ON THE MECHANICAL EQUIVALENT OF HEAT 433 



for the engine friction, we have about 140 foot-pounds of work re- 

 quired per revolution. Taking the most unfavorable case, where all 

 the power is given to the engine at one point, the velocity changes 

 during the revolution about four per cent, or c would nearly equal .02, 

 causing an error of 1 part in 2500 nearly. By means of the shaking 

 of the calorimeter, I have estimated c as follows, the value of m being 

 changed by changing the weight on the inertia bar, or taking it off 

 altogether. The estimate of the shaking was made by two persons 

 independently. 



m. x observed. c calculated. 



2,200,000 grms. cm. a -6 mm. '016 



3,100,000 " -36 " -013 



11,800,000 " -13 " -017 



Mean, c = '015 



causing a correction of 1 part in 5000. 



Another method of estimating the irregularity of running is to put 

 on or take off weights until the calorimeter rests so firmly against the 

 stops that the vibration ceases. Estimated in this way, I have found 

 a little larger value of c, namely, about -017. 



But as one cannot be too careful about such sources of error, I 

 have experimented on the equivalent with different velocities and with 

 very different ways of running the engine, by which c was greatly 

 changed, and so have satisfied myself that the correction from this 

 source is inappreciable in the present state of the science of heat. 



Hence I shall simply put for the work 



w = xNWD, 



in gravitation measure at Baltimore. To reduce to absolute measure, 

 we must multiply by the force of gravity given by the formula 

 g = 9-78009 + -0508 sm s ? , 



which gives 9-8005 metres per second at Baltimore. If the calorimeter 

 moved without friction, no work would be required to cause it to 

 vibrate back and forth, as I have described; but when it moves with 

 friction, some work is required. When I designed the apparatus, I thus 

 had an idea that it would be best to make it as immovable as possible 

 by adding to its moment of inertia by means of the inertia bar and 

 weights. But on considering the subject further, I see that only the 

 excess of energy represented by c 2 xNWD can be used in this way. For, 

 when the calorimeter is rendered nearly immovable by its great moment 

 28 



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