For in this case the second of the equations (B) be- 
comes 4'=0' cosine (at+c), or 1= cosine (a’é+c’), and, as =O, we 
may take e’=0, and then the expressions of x, y will become. 
a = 6 cosine (at+c) a 
y = 6 cosine at ), 
which may be omnia equally general as the equations (B). _ 
