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



pieces of which a pendulum of complicated form is composed. Since the value of the factor n 

 and that of the weight of air are merely two different expressions for the result of the same 

 experiment, it would be sufficient to compare either with the result calculated from theory. 

 In some cases, however, I have computed both. In almost all the calculations I have employed 

 4-figure logarithms. The experimental result is sometimes exhibited to four figures, but no 

 reliance can be placed on the last. In fact, in the best observations, the mean error in different 

 determinations of tt for the same pendulum appears to have been about the one-hundredth 

 part of the whole, and that it should be so small, is a proof of the extreme care with which 

 the experiments must have been performed. 



55. I commence with the 13th set of experiments — Results with plain cylindrical rods 



page 441. This set contains three pendulums, each consisting of a long rod attached to a 

 knife-edge apparatus. The result obtained with each pendulum furnishes an equation for the 

 determination of #', and the theory is to be tested by the accordance or discordance of the 

 values so obtained. The principal steps of the calculation are contained in the following table. 



In this table the first column explains itself. The next contains the reference number. 

 In the case of the copper rod I have replaced 42 by 21, under which number the details of 

 the experiment will be found. The diameters of the rods are expressed in decimals of an 

 inch. The time of vibration of the pendulum No. 21 may be got from the tables at the end 

 of Baily's memoir, which contain the details of the experiments. Nos. 43 and 44 belong to the 

 " additional experiments," of which all the details are suppressed. Baily has not even given 

 the times of vibration, not having been aware of the circumstance, indicated by the theory of 

 this paper, that the factor tt and the weight of air which must be conceived as dragged by the 

 pendulum are functions of the time of vibration. Accordingly, in the cases of the pendulums 

 Nos. 43 and 44, and in all similar cases, 1 have calculated the time of vibration by the 

 ordinary formulae of dynamics. In calculating r, I have added I'M inch, the length of the 

 shank of the knife-edge apparatus, to the length of the rods. The result so obtained is 

 abundantly accurate enough for my purpose. Had the rod, retaining its actual length, been 

 supposed to begin directly at the knife-edge, the error thence resulting in the value of t, or 

 rather the correspoding error in the calculated value of tt or k, might just have been sensible. 

 The fifth column in the above table is copied from Baily's table. The next contains a small 

 correction necessary to reduce the value of tt got from observation to what would have been 

 got from observations made in an unlimited mass of fluid. It is calculated from the formula 



