MEAN DENSITY OF THE EARTH. G39 



exceptions, separated from one another by a complete double swing. 

 The observations were repeated, so as to have two or three sets of four 

 readings for each day. The arc of oscillation gradually decreased to a 

 fixed limit, since the series were so arranged that the transfer of the 

 weights could be made to follow that phase of oscillation in which the 

 change in the directiou of the force causes a retardation of its motion. 

 The amplitude of the arc was between three degrees and a few minutes, 

 with about 45' as an average. 



With the determination of the position of equilibrium that of the du- 

 ration of the oscillation is closely allied. The time of the transit of a 

 division of the scale over the wire of the telescope could be estimated 

 within 0.1 second. These transits were usually observed on three divis- 

 ions. If the times of transits of the same phase were observed, the dif- 

 ference would give an approximate value for the time of a double oscilla- 

 tion ; which, however, must be corrected for the decreased arc owing to 

 the resistance of the air. 



For the reduction of the observations there is still needed a deter- 

 mination of the sensitiveness of the pendulum. This is also found from 

 the period of oscillation, by changing the position of tlie supplemental 

 weights attached to the upper end of the pendulum. Each observed 

 period in combination with the normal period gave the moment of in- 

 ertia and the distance of the center of gravity from the knife-edge. 



In all the observations a chronometer giving stellar time was used, and 

 was compared both before and after each series with the standard clock 

 of the observatory. Barometric readings were made, as well as those 

 for temperature, which were taken from thermometers placed in various 

 parts of the room. 



Laplace noticed, and Bessel proved by experiments, that the shape of 

 the knife-edge supporting a ])endulnm exerted an appreciable effect 

 upon the period of oscillation and the diminution in the amplitude. 

 Since this period furnislies an important element in all reductions, it 

 was necessary to investigate the effect of the dulling of the knife-edge. 

 At the same time the resistance of the air and its resulting interference 

 were investigated. 



The computation of the moment of inertia was divided into parts, 

 taking up first the moment for the mean position of the instrument as 

 previously determined, using in this connection the moment of a mate- 

 rial line coincident with the axis of the pendulum rod and perpendicu- 

 lar to the line joining the centers of the attracting masses. The at- 

 traction of the masses is : 



27tfm g 6{ V{a-hf+W- V(^-\-hy^W-^2h) 

 in which mg is the weight of the ball,/ a constant, 6, 2/t, and R the 

 specific gravity, height, and radius of the cylinder, and a the distance 

 of the middle point of the ball to the center of the cylinder. If I is the 

 distance of the center of the ball from the knife-edge, the moment will be : 



