Neio form of Roller for the Dish- and- Roller Integrator. 59 



in which /3 is a fresh constant to be specially determined for 

 each machine. 



The axis of this magnetic moment P has the same direction 

 as the resultant of the magnetizing forces exerted by the fixed 

 electromagnet and by the coil. Hence if we denote the angle 

 of this axis with the two directions of the force at right angles 

 to each other, the former of which is the opposite direction of 



the axis of the fixed electromagnet, by <£ and ^ --(£, we have 



the equations for determining c£, 



C0S * = 7ra ; sin * = 7WW* ■ • (15) 



With the help of these equations we can decompose the mag- 

 netic moment P into two components in reference to both 

 those directions, the introduction of which is convenient for 

 the following considerations. We obtain for the determi- 

 nation of these components, which may be called P x and P 2 , 

 the following equations : — 



P^Pcosc/)^ 

 P 2 = Psin<£= 



CM ^ 



[To be continued.] 



(16) 



VI. A new form of Roller for the Disk-and-Roller Integrator. 

 By Frederick John Smith, B.A.* 



THE disk-and-roller integrating apparatus as used to 

 register the results in an ergometer, or as applied in 

 Ashton and Storey's steam-power indicator, has been objected 

 to because of two defects. The first is that the roller in contact 

 with the disk has a grinding action, and it has this because, 

 while its edges have the same linear velocity, they have to 

 travel in paths which are concentric circles on the disk by 

 which the roller is driven. The second defect is that, since 

 the roller has to be moved with its axis parallel to a radius of 

 the driving-disk, its edge has to be scraped across the disk. 

 The result of this is that, while a certain amount of friction is 

 required to ensure good rolling contact, this very friction 



* Communicated bv the Author. 



