788 
DR. T. R. ROBINSON ON THE DETERMINATION OF 
motion. This weight, divided by four, is considered to represent the moment of 
friction at the centre of the cups after a correction for the increase of friction due 
to its own pressure. 
1. The normal friction f is larger than in ordinary instruments on account of the 
long shaft, its horizontal position, and the weight of the brake apparatus : “ with the 
disc in place the moving parts weigh 282 oz. The measurements at Rathmines gave 
values from 100 to 120 grains; but I adopt one which I obtained at Armagh by a 
better process : that used by Atwood in determining the constants of his celebrated 
machine. If a weight W be hung to the disc, W— f accelerates a mass W-|-M; 
M being the moment of inertia of the moving parts reduced to the circumference of 
the disc, and we have by the law of uniformly accelerated motion gx ( w + M / h’ 
S being the space through which W descends in the time T. We get S most easily 
by taking a given number of the disc’s revolutions. M was got by suspending the 
disc and its appendages in the sector tower of the Observatory with a bifilar sus- 
pension whose lines were 62 - 5 inches long and 3 '01 inches apart. A graduation fixed 
on the disc enabled me to note the arcs of vibration ; 300 complete vibrations were 
taken for each trial, and by the usual formula x 2 the square of the distance of the 
This x W 
centre of gyration was found. — w — gave by ten sets M=25,773'6 grains. Hence 
we get f far more consistently than in the former method.f I obtained 72 obser- 
vations with W from -fth of an oz. to ly oz., and divided them into three groups to 
see if f varied with the velocity. The first 24 gave /=114T8 ; v=l'33'. The second 
gave /==110'41 ; t’=2T3'. The third /=108'20 ; v=2'87. There is a decrease, but 
I think it is mere error of observation, for the effect of an error in noting the time 
acts inversely as T 3 ;j so I take the simple mean=110'93. To obtain from this the 
f for each of the anemometers, 2 lb. were hung on the axle, and ten observations gave 
* In its present position with its axes vertical the normal friction is only 22 grains, 
t As the rotation of the disc is liable to be disturbed at its commencement by any casual irregularity 
of the friction, it is better to reject this part and take two spaces immediately consecutive. In this case 
it is easily shown that g — £1 = '. ^ } or (if S' = S)=- * **^ - - — Both S and t are given by the 
W -f M tt tt (t-\-t) 
chronograph, of which, however, I could not then avail myself. This method has over that which I used 
at Rathmines the advantage of giving the friction during actual motion over a considerable space. If 
when the descent of W has given a rapid angular motion to the disc it he detached from it, the disc will 
continue to revolve till stopped by the friction. This is equivalent to supposing W = 0 in the equation; 
and if f be so small that it makes twenty or thirty revolutions, it is ascertained with great precision. It 
is much to be regretted that this process did not occur to me at Rathmines, for it would probably have 
very much improved my results. Had I then possessed my present knowledge, I would have made an 
arrangement to give the mean friction during each experiment, which could have been effected by a 
modification of the means (hereafter described) used to measure a alpha. 
X Some observations made with the anemometer’s axis vertical show that f does not change with v, at 
least within the limits of 29'6 and 7‘1 miles. 
