Measurement of Mechanical and Electrical Forces. 79 



the tangent-wheel, but must be made to reciprocate. This 

 motion is most readily produced by use of a "mangle-motion," 

 which converts uniform circular into uniform reciprocating 

 motion. Xow, when the motion of the cylinder is reversed, 

 so also is the direction of its rotation ; and therefore either 

 the action of the tangent-wheel on the cylinder must be re- 

 versed, or there must be a reversing-gear between the cylinder 

 and the mechanism employed to count its revolutions. The 

 action of the tangent-wheel on the cylinder is most easily 

 reversed by having two of them mounted in a frame so that 

 they lie in the same plane, but that one is on one side of the 

 cylinder and the other is on the opposite side. The cylinder 

 is made to bear against one during its forward stroke, and 

 against the other during its return stroke — a change readily 

 effected by the mangle-motion. Then the rotation of the 

 cylinder is independent of the direction of its longitudinal 

 motion. "When it is preferred to use only one tangent- wheel, 

 the reversal between the cylinder and the counting mechanism 

 can be easily and perfectly produced by using three bevel 

 wheels and a friction-clutch actuated by the mangle-motion 

 or even by the change of motion of the cylinder. 



If the cylinder could be made long enough and the ends bent 

 roand so as to join one another, then continuous revolution of 

 the whole ring would take the place of the reciprocation of the 

 cylinder, and the integral would be determined by the rotation 

 of the ring round its circular axis. Such a "smoke-ring" 

 can scarcely be made; but an equivalent can be produced 

 without difficulty. Let there be four barrels, each with a con- 

 cave instead of a convex outline, mounted on a wheel with 

 their axes in one plane, and with some one generating line 

 on each a quadrant of a common circle concentric with the 

 axis of the wheel. Also let the four barrels be geared to one 

 another by bevel wheels (fig. 1, Plate III.). Now let a tan- 

 gent-wheel be placed inside the common circle so as to touch 

 it at its lowest point ; then, if the tangent- wheel lies in the 

 same plane as the circle, revolution of the wheel supporting 

 the barrels will produce no rotation of those barrels ; but if 

 the tangent-wheel is inclined at all, the rotation of the bar- 

 rels will be directly proportional to the tangent of its inclina- 

 tion, and inversely proportional to the radius of the barrel at 

 the point of contact. This periodical inequality, due to the 

 changing radius of the barrel, may be eliminated by using a 

 second mechanical smoke-ring made of a series of convex 

 barrels mounted on a wheel, with some one generating line of 

 each a portion of a common circle which lies outside instead 

 of inside the barrels. In this, which may be called an outside 

 H2 



