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



satisfy them both. The numbers in the last column of the preceding table are, however, 

 far too regular to be attributable to mere fortuitous errors of observation. If we suppose 

 Bessel's results to have been nearly exact, there must have been something in the mode either 

 of making or of reducing Dubuat's experiments which caused a tendency to error in one 

 direction. 



With respect to the reduction of the experiments it may be observed that the length I was 

 measured from the centre of oscillation, whereas in the formula (148) it is supposed that the mass 

 of which the weight is IcP or (tl — 1) P is collected at the centre of the sphere. If h be the 

 distance of the centre of the sphere from the axis of suspension, the observed value of 11 - 1 

 ought in strictness to be increased in the ratio of h? to I 8 , or the calculated value diminished in 

 the ratio of P to h 2 , before comparing the results of theory and experiment. In the case of 

 the loaded spheres especially, the theoretical value of II would thus be a little diminished ; but 

 except in a very few cases, in which either I or a — I is small, the diminution is hardly worth 

 considering. After having been for a good while at a loss to account for the regular occur- 

 rence of rather large negative errors, the following occurred to me as the probable solution 

 of the difficulty. 



When a pendulum oscillates in water, the arc of oscillation rapidly decreases ; this rapid 

 diminution forms in fact the grand difficulty in experiments of this kind. In Dubuat's experi- 

 ments, it will be remembered, the suspending thread was lengthened or shortened till the time of 

 oscillation was an exact number of seconds, or occasionally half a second. Now, it is probable 

 that the observer occasionally gave the suspending thread a slight push as the pendulum was 

 commencing its return, in order to keep the oscillations going for a sufficient time to allow of 

 tolerable precision in rendering the time of oscillation equal to what it ought to be. If so, 

 these pushes would slightly accelerate the oscillations, and therefore cause the length of thread 

 fixed on by observation to be a little too great, which would make the effect of the water in 

 retarding the oscillations appear a little too small. On inspecting the table of differences, 

 it may be observed that sometimes when the same sphere differently loaded is swung in the same 

 time as before, the numbers in the table of differences are altered more than appears to be 

 attributable to merely fortuitous errors of observation. This accords very well with the con- 

 jecture just mentioned, and seems difficult to account for in any other way, inasmuch as 

 everything relating to the fluid must have been almost exactly the same in the two 

 cases. 



The occurrences of positive differences in the case of the large wooden sphere may be 

 accounted for by the limitation of the fluid mass by the sides and bottom of the vessel, and by 

 the free surface, which, except in the case of very short oscillations, would have much the same 

 effect as a rigid plane, inasmuch as it would be preserved almost exactly horizontal by the 

 action of gravity. The vessel which contained the water was 51 inches long and 17 broad, 

 the water was 14 inches deep, and the spheres were plunged to about 3 inches below the 

 surface, so that the effect of the confinement of the fluid mass would have been quite sensible 

 in the case of such large spheres. If it be objected that the same sphere gave negative differ- 

 ences in the case of the first group of experiments, it must be observed, that when the appa- 

 rent weight of so large a sphere was only 2102 French grains, the resistance would quickly 



