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



pendulum, we may suppose I + a = \, and replace P (I + a)~ 2 by 1 - 2aX~\ since a is small 

 compared with X. We thus get, putting AH for the correction due to the wire, 



A^i^l-X)^ 



Substituting for A;,- 1 from (115), and for tn from (147), in which equations, however, At,, 

 a, must be supposed to be written for k, a, expressing V lt V in terms of the diameters of the 

 wire and sphere, and neglecting as before a 2 in comparison with X 2 , we get 



(2X - S x %a) ix t 



Att= 7 TTTn ' (151) 



where 



- L m log, — V— - 0-5772 (152) 



2a t 7r 



It is by these formula? that I have computed the correction for the wire in the following 

 table. In the experiments, the time of oscillation was so nearly one second that it is sufficient 

 in the formulae (148), (151), and (152) to put t = 1, and take \ for the length of the seconds 

 pendulum, or 39 - 14 inches. 



With respect to the correction for confined space, it seems evident that the vacuum tube 

 must have impeded the free motion of the air, and consequently increased the resistance experi- 

 enced by the pendulum when it was swung in air, and that the increase of resistance caused by 

 the cylindrical tube must have been somewhat less than that which would have been produced 

 by a spherical envelope of the same radius surrounding the sphere. The effect of a spherical 

 envelope has been investigated in Section II., Part I. ; but as we are obliged at last to have 

 recourse to estimation, it is needless to be very precise in calculating the increase of resistance 

 due to such an envelope, and we may accordingly employ the expression obtained from the 

 ordinary theory of hydrodynamics. According to this theory, the increase of the factor k, which 

 is due to the envelope, is equal to || a 3 (b 3 - a 3 ) -1 , or & a 3 b~ 3 nearly, when b is large compared 

 with a. The increase due to a cylindrical envelope whose axis is vertical, and consequently 

 perpendicular to the direction of oscillation of the sphere, may be estimated at about two-thirds 

 of the increase due to a spherical envelope of the same diameter. I have accordingly taken 

 + a 3 b~ 3 for the correction for confined space, and have supposed 26 = 6-5 inches. 



The diameter of the wire employed in the pendulums Nos. 1, 2, 3, 5, 6, and 7, is stated to 

 have been about the ^th of an inch, and that of the wire employed with the heavy brass sphere 

 No. 66, about 0-023 inch. The ivory sphere No. 4 was swung with a fine wire weighing 

 rather more than half a grain. Taking the weight at half a grain, and the specific gravity of 

 silver at 105, we have for this wire 2a,= 0-00251 nearly. The diameters of the three brass 

 spheres in the following table are taken from page 447 of Baily's memoir. The several parts of 

 which, according to theory, tt is composed, are exhibited separately. 



