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



63. We have next to investigate the correction for the wire. The effect of the inertia of 

 the air set in motion by the wire was altogether neglected by Bessel, and indeed it would have 

 been quite insensible had the parts of the correction for inertia due to the wire and to the 

 sphere, respectively, been to each other in nearly the same ratio as the parts of the correction 

 for buoyancy. Baily, however, was led to conclude from his experiments that the effect of the 

 wire was probably not altogether insignificant, and the theory of this paper leads, as we 

 have seen, to the result that the factor It is very large in the case of a very fine wire. 



The ivory sphere in Bessel's experiments was swung with a finer wire than the brass 

 sphere. It was for this reason that I did not from the first suppose k\=k l and k' 2 = k 2 . 

 Let Ak, A&j &c. be the corrections due to the wire. The values of Ak ly Ak 2 , Ak\, Ak\, 

 may be got from the formula (151), in which it is to be remembered that \ denotes the length 

 of the isochronous simple pendulum, not, as in Bessel's notation, the length of the seconds' pen- 

 dulum. It is stated by Bessel (p. 131), that the wire used with the brass sphere weighed 10Q5 

 Prussian grains in the case of the long pendulum, and 3-58 grains in the case of the short. 

 This gives 7*37 grains for the weight of one toise or 72 French inches. The weight of one 

 toise of the wire employed with the ivory sphere was 6-28 — 204 or 4-24 grains (p. 141). The 

 specific gravity of the wire was 7'6 (p. 40), and the weight of a cubic line (French) of water is 

 about 0-1885 grain. From these data it results that the radii of the wires were 0-003867 and 

 0-002933 inch English. The formula (147) gives TO, whence L is known from (152). The 

 lengths of the isochronous simple pendulums were about 39'20 inches for the short pendulum, 

 and 116-94 for the long. On substituting the numerical values we get from (151), since 

 *i = n> ~ 1 an ^ *2 = tl 2 - 1, 



A&! = 0-0107, Ak 2 = 0-0286, Ak\= 0-0090, Ak\= 0-0244. 



The specific gravities of the two spheres were about 8190 and 1*794, whence we get from 

 (159) Ak = 0-0308, or 0-031 nearly. 



The value of k deduced by Bessel from his experiments was 0-9459 or 0-946 nearly, which 

 in a subsequent paper he increased to 0-956. In this paper he contemplates the possibility of 

 its being different in the cases of the long and of the short pendulum, and remarks with justice 

 that no sensible error would thence result in the length of the seconds' pendulum, as deter- 

 mined by his method, but that the factor k would belong to the system of the two 

 pendulums. 



The following is the result of the comparison of theory and experiment in the case of 

 Bessel's experiments on the oscillations of spheres in air. 



Value of k belonging to the system of a long and a short pendulum, as 



determined experimentally by Bessel 0-956 



Value deduced from theory, including the correction for the wire, but 



not the correction for confined space 0-817 



difference + 0-139 



I cannot find that Bessel has stated exactly the distance of the centre of the sphere 

 from the back of the frame within which it was swung, but if we may judge by the sketch of 



