for calculating Efficiency. 197 



Harmonic Dividers. 



All harmonic dividers depend on the steering-power of 

 wheels, an action which renders wheels of ordinary construc- 

 tion useless in the case of the logarithmic divider. The steer- 

 ing action, however, is not determined by any direct effect, 

 as in the case of my cart integrating-machine, or in the more 

 familiar case of a common bicycle, but depends on an inter- 

 mediate action, and is in this respect exactly similar to the 

 steering arrangements in that most beautiful and ingenious 

 machine the " Otto" bicycle. In this the rider produces a 

 difference in the speeds of two wheels, one on each side of 

 him; the angular deviation therefore is the integral of the dif- 

 ference in speed between the two wheels, while the linear 

 deviation from the original straight course is the integral Avith 

 respect to the distance run of the sine of the angular devia- 

 tion. The method of adapting this principle is exactly analo- 

 gous to the case of the disk-cylinder integrator. That machine 

 was developed in this way : — Take a cart integrator running 

 on fixed ground, remove the whole of the cart except its 

 steering-wheel, which fix in position, then give it movable 

 and cylindrical ground to run on ; a disk-cylinder integrator 

 will be the result. In this case do away with the whole of 

 Otto's machine except the two wheels, fix them in position, 

 and give them each a movable floor to run on. Fig. 4 is a 

 side view, and fig. 5 is a plan, of a machine of this kind. 

 A A x are the two steering wheels mounted independently on a 

 common axis ; B B x are a pair of disks geared together by their 

 edges, and they form the movable floors for the disks A A to 

 rest upon, c c x are the supporting wheels of a frame F, and 

 are capable of running on rails parallel to the common axis of 

 A A v The frame F carries a block D swivelled on a vertical 

 axis passing through the centre of both F and D. The axes 

 of B B x are supported by D. If A A 1 are caused to turn with 

 speeds proportional to their distances from the centres of B Bj 

 and in the same direction, B B x will revolve at equal speeds in 

 opposite directions, and neither J) nor F will be affected; but 

 if either A or A x is made to revolve a little faster than is due 

 to its central distance, D will begin to turn in its swivel- 

 frame. But no sooner does D begin to twist, than the disks 

 A A 1; which previously were describing circles on B B x , tend 

 to move in spiral paths, the faster one receding from, and the 

 slower one approaching, the centres of the disks B B x on which 

 it is moving. But as A Ax are incapable of any movement but 

 rotation, while the disks B B, can, from the nature of their 

 support, accommodate themselves to every kind of movement 



