specific Gravity, and comparative Wear of Gold. 145 
of the windlass. A counter is placed so as to show the number 
of revolutions of the windlass. 
If the two frames had performed their vibrations in the same 
time, no advantage would have been gained, for the pieces of 
coin would still have moved upon each other always in the same 
e b f line ; but, as their vibrations are per- 
formed in different times, the effect 
is quite different ; for, let C, in the 
annexed figure, be the centre of one 
of the pieces in the lower frame. 
Draw the lines B b and D d in the di- 
rections of the motion of the lower and 
upper frame, and equal to the space 
which those frames describe in one 
semi-revolution of the cranks, and complete the square of ef EF„ 
Then, if the upper frame is moving with its greatest velocity in the 
direction D d, at the same time that the lower one is moving with 
its greatest velocity in the direction B b, the motion of the upper 
piece on the lower one will be in the diagonal / F ; but if, at that 
time, the lower frame is moving with its greatest velocity in the 
contrary direction bB, the motion will be in the other diagonal E^e. 
If one frame is moving with its greatest velocity, while the 
other is at the extremity of its vibration, the motion will be in 
the circumference of the circle bDB d, inscribed within the 
square ; and, in the intermediate cases, it will be in the circum- 
ference of an ellipsis, which is inscribed in the same square, and 
whose axes are in the diagonals eE and /F, but in which the 
proportion of the axes is continually changing; that axis which 
is placed in F f being sometimes the greatest, and at other times 
the least. 
MDCCCIII. 
U 
