22 L. B. Fletcher — A Determination of the B.A. Unit 



Art. III. — A Determination oj the B. A. Unit in Terms of the 

 Mechanical Equivalent of Heat ; by Laurence B. Fletcher, 

 Ph.D. 



The experimental work of the following investigation was 

 completed in 1881, and forms the subject of a thesis submitted 

 to the Johns Hopkins University in that year. In the present 

 paper a more accurate method of calculating the currents from 

 the deflection-curves is used, and some of the other calculations 

 have been revised. The results of the two papers are sub- 

 stantially the same. 



The experiment consisted of simultaneous thermal and elec- 

 trical measurement of the energ}^ expended by a current in a 

 coil of wire immersed in a calorimeter. The result depends upon 

 the values of the mechanical equivalent and the unit of resist- 

 ance, and gives a determination of either in terms of an assumed 

 value of the other. 



The old determinations of Quintus Icilius and Lenz have 

 no value, as the resistance is uncertain as pointed out by 

 Eovvland and H. F. Weber. 



Joule,* in 1867, made a determination of the mechanical 

 equivalent by this method, assuming the B. A. unit as deter- 

 mined by the committee in 1863-4 to be equal to 10 9 C. G\ S. 

 units. The value of the mechanical equivalent thus obtained 

 is more than one per cent greater than Joule's water-friction 

 value. H. F. Weber, f in 1878, used a similar method, employ- 

 ing the Siemens unit, the value of which he also measured in 

 C. G. S. units. Weber's value of the mechanical equivalent is 

 about one part in two hundred greater than Joule's water- fric- 

 tion value and one part in four hundred greater than Bowland's 

 water-friction value. 



In both Joule's and Weber's experiments a possible source of 

 error seems to have been ignored. The wire was assumed to 

 be at the temperature of the water in which it was immersed, 

 and its resistance was calculated on this assumption. It is 

 evident, however, that the wire was hotter than the water, inas- 

 much as it was giving heat to the water. The error due to this 

 cause is of uncertain amount. If corrected for this error the 

 value of the equivalent would be increased and their excess 

 over the water-friction values would become greater than before. 

 To avoid this source of error, the research described below was 

 planned. The suggestion and general plan of the research I 

 owe to Professor Rowland. 



The theory of the method is as follows: A current c, flow- 



* Report of B. A. committee on electrical standards, 1S73. 

 f Phil. Mag., Series 5, vol. xxx. 



