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



have been obliged to calculate the time of oscillation from the ordinary formulae of dynamics, 

 but the results will no doubt be accurate enough for the purpose required. In all the calcu- 

 lations I have supposed the rod to reach up to the axis of suspension, and have conse- 

 quently added 1*55 inch (the length of the shank of the knife-edge apparatus) to the length of 

 the rod, and have added to the weight of the rod a quantity bearing to the whole weight the 

 ratio of T55 inch to the whole length. 



In the case of the spheres attached to the ends of the rods (sets 14 and 16) the process of 

 calculation is as follows. Let I be the length of the rod increased by 1*55 inch, W, its weight, 

 increased as above explained, a the radius and W the weight of the sphere, X the length of the 

 isochronous simple pendulum. Then supposing the masses of the rod and sphere to be respec- 

 tively distributed along the axis, and collected at the centre, which will be quite accurate 

 enough for the present purpose, and putting a for the ratio of a to I, we have by the ordinary 

 formula 



X - iWl + (l + a)W l > (153) 



whence t, the time of vibration, is known. The formula (148) then gives k, which applies to 

 the sphere, and (147) gives HI, the a in this formula being the radius of the rod, from whence 

 k u which applies to the rod, may be got by interpolation from the table in Part I. Let Ah, 

 A&i be the corrections which must be applied to k, k x on account of the confined space of the 

 vacuum apparatus, and let S u S be the specific gravities of the rod and sphere respectively ; 

 then we get by means of the formulae (149), (150) 



The first of the two factors connected by the sign x in this equation is equal to a~ x I 'I~ l , 

 and if we want to calculate the weight of air which we must conceive attached to the centre 

 of gyration of the pendulum in order to allow for the inertia of the air, we have only to mul- 

 tiply the factor just mentioned by a and by the weight of the whole pendulum. The follow- 

 ing table contains the comparison of theory and experiment in the case of the 14th set. The 

 rods here mentioned are the same as those which composed the pendulums Nos. 21, 43, and 

 44, and the spheres are the three brass spheres of Nos. 3, 5, and 66. It appears from p. 432 

 of Baily's paper that his results are all reduced to a standard pressure and temperature, on 

 the supposition that the effect of the air on the time of vibration is proportional to its density. 

 The theory of the present paper shews that this will only be the case if p! be constant, which 

 however there is reason for supposing it to be when the pressure alone varies. Be that as it 

 may, no material error can be produced by reducing the observations in this way, because the 

 difference of density in any pair of experiments did not much differ from the density of air 

 at the standard pressure and temperature. The standard pressure and temperature taken 

 were 29*9218 inches of mercury and 32° F, and the assumed specific gravity of air at this pres- 



