Measurement of Mechanical and Electrical Forces. 81 



inclination of A above the horizon ; so that if A is horizontal, 

 no rotation about A as an axis will produce any effect; but as 

 A rises higher, increased rotation of the cylinder will be pro- 

 duced, the maximum being when A is vertical. As in the 

 former case, so here, the inclination of A should be brought 

 back to its original value before the rotation of the cylinder is 

 measured. This is the method of steering a wheelbarrow when 

 pushing it. The elevation of the handles corresponds to the 

 inclination of A with the horizon ; the equality of the elevation 

 of the two handles corresponds to absence of rotation about A; 

 therefore the barrow goes straight. When turning a corner 

 the outer handle is elevated more than the inner one ; this 

 corresponds to rotation about A: and the tangent of this rota- 

 tion, multiplied by the sine of the elevation of the handles, 

 measures the deviation of the barrow from its straight course. 

 This deviation, then, is greater as the elevation of the handles 

 is greater, and therefore in going round a sharp corner the 

 handles should be raised as much as possible. By the means 

 above described, either the quotient or the product of two 

 functions may be directly integrated. 



As in my former integrating-machine, so with these, the 

 reciprocal of a function may be integrated by first inclining the 

 tangent- wheel through a right angle; then, when a function 

 passes through from + to — , the tangent- wheel describes 

 on the surface of the cylinder a cusp showing a momentary 

 infinite motion. A machine so arranged may be used to 

 integrate, not the reciprocal, but the function itself, if, instead of 

 moving the cylinder longitudinally, it is caused to rotate, when 

 the longitudinal motion, or the number of reciprocations if 

 suitable gearing is employed, will measure the integral. In a 

 similar way the machine as first described will integrate a 

 reciprocal. 



If for any purpose, in addition to the total result, the inte- 

 gral up to any time is required, a diagram must be drawn. 

 This can be effected by covering the cylinder with a layer 

 of black tracing-paper, and allowing a band of paper as wide 

 as the cylinder is long to pass between the tangent-wheel and 

 the black surface. The length of paper passed through the 

 machine represents the integral; and the curve drawn shows 

 its rate of growth continuously. Should it only be required 

 to know the amount of growth during each of a series of short 

 intervals of time, a narrow band (which is more manageable) 

 may be used wrapped round a small wheel at the end of the 

 cylinder, and so arranged that at the end of each double stroke 

 of the cylinder it is caused to bear against the point of a sta- 

 tionary pencil ; then the pencil-marks represent equal intervals 



