[80] PROFESSOR STOKES, ON THE EFFECT OF THE INTERNAL FRICTION 



divide the sum of the products by 510 + 152 + 77 or 739, we get 0.05551. We may then take 

 0.555 as the result of the experiments. Assuming \Z/j.'= 0.0555 we have 



log (1 - rn)~ l from experiment 0.0568 in No. 1, 0.021 in No. 2, 0.0135 in No. 3, 

 from theory 0.0571 0.0206 0.0137 



difference - 0.0003 + 0.0004 - 0.0002 



65. So far the accordance of the theoretical and observed results is no very searching test 

 of the truth of the theory. For, in fact, the theory is involved in the result only so far as 

 this, that it shews that the resistance experienced by a given small element of a disk oscillating 

 in a given period varies as the linear velocity ; since the difference of periods in Coulomb's 

 experiments was so small that the effects thence arising would be mixed up with errors of 

 observation. This law is so simple that it might very well result from theories differing in 

 some essential particulars from the theory of this paper. But should the numerical value of 

 \Zfi determined by Coulomb's experiments on disks be found to give results in accordance 

 with theory in totally different cases, then the theory will receive a striking confirmation. 

 Before proceeding to the discussion of other experiments, there are one or two minute 

 corrections to be applied to the value of /y/ju.' given above, which it will be convenient to 

 consider. 



In the first place, the result obtained in Art. 8 is only approximate, the approximation 

 depending upon the circumstance that the diameter of the revolving body is large compared 

 with a certain line determined by the values of p and t. In the particular case in which the 

 revolving solid is a circular disk, it happens that the approximate solution satisfies the general 

 equations exactly, except so far as relates to the abrupt termination of the disk at its 

 edge*. In consequence of this abrupt termination, the fluid annuli in the immediate 

 neighbourhood of the edge are more retarded by the action of the surrounding fluid than they 

 would have been were the disk continued, and consequently the resistance experienced by the 

 disk in the immediate neighbourhood of its edge is actually a little greater than that given by 

 the formula. I have not investigated the correction due to this cause, but it would doubtless 

 be very small. 



In the second place, the formula (15) is adapted to an indefinite succession of oscillations, 

 whereas Coulomb did not turn the disk through an angle greater than the largest intended 

 to be observed, and suffer one or two oscillations to pass before the observation commenced, 

 but took for the initial arc that at which the disk had been set by the hand. Probably the 

 disk was held in this position for a short time, so that the fluid came nearly to rest. If so, 

 the resulting value of -y/V, as may readily be shewn, would be a little too small. For in the 

 course of an indefinite series of oscillations, the disk, in its forward motion, carries a certain 

 quantity of fluid with it, and this fluid, in consequence of its inertia, tends to preserve its 

 motion. Hence, when the disk, having attained its maximum displacement in the positive 

 direction, begins to return, it finds the fluid moving in such a manner as to oppose its return, 



• (See Note A at the end.) 



