Relation to the Measurement of Activity. 7 



equidistant sectors of 30° each cut out of it, and its initial 

 position on the dial A A' is indicated by dotted lines. All the 

 spirals are produced until 120° of arc are swept over, and if a 

 radial millimeter is to correspond to a degree, the effective 



radius of the dial will be 120 millimeters added to the radius 

 of the small internal circle of attachment, 0. For practical 

 reasons the diameter may be made somewhat larger than this 

 in order that the removed sectors may appear as windows in 

 the index ]3late. 



Obviously all the sectors move over corresponding spirals in 

 like manner, and hence the visibility of the protruding end of 

 any partial circle is not only increased threefold but errors in 

 drawing are reduced in value, no matter how fast the system 

 may spin around its center. Again there are always two read- 

 ings in view, one for the emergence of the front edge of the 

 spiral band and the other for the recession of the rear edge. 

 These angles (a) are 30° apart and from their mean value 

 ^(a + (a+30)) — 15, the eccentric error mentioned is the preced- 

 ing paragraph has been eliminated. Other systems are easily 

 devised. 



7. Measurement of activity. — The present method of goni- 

 ometry is peculiarly applicable to problems in which the 

 quantity to be measured fluctuates about a mean value to a 

 degree greater than the error of reading discussed above. Such 

 is usually the case with the rate at which a motor works. In 

 approaching this problem from the mechanical side, physicists 

 have usually preferred to find the angular speed at which a 

 measurable twist on the shaft is maintained, chiefly perhaps 

 because the method is capable of great refinement, as for in- 

 stance in Rowland's* researches on the mechanical equivalent 

 of heat. 



* Rowland: Proc. Am. Acad., xv, p. 157, 1880. 



