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



the pendulum as a solid rod. The tube was furnished with six agate planes, represented in 

 the wood-cut at page 417, which rested on fixed knife-edges. The pendulums Nos. 35, 36, 

 37, and 38 consisted of the same tube swung on the planes marked A, C, a, c. In air the pen- 

 dulum swung at the rate of about 90080 vibrations in a day, so that t = 0-9596 nearly. 

 The values of tl obtained with the end planes A, c were slightly though sensibly greater than 

 the values obtained with the mean planes C, a. I shall suppose the mean of the four values 

 of tt, namely 2*290, to be the result of the experiments. In the following table the difference 

 between the theoretical and experimental values of n is exhibited both by decimals and as a 

 fractional part of the former of these values. 



Baily's results with a long brass tube and with long cylindrical rods. 



It will be seen at once how closely the experiments are represented by theory. The 

 largest proportionate difference occurs in the case of the brass tube, and even that is less than 

 one thirtieth. A glance at Baily's wood-cut at page 417 will shew that the six planes with which 

 the tube was furnished caused the whole figure to deviate sensibly from the cylindrical form. 

 Moreover the resistance experienced by each element of the cylinder has been calculated by 

 supposing the element in question to belong to an infinite cylinder oscillating with the same 

 linear velocity, and the resistance thus determined must be a little too great in the immediate 

 neighbourhood of the ends of the cylinder, where the free motion of the air is less impeded 

 than it would be if the cylinder were prolonged. Lastly, the correction for confined space is 

 calculated according to the ordinary equations of hydrodynamics, and on that account, as well 

 as on account of the abrupt termination of the cylinder, will be only approximate. The small 

 discrepancy between theory and observation, as well as the small difference (amounting to 

 about the 1-83 rd of the whole) detected by experiment between the results obtained with the 

 extreme planes and those obtained with the mean planes, may reasonably be attributed to some 

 such causes as those just mentioned. In the case of the steel rod or wire, the difference be- 

 tween theory and observation may be altogether removed by supposing a very small error to 

 have existed in the measurement of the diameter of the rod. Since, as we have seen, the observa- 

 tion is satisfied by TO = 0-2822, and (147) gives a cc ttl when // and t are constant, it is suffi- 

 cient, in order to satisfy the experiment, to increase the diameter of the rod in the ratio of 

 0-2759 to 0-2822, or to suppose an error of only 0.0017 inch in defect to have existed in the 

 measurement of the diameter. 



57. I proceed next to the experiments on spheres attached to fine wires. The pendu- 

 lums of this construction comprise four 1^-inch spheres, Nos. 1, 2, 3, and 4; three 2-inch 



