1888 - 89 .] Dr Sang on Air’s Resistance to Oscillating Bodies. 187 
no resistance. The diminution of the space compensates for that of 
the distance ; hut this compensation is not equally distributed. 
Thus, in the quarter of the time of an oscillation, the position is 
got by making at = 90°, which gives 
X" = +1/JX 2 , 
so that the distance passed over has been 
X- IjSX*. 
whereas the distance described in the second quarter of the oscilla- 
tion is only X - ^-/?X 2 
In order to get the actual effect on the clock above mentioned, we 
observe that, since the half oscillation is performed in one second, 
we must have a = T. Xow the extreme distance is 1*3, wherefore 
the greatest incitement to motion is l‘3x7r 2 . But the maximum 
velocity is 1*3 x t, and the maximum air’s resistance /3 x 1*3 2 x 7r 2 , 
so that 1 * 3 x 7J- 2 = 20000 x 1 • 3 2 x , whence £ = — i_. In 
26000 
this way we find the shortcoming at the end of a half oscillation to 
5 1 
he — /3 x 1 *3 2 = P ar ^ an i nc h> a quantity very small 
even in comparison with that due to the imperfect resistance of the 
suspending spring. 
In the case of the chronometer, the half oscillation is performed 
in the quarter of a second, wherefore a = At, and the effect is, there- 
fore, sixteen times as great as in the case of the clock, on this 
account alone ; but the ratio of disparity is only 2000 ; wherefore we 
must augment the above computed shortcoming 160 times, giving 
the 115th part of an inch. 
These two examples may serve to give a general idea of the 
magnitude of the disturbance due to the air’s resistance. In neither 
case is the time of the oscillation changed; in clock-work the ex- 
tent of the arc is slightly lessened, so slightly that the diminution 
is scarcely worthy of attention. In watch-work it is so considerable 
as to require perceptible greater maintaining force. 
