MEAN DENSITY OF THE EARTH. 643 



of the amplitude is owiug: to unsteiuliiioss which was caused by the 

 change of the weights, and therefore iiitluences the tirst reading of e;»ch 

 series. But it is not easy to see how the disturbance, which was so regu- 

 h>r, can be exphiined in this manner. esi)ecially since Baily has ex- 

 pressly referred to the perfect isolation of tlie masses, and their easy 

 motions free from jar. He did not explain with equal clearness the way 

 in which he obviated such disturbances as might arise from change of 

 temperature, disturbances wliich, at the beginning of his observations, 

 caused serious difficulties. The supposition of a difference of temper- 

 ature, scarcely shown by a thermometer, between the masses and the 

 balance inclosed in a thick box seems justified, and such differences 

 are snfficient to explain the distnrbances of a system swinging with 

 such a slight inertia. They would be analogous to the irregularities 

 which have been observed in these experiments to exist between the 

 temperature of the two sules of the pendulum-rod and which were in 

 direct dependence upon the algebraic sign of the motion of the zero 

 point from the source of heat. The disturbances which showed them- 

 selves in Baily's series of observations were regarded as a change of 

 sign in the course of the zero point, which produced such an eliect that 

 the observed deflection grew regularly with the time since the transfer 

 of the weights to their new position. The plan of computing the posi- 

 tion of equilibrium from the last three numbers of each series, a method 

 which leads to a much smaller value, was set aside by Cornu and 

 Bailie for one which will increase the error in the reduction of Bail\'s 

 work. It would have been too much to expect for this reason a smaller 

 value for the mean density of the earth from Baily's observations than 

 would have resulted from the avoidance of this error, a remark intensi- 

 fled by the deviation of his result from those deduced by others from 

 the torsion balance. Unfortunately it is not possible to reach from the 

 observations any conclusion regarding the two opposing hypotheses, 

 since no readings are given of a long series without changing the 

 weights. 



The observations here given have shown that the pendulum is a most 

 excellent instrument for the determination of gravity, a problem which 

 for a time it did not seem competent to solve. It is to be hoped that 

 its somewhat restricted domain may be extended. In this connection 

 there may be mentioned the determining of inner friction, a matter of 

 great importance in the mechanical theory of gas. Since the resist- 

 ance of the air in the case of a sensitive pendulum causes a rapid de- 

 crease in the amplitude of the arc, the amount of retardation is so con- 

 siderable that an accurate determination of the desired quantity can 

 best be secuied from a few observations. The results might be modi- 

 iied by an ai)preciable change in the sensitiveness, atmospheric press- 

 ure, or temperature. Stokes has discussed the case in which an infin- 

 itely long cylindrical rod oscillates so that its axis remains parallel. 

 The solution of this is closely related to that of a rod swinging about 



