ON THE MECHANICAL EQUIVALENT OF HEAT 441 



towel, and placed in the apparatus half an hour to an hour before the 

 experiment, exposed freely to the air. The surface being polished, the 

 slightest deposit of dew was readily visible. The greatest care was 

 taken to guard against this source of error, and I think the experiment 

 is free from it. 



(d.) Results 

 1. CONSTANT DATA 



Joule's equivalent in gravitation measure is of the dimensions of 

 length only, being the height which water would have to fall to be 

 heated one degree. Or let water flow downward with uniform velocity 

 through a capillary tube impervious to heat; assuming the viscosity 

 constant, the rate of variation of height with temperature will be 

 Joule's equivalent. 



Hence, besides the force of gravity the only thing required in abso- 

 lute measure is some length. The length that enters the equation 

 is the diameter of the torsion wheel. This was determined under a 

 microscope comparator by comparison with a standard metre belong- 

 ing to Professor Eogers of Harvard Observatory, which had been 

 compared at Washington with the Coast Survey standards, as well as 

 by comparison with one of our own metre scales which had also been 

 so compared. The result was -26908 metre at 20 C. 



To this must be added the thickness of the silk tape suspending the 

 weights. This thickness was carefully determined by a micrometer 

 screw while the tape was stretched, the screw having a flat end. The 

 result was -00031 m. 



So that, finally, D' ~ -26939 metre at 20 C. Separating the con- 

 stant from the variable parts, the formula now becomes 



JL = j*6-324^ ^ + .ooooiS 0" - 20) + * 



g = 9-8005 at Baltimore. 



It is unnecessary to have the weights exact to standard, provided they 

 are relatively correct, or to make double weighings, provided the same 

 scale of the balance is always used. For both numerator and denomi- 

 nator of the fraction contain a weight. 



2. EXPEBIMENTAL DATA AND TABLES OF RESULTS 



In exhibiting the results of the experiments, it is much more satisfac- 

 tory to compute at once from the observations the work necessary to 

 raise 1 kil. of the water from the first temperature observed to each sue- 



