82 On Pendulums, 



three to five : then, if the expansion of one of the extreme 

 steel rods raises the top bar three degrees nearer the point 

 of suspension, the brass rod, which is joined to the steel 

 rod at the top, will remove the cross bar fixed to its lower 

 end, only two degrees from the same point. 



To investigate the ratio of the weights of these cross 

 pieces, that the centre of gravity of the pendulum may re- 

 main at the same distance from the point of suspension, 

 in all degrees of heat ; — Let CG represent an inflexible 

 lever, considered as without weight, kept in equilibrio upon 

 the fulcrum F, bv three weights, A, B, and W. And let 

 CF=.r, DF=y, and FG=z. 



C D F G 



B W 



Then per mechanics A x x •{• B x y =W x z f or Ax-\-By 

 =Wz. And supposing x and y to flow in contrary di- 

 rections, we have j; + ixA+y-5*xB = Wz = Ax -f By, 

 Therefore, Ax = By, and consequently, A : B : : y : x. 



Hence, if the weights of the cross pieces be inversely as 

 their motions, they will not alter the distance of the centre 

 of gravity from the point of suspension, and " the distance 

 of the centre of suspension from the centre of percussion 

 or oscillation, in the same body, will always remain the 

 same; if the distance of its centre of gravity from the 

 point of suspension, and the plane of its motion (in regard 

 to the body) remain the same*." 



This alteration might improve the gridiron pendulum \ 

 but it would be very difficult to exhibit a theorem com- 

 pletely accurate for a mode of compensation which is 

 liable to so many irregularities. A pendulum of a more 

 simple construction, and that might be more easily ad- 

 justed for heat and cold v is still an object that merits the 

 attention of the astronomer. 



The mercurial pendulum is founded on principles mor6 

 simple and correct than any other compound pendulum 

 that has yet been invented j but the manner of construct- 

 ing it with a glass rod has- prevented its being more gene- 

 rally used in the best clocks. This objection is now ob- 

 viated, by the application of a steel rod with a glass vessel 

 attached to it containing quicksilver, so that when the 



* Emmon's Flnxions, j»age 312. Steel 



