Instrument for measuring the expansion of Solid Bodies. 327 



compensation is exact, and the expansion of each bar is equal in 

 length. 



This method, although sufficiently accurate for most purposes, 

 has its limit in delicacy, and is not as exact as many philosophical 

 investigations require. I propose to employ another and a better 

 method of verifying the accuracy of the compensating expansibili- 

 ties, one that is capable of demonstrating to any degree of exact- 

 ness that may be desired, whether the expansion of one of the bars 

 compensates perfectly for the expansion of the other ; or in other 

 words, whether the distance between the extremities of the two bars 

 be uniformly the same at all temperatures to which the mass may 

 be subjected. 



This mode is^ to use the combined mass as a pendulum the knife 

 edge of suspension being on the plane of the end of the longer bar, 

 and the mass being so adjusted as to throw its centre of gravity in 

 the plane of the extremity of the shorter bar. It is a well known 

 mechanical principle that the product of the distance from the point 

 of suspension to the centre of gravity, into the distance from the 

 centre of gravity to the centre of oscillation is a constant quantity. 

 From this it follows, that a pendulum keeping uniform time, must 

 have its centre of oscillation remain at a constant distance, else, the 

 length of the pendulum varying, the time kept by it will vary. If 

 the pendulum under consideration keeps uniform time at varied tem- 

 peratures, it demonstrates that the centres of oscillation and gravity 

 remain at invariable distances from the point of suspension, and con- 

 sequently, that the distance from the extremity of the longer to 

 that of the shorter bar remains of a constant length and solves the 

 proposition, viz. to obtain two points which shall remain at an inva- 

 riable distance at different temperatures. Suppose the pendulum at 

 a mean temperature of 32° Farenheit, beats [m) times in a week, 

 and at a mean temperature of 100° Farenheit it also beats (m) 

 times in the same period ; it follows that the distance of the centres 

 of oscillation and gravity remain at a constant distance from the 

 point of suspension, and that the compensation for unequal expansi- 

 bility is exact. This mode of verification may be carried to any 

 degree of exactness that circumstances may render expedient. One 

 thing has been supposed that is not rigidly true, viz. that the metals 

 used for the bars each expand uniformly for equal increments of 

 temperature ; but as the uses for which the instruments will be most 

 valuable, do not require higher ranges of temperature than those of 



