212 On a new form of Amperemeter and Voltmeter. 



Time of swing of the two coils. — The time of the swing varies 

 with the 'v/moiiieiit of inertia. 

 In fig. 9 the moment of inertia is 



and for fiof. 10 



■6-40 



where m stands for the mass of unit length of the periphery. 

 Therefore 



Ii r 1 2 (3Z-2r 1 ) 

 I 2 2r 2 %3l-8r 2 )' 



Hence for the particular size of coils under consideration, 



Ix 1080 

 1 2 19 * 



So that I 1 = 57 I 2 nearly. 



Therefore, the time of swing of the coil in fig. 9 will be 7*5 

 times that for the coil in fig. 10, and the deflecting-moment 

 or the sensitiveness of the coil in fig. 9 for continuous currents 

 will be 7 times that of the coil in fig. 10. 



Now as regards the "throw/' The relative throws of the 

 two coils for the same quantity of electricity will be 



Mi. . /5_ 7 



M 2 V I 1 = 73 about - 



So that we have for the two coils throws of nearly equal 

 magnitudes, although one coil moves 7*5 times as slowly as 

 the other. 



It is almost needless for me to mention that I have been 

 greatly assisted during the experimental period of the mea- 

 suring instruments described above, and I wish to express 

 my gratitude to Professor Oliver Lodge not only for his sug- 

 gestions and criticisms but also for his kind encouragement 

 at all times. I am also much indebted to Dr. Alexander 

 Muirhead for much help in practical details, and for the con^ 

 siderable experimental facilities he has always been ready to 

 present. 



