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



would reduce itself to (177), or equal to Ba % . In the case of the long pendulum with 

 the brass sphere, the corrected value of A, deduced from the formula (177), was equal to 

 about 0.77 of the first approximate value. 



I have not considered it necessary to go through all Bessel's experiments, as it was 

 not to be expected that the formula should account for the whole observed decrement. I 

 have only taken four experiments for each kind of pendulum, namely, I. a, b, e, and / 

 for the long pendulum with the brass sphere ; I. c and d and II. c and d for the short 

 pendulum with the brass sphere; XII. a, b, c, and d for the long pendulum with the ivory 

 sphere, and XII. a, b\ c, and d" for the short pendulum with the ivory sphere. The 

 formula (177) gave the following results. First case, Log e. tA = .0000759; mean error 

 = .0000020. Second case, Log e. tA = . 0000504; mean error =.0000075. Third case, L,oge.A 

 = .000631; mean error = .000046. Fourth case, Loge . A = .000167; mean error = .000074. 

 Now |ari| and therefore, to get the values of I deduced from experiment, it will be 

 sufficient to divide the numbers above given by the modulus of the common system of 

 logarithms. The theoretical value of \ will be got from (169), if we add to k' the 

 correction Ak' depending upon the wire. The following are the results: 



long p. brass s. short p. brass s. long p. ivory s. short p. ivory s. 



1000000 I for sphere alone in an unlimited 



mass of fluid, by theory 67 50 298 222 



additional for wire 27 9 114 39 



94 59 412 261 



1000000 I by experiment 175 116 1453 384 



It appears then that the calculated rate of decrease of the arc amounts on the average 

 to about half the rate deduced from observation. This is about what we might have 

 expected, considering the various circumstances, all tending materially to augment the rate 

 of decrease, which were not taken into account in the calculation. 



77- Of Baily's pendulums I have compared the following with theory in regard to the 

 decrement of the arc of vibration. No. 1 (the 1 J-inch platina sphere), experiments 1 to 8 ; 

 No. 3 (the brass l^-inch sphere), experiments 9 to 16; No. 6 (the 2-inch brass sphere), experi- 

 ments 33 to 40 ; No. 21 (the 0.410 inch long copper cylindrical rod), experiments 109 to 112 ; 

 and No. 35 — 38 (the 1^-inch long brass tube), experiments 167 to 174. I have'not thought it 

 worth while to compute the results obtained with the other 1^-inch and 2-inch spheres, inas- 

 much as they were of the same size as the brass spheres, and moreover the observation of the 

 decrement of the arc was not the object Baily had in view in making the experiments. The 

 3-inch sphere, and all the other cylindrical rods and combinations of cylindrical rods and 

 spheres, belong to the " additional experiments'''' for which the arcs are not given. 



The mode of performing the calculation will best be explained by an example. Take, for 

 instance, the pair of experiments Nos. 1 and 2. In No. 1 the total interval was 4.22 hours, the 

 initial arc was 0°.77> the final arc 0°.29, the mean height of the barometer 30.24 inches, and the 

 temperature about 38^° F. The difference of the common logarithms of the initial and final 



