CHAP, iv.] APPLICATIONS OF THE LAWS OF HEAT. 371 



the elongations produced by the dilatation of the bars of steel tend 

 to lower the centre of oscillation, while that of the brass in an upward 

 direction tends, on the contrary, to raise it. The centre bar, which 

 is made of steel, is the one which supports the bob, and it passes 

 through holes in the cross pieces so as to be independent of them. 

 The suspending rod is, on the other hand, fixed to the topmost piece 

 which joins the outer bars. The lengths of these pairs of bars must 

 be calculated from the coefficients of expansion of steel and brass in 

 order that the lengthening due to the steel may be exactly equal to 

 that due to the brass. 



This affords only an approximate compensation, because the 

 centre of oscillation of a compound pendulum does not coincide either 

 with the centre of gravity of the bob,, or with that of the whole 

 apparatus. This compensation has therefore to receive its final 

 adjustment by means of experiment. 



Leroy's compensation pendulum (Fig. 254) consists of a brass 

 tube fixed over a bevelled opening, giving passage to a steel rod, 

 which is fixed within the upper end of the tube. This steel rod is 

 in two parts, joined by a thin spring of the same metal, which is 

 flexible at the top of the slit. The distance of this slit from the 

 centre of oscillation gives the true length of the pendulum, the 

 former being the true point of suspension. The method is not a good 

 one, for if the slit is wide enough to allow the spring to slide freely, it 

 is not close enough for accurate time-keeping. 



When expansion takes place, the tube of brass rises, and the 

 centre of oscillation follows the motion. On the other hand, the 

 rod tends to descend, and the proper dimensions of the different 

 parts may be easily calculated, so that there shall be compensation. 

 This is rendered more complete by the same means as that adopted 

 in the gridiron pendulum, and in all the other compensating systems, 

 that is by trial. 



We will notice two more systems besides these : Ellicot's plan, 

 which is represented in Fig. 256, and Graham's, which was the first 

 adopted (Fig. 255). 



In the first of these, the iron rod /, which supports the bob, is 

 furnished at the upper end with a cross-bar, to which are joined two 

 brass rods c, c, dilating freely at their lower ends and supported upon 

 two -levers a, a, fixed to the bob. These levers act upon the bob by 



B B 2 



