88     ON THE  EFFECT OF THE INTERNAL  FRICTION  OF  FLUIDS
in this formula being the radius of the rod, from whence k_l9 which applies to the rod, may be got by interpolation from the table in Part I. Let Afc, A/^ be the corrections which must be applied to jfe, fc on account of the confined space of the vacuum apparatus, and let 8 , S be the specific gravities of the rod and sphere respectively ; then we get by means of the formulae (149), (150)
^n~^1==
, + (1 H- a)* W
_x»F_| _+ (l_+a)F......_(154)_
^Sl                  ^S
The first of the two factors connected by the sign x in this equation is equal to cr'^1 /' I~^1_9 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 multiply the factor just mentioned by cr and by the weight of the whole pendulum. The following 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 // 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 pressure arid temperature was the 1-770th of that of water, so that in the calculations from theory it is to be supposed that cr~^l = 770.
If w be the weight of the whole pendulum, w' that of the air which we must suppose attached to the pendulum at its centre of