MECHANICS. 29 
The machine consists of a post, F, about 7 feet high, with its base, S, 
capable of being rendered perfectly vertical by the four adjusting screws ; 
on its upper end there is a frame, T, carrying the proper apparatus. ‘This 
apparatus consists of a wheel, K, united to the axis by the spokes, a, }, e, d, 
and over which runs a string to which hang the weights, A and B. Each 
end of the axis rests in the angle of two overlapping friction wheels, L, M, 
and N, O, so that the friction wheels taking part in the motion of the main 
axis, reduce the friction to its minimum. A divided scale, G, is fastened to 
the foot by the clamp, R, and upon this scale the two shifting platforms, H 
and C, may be fastened at pleasure by screws. The clock, D, attached to 
the post, F’, indicates seconds, thus serving as a measure of the times of 
falling. 
As the weights, A and B, are perfectly equal, they will be in equilibrium 
when attached to the two ends of the string passing over the wheel, K. 
This equilibrium will, however, be disturbed when an extra weight, 7, is laid 
upon one of them, the heavier weight falling, and the lighter rising with 
accelerated velocity. As the motion of the two weights is entirely the re- 
sult of the extra weight laid upon the one, it takes place slower than in a 
freely falling body, and this retardation of velocity is in the same proportion 
which the extra weight, or the difference of the two weights, bears to their 
sum; it takes place, however, as to the rest, according to the laws of freely 
falling bodies. Thus, if m indicate each one of the originally equal weights, 
and 2 the superimposed extra weight, then the velocity and the space fallen 
- of the velocity and 
m+n 
the interval of time, which takes place in the same time in a free fall. If, 
for example, m= '7oz., and n=1loz., then the space traversed in the first 
second is only 1 foot, that in the second, 2 feet, in the third, 3, &c.; and by 
diminishing z in proportion to m, the motion may be rendered as slow as 
may be desired. To measure the space fallen ihrough, the scale, G, is 
divided off into fractions of inches; the two platforms may be attached to 
any part of the scale, and of these the upper has a hole large enough to 
allow the passage of one weight after the removal of the small bar, I. If 
through for any given interval of time, is only 5 
the extra weight, n, be so adjusted that Yel Rb sige sil or more precisely, 
2m+n 180 
that the space fallen through in one second shall be equal to one inch; if 
furthermore it be so arranged as to pass through the upper platform, and if 
the lower one be placed successively at a distance of 1, 4, 9, 16, 25, 36, 49, 
64 inches below the 0 of the scale, then the weight will be heard to strike 
this lower platform after successive intervals of 2, 3, 4, 5, 6, '7, 8 seconds, 
agreeably to the theory. If again the extra weight be so adjusted as not to 
pass through the upper shifter, then the descending weight, from the mo- 
ment of separation from the extra weight, will continue its motion with an 
equable velocity. Furthermore, as in this case the accelerating force, 
namely. the extra weight, n, ceases to act, it will be found by placing the 
upper platform at a distance of 1, 4, 9, 16 inches beneath the zero point, and 
203 
