for calculating Efficiency. 199 



in ratio, because a heavy magnetic needle subjected to rapidly 

 alternating currents, which produce rapid variations in the 

 direction of the magnetic field, is unaffected by these currents, 

 but steadily maintains its position in the mean direction of the 

 field. The most complex possible case is a combination of 

 rapidly alternating and slowly changing ratios with occasional 

 sudden changes. The first two are properly considered by 

 the machine, while the sudden changes merely cause the frame 

 F to oscillate on either side of its correct position. As in the 

 case of the logarithmic divider, so here; a curve may be drawn 

 on a travelling band of paper by a pencil attached to the 

 frame. 



A more simple arrangement is shown in fig. 6, where the 

 disks B B x and the frame and block are replaced by a sphere 

 S with its axis horizontal mounted in a horizontal ring B, and 

 where this ring is supported in a crutch c which is capable of 

 moving round on a vertical axis. Thus, when B is hori- 

 zontal, the sphere can turn independently round three axes at 

 right angles to one another. Then, if the disks A K x touch 

 the sphere in points 90° apart, the ratio of their speeds will be 

 measured by the tangent of the inclination of B, while the de- 

 viation of c will correspond to the obliquity of the block D in 

 the last machine. 



The most simple harmonic divider that I can imagine is 

 made by mounting, as shown in fig. 7, two iron cones with 

 their bases adjacent, and with the lowest generating line in 

 each horizontal and in one straight line. Then, if a mag- 

 netized steel reel is hung on and the two cones are turned, the 

 reel will travel about and find the ever-varying value of the ratio 

 of their speeds. The method of attaching a recording-pencil 

 is too obvious to need description. If the two cones were 

 placed so that their bases were turned away from one another 

 instead of being adjacent, then the reel would change its speed 

 of moving away from its correct position with a speed propor- 

 tional to its distance from it. This kind of action could only 

 exist, of course, for a very short time. 



Whether dividing-machines are likely to be of general value 

 for practical or experimental purposes, it is difficult to say; 

 but there can be little doubt that cases might arise in which 

 some machine such as I have described might be used with 

 advantage. 



