272 PHILOSOPHICAL TRANSACTIONS. [anNO 1751. 



dulum. With this view, not long afterwards he contrived the pendulum repre- 

 sented by fig. 1, pi. 7- In which ab represents a bar of brass, made quite fast 

 at the upper part by pins, and held contiguous, at several equal distances, by the 

 screws 1, 2, 3, &c. to the rod of the pendulum, which is a bar of iron; and so 

 far as the brass bar reaches is filed of the same size and shape, and consequently 

 does not appear in the figure; but a little below the end of the brass bar, the 

 iron is left broader, as at dd, for the conveniency of fixing the work to it, and 

 is made of a sufficient length to pass quite through the ball of the pendulum to 

 c. The holes 1, 2, &c. in the brass, through which the shanks of the screws 

 pass into the iron rod of the pendulum, are filed as in the drawing, of a length 

 sufficient to suffer the brass to contract and dilate freely by heat and cold under 

 the heads of the screws; eeee represents the ball of the pendulum; f, f, two 

 strong pieces of steel, or levers, whose inner centres, or pivots, turn in two holes 

 drilled in the broad part of the pendulum rod, and their outer ones in a strong 

 bridge, or cock, screwed on the same part of the rod, but omitted in the draft ; 

 because, when put on, it covers this mechanism ; g, g, are two screws entering 

 at the edge, and reaching into the cavity near the centre of the ball. The ends 

 of these screws next the centre are turned into the form represented in the draw- 

 ing, which, pressing with the weight of the ball against the longer arms of the 

 levers, cause the shorter arms to press against the end of the brass bar at b. 

 Things being in this situation, let us suppose that the rod of the pendulum, and 

 the brass annexed to it, grow longer by heat; and that the brass lengthens more 

 than the iron of the same length ; then the brass, by its excess of dilatation, 

 will press the short ends of the levers downwards at b, and at the same time 

 necessarily lift up the ball, which rests on the long ends of the same levers at 

 f, f, to any proportion necessary; and provided the ends of the screws press on 

 the levers at a proper distance from the centres, the ball will be always kept at 

 the point of suspension, notwithstanding any alteration the rod of the pendulum 

 may be liable to from heat or cold. What this distance ought to be, may very 

 nearly be determined, if the difference of the expansion between the brass and 

 iron bars be known; for the proportion the shorter arms of the levers ought to 

 bear to the longer ones, will always be as the excess of the expansion of the 

 brass is to the whole expansion of the iron, as may be thus easily demonstrated. 

 Let the line ab, fig. 2, drawn perpendicular to the line ef, represent a bar of 

 iron; the line cd a bar of brass; the pricked line bg the expansion of the iron, 

 and dh the expansion of the brass bar, by the same degree of heat; let the line 

 gi be drav/n parallel to the line ef, then will ih represent the difference of the 

 expansion of the two metals; through the points h, g, draw a right line cutting 

 the line ef, as in k; this line may be supposed to represent one of the levers 

 turning on its centre at g, h the point where the brass bar acts on the shorter 



