166 PROCEEDINGS OF THE AMERICAN ACADEMY 



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 = ttNWD, 



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 -f- .0508 sin 2 <£, 



which gives 9.8005 meters per second at Baltimore. If the calo- 

 rimeter 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 ttN WD can be used in 

 this way. For, when the calorimeter is rendered nearly immovable 

 by its great moment of inertia, the work ,done on it is, as we have 

 seen, -n-NWD (1 -|- c 2 ) ; but if it had no inertia, it is evident that 

 the work would be only ttNWD. If, therefore, the calorimeter is 

 made partially stationary, either by its moment of inertia or by fric- 

 tion, the work will be somewhere between these two, and the work 

 spent in friction will be only so "much taken from the error. Hence 

 in the latter experiments the inertia bar was taken oft", and then the 

 calorimeter constantly vibrated through about half a millimeter on the 

 torsion scale. 



Besides this quick vibration, the calorimeter is constantly moving to 



