OF FLUIDS ON THE MOTION OF PENDULUMS. [81] 



and therefore it experiences a greater resistance than if it had started from the same position 

 with the fluid at rest. In fact, it appears from the expression for G in Art. 8, that the 

 moment of the resistance vanishes, in passing from negative to positive, not when the disk has 

 reached the end of its excursion in the positive direction, but the eighth part of a period 

 earlier. Hence, had the observation commenced during a series of oscillations, a larger initial 

 arc would have been necessary, to overcome the greater resistance, in order to produce, after a 

 given number of oscillations, the same final arc as that actually observed. I have investigated 

 the correction to be applied on account of this cause, and find it to be about + 0.009, but I 

 must refer to a note for the demonstration, in order not to interrupt the present discussion*. 

 I shall assume then, in the following comparisons, that for water 



yV = 0.0564, 



the units being the same as before, namely, an English inch and a second. That y! is inde- 

 pendent of the pressure of the fluid, or at least very nearly so, appears from an experiment of 

 Coulomb's, in which it was found that the decrement of the arc of oscillation of a disk oscil- 

 lating in water was the same in an exhausted receiver as under the full atmospheric pressure. 



I will here mention another experiment of Coulomb's which bears directly on one part of 

 the theory. On covering the disk with a thin coating of tallow, the resistance was found to 

 be the same as before ; and even when the tallow was sprinkled with powdered sandstone, by 

 means of a sieve, the increase of resistance was barely sensible. This strikingly confirms the 

 correctness of the equations of condition assumed to hold good at the surface of a solid. 



66. I will now compare the formula (148) with the results obtained by Bessel for the 

 oscillations of the brass sphere in water, which will be found at page 65 of his memoir. This 

 sphere was suspended so as to be immersed in the water contained in a large vessel, and was 

 swung with two different lengths of wire, the same as those employed for the experiments in 

 air. The times of oscillation were 1-9085 second for the long pendulum, and 1-1078 for the 

 short. The results are 



Long pendulum. Short pendulum. 



k, by experiment 0-648 0-602 



k, by theory 0-631 0-600 



difference + 0-017 + 0-002 



The depth to which the spheres were immersed is not stated, but it was probably sufficient to 

 render the effect of the free surface small, if not insensible. The vessel was three feet in 

 diameter, and the water 10 inches deep, so that unless the spheres were suspended near the 

 bottom, which is not likely to have been the case, the effect of the limitation of the fluid by 

 the sides of the vessel must have been but trifling. The agreement of theory and observation, 

 as will be seen, is very close. 



67. In the same memoir which contains the experiments on disks, Coulomb has given 

 the results of some experiments in which the disk immersed in the fluid was replaced by a 



• (Am Note B at the end.) 



Vol. IX. Paet II. 35 



