131 
Mysina - ^Mxsinai | 1 + 
; W 
The initial tension will be ^^ n ._ 
If the external end of the tape were attached to the con- 
tiguous coil so that it could not unroll, the tension at the 
fixed point would be M(/sina. If the fastening suddenly 
gave way, the tension would immediately alter and become 
only one third of its previous value. 
If we suppose the length of the tape to be infinite, then 
the velocity after describing any finite space will be 
v 
^sina.# 
If we suppose the motion to take place on a horizontal 
plane, the equation of motion changes; the differential 
equation now becomes 
d?x _ c / dx V _ q 
dP 2 ^y\dt) ~ 
A first integral of this equation will be 
rdx V _ A 
\dt) 7 rB?-CX 
( 1 ) 
To determine A, suppose the mass set in motion by a 
blow parallel to the plane so that the initial velocity is V, 
thus A = 7 tR 2 V 2 . 
Substituting, integrating again, and determining the con- 
stant, we have 
-iH'-e-m « 
To unwind the whole length of the tape, this equation 
would make the time to vary as the length directly and as 
the initial velocity inversely. 
Equation (1) may also be written 
