.Relation to the Measurement of Activity. 9 



of displacement of index and dial is known, the moment of 

 torsion for any observed displacement is given at once. This 

 quantity multiplied by the angular speed is the activity sought. 

 Thus if the number of revolutions is n per minute, the angu- 

 lar speed will be to = 2^m/60 ; and if the moment of torsion 

 m be expressed in kilogram-meters 



com J 75 



is the activity required in horse powers. 



The calibration may be made once for all by twisting the 

 rod ah in place by a known couple, and noting the correspond- 

 ing deflection on the dial. Radial holes may be left in the 

 pulleys for this purpose, in which spokes of known length 

 are inserted. From the hookshaped ends of these, given 

 weights are suspended so that if m' be the moment of the 

 couple per degree of deflection at the dial and o any observed 

 deflection, m = m' o. To fix the ideas suppose a steel rod 

 0'4 em in diameter and 50 cm in efficient length were chosen : 

 then one degree of deflection at 1000 revolutions per minute 

 would correspond to about - 01 horse power. 



8. Tachometer . — The construction of the speed indicator is 

 easily inferred from the preceding paragraph. As shown by 

 the diagram figure 6, ah is a short rod capable of revolving in 

 a journal fixed to the bed plate B. The end a is suitably at- 

 tached to the shaft. Near its middle parts the rod is doubly 

 shouldered and surrounded by a cylindrical box or drum cc, 

 which would be free to revolve around the rod but for a watch 

 spring rr, one end of which is fastened to the rod ah and the 

 other to the circumference of the drum cc. In this case the 

 dial eld is attached to the front face of the drum, the index 

 nn to the end h of the rod, and a scale S facilitates the read- 

 ing as before. The outside of the box cc carries two vanes or 

 propeller blades _£>_£> by which the rotation of the box is resisted. 

 Suppose these removed or placed in the plane of rotation, no 

 deviation would be indicated between the index and the dial 

 however fast the system rotates. If however they are fixed in 

 place (as in the figure), the angular deviation registered by the 

 system of dial and index will in a general way be proportional 

 to the square of the speed. 



The instrument is capable of considerable adjustment so 

 that it would appear to* be adapted for measuring large ranges 

 of speed. Thus one might alter the obliquity of the propeller 

 blades, pp, relative to the plane of rotation, or by a suitable 

 adjustment successively tighten or twist the watch spring rr. 

 Consecutive notches would then correspond to given intervals 

 of speed. The definite graduation would have to be made 

 empirically, though it is seen that a subquadratic spiral is more 



