OF FLUIDS ON THE MOTION OF PENDULUMS. [93] 



arcs is 0.424, and this divided by the total interval gives 0.1005 for the difference of logarithms 

 for one hour. The second experiment, treated in a similar way, gives 0352, which expresses 

 the effect of friction at the point of support, communication of motion to the support itself, 

 &c, together with the resistance of highly rarefied air at a pressure of only O.97 inch of mer- 

 cury. Since we have reason to believe that p' is independent of the density, we may get the 

 effect of air at a pressure of 30.24 - O.97 or 29.27 inches of mercury by subtracting 0.0352 from 

 0.1005, which gives 0.0653. Reducing to 29 inches of mercury for convenience of comparison, 

 we get O.0649. Each pair of experiments is to be treated in the same way. Since the tempe- 

 rature was nearly the same in the experiments made with the same pendulum, we may suppose 

 it constant, and equal to the mean of the temperatures in the experiments made under the 

 full atmospheric pressure. The experiments reduced consist of four pair for each pendulum, 

 except No. 21, for which only two pair were performed. The following are the results. For 

 the ll-inch platina sphere 0.0644, mean error 0.0044. For the 1^-inch brass sphere 0.180, 

 mean error 0.024. For the 2-inch brass sphere O.O94, mean error 0.013. For the copper rod 

 0.486, mean error 0.113. For the brass tube the results were 0.145, 0.363, 0.338, 0.305. 

 Rejecting the first result as anomalous, and taking the mean of the others, we get 0.335, mean 

 error 0.030. To obtain I from the mean results above given we have only to divide by 3600 

 times the modulus, and multiply by t, and for the experiments with spheres we may suppose 

 t = 1. 



The mode of calculating I from theory in the case of a sphere suspended by a fine wire 

 has already been explained. For the sake of exhibiting separately the effect of the wire, I will 

 give one intermediate step in the calculation. 



1.44 inch sphere. 



k', for sphere alone 0.326 



Ak', the correction for the wire... 0.130 



Total, to be substituted in (169).. 0.456 0.450 0.265 



The formula (168), which applies to a sphere suspended by a wire, will be applicable to a 

 long cylindrical rod if we suppose M = 0. Hence the same formula (169) that has been used 

 for a sphere may be applied to a cylindrical rod if we suppose k' to refer to the rod. For the 

 copper rod k'= 1.107, and for the tube k'= 0.2561. The following are the results for the three 

 spheres and two cylinders. 



No. 1. 

 10000001, from experiment... 41 

 from theory 39 



Difference +2 +9 +78 +50 



It appears that the experiments with spheres are satisfied almost exactly. The differences 

 between the results of theory and observation are much larger in the case of the long cylinders. 

 Large as these differences appear, they are hardly beyond the limits of errors of observation, 

 though they would probably be far beyond the limits of errors of observation in a set of 

 experiments performed on purpose to investigate the decrement of the arc of vibration. It 



