194 Mr. C. V. Boys on Apparatus 



of two integrals so found one by the other, and continuously 

 recording the quotient. Before describing any of these 

 machines, it may be well to give an example showing an ap- 

 plication of a divider to some useful purpose. Let there be a 

 steam-engine driving a dynamo-electric machine, which is 

 employed to produce an electric light. Steam does work on 

 the piston of the engine, which may be integrated as already 

 described. This is the work put in. The electricity does work 

 in the electric arc and in the conducting wires, which may be 

 integrated. This is the work taken out. If after any time, 

 say one hour, the work taken out is divided by the work put in, 

 the quotient will represent the average efficiency of the engine 

 and machine combined during the hour. In like manner, if 

 the readings are taken after a minute, the quotient will give 

 the average efficiency during the minute. If instead of a 

 minute an indefinitely short period of time is occupied, then 

 the quotient obtained will give the true efficiency at that time. 

 Now, if by mechanism or otherwise a curve can be drawn in 

 which the ordinates represent the true efficiency, while the 

 abscissae are time, then an inspection of the curve will show 

 exactly how well the machines have clone their work at every 

 moment, and the highest points will indicate the time at which 

 the best results have been obtained. What is wanted in 

 practice is not a curve giving the true efficiency as above de- 

 scribed, because work is not put into an engine uniformly, but 

 intermittently, but a curve showing the average efficiency for 

 the last few seconds or minutes as the case may be ; and it is 

 this that the mechanism I am going to describe accomplishes. 

 If one of the integrals represents time, and the other work done 

 in an engine, then the curve gives the continuous value of the 

 horse-power per hour ; or if one integral represents turns of a 

 dynamo-machine, while the other represents electric current 

 or electric energy, then the curve gives current-quantity or 

 current-energy per turn. Or, generally, if two things are 

 turning, either or both at a variable rate, a dividing machine will 

 give the ever-varying value of the quotient of one by the other. 

 I have made use of two principles in the construction of 

 dividing machines, which may therefore be classed under two 

 heads. In the first class a pointer, if at a wrong position on the 

 scale of quotients, moves towards its right place with a speed 

 proportional to its distance from it : its motion is therefore 

 of a logarithmic nature. In machines of the second class a 

 pointer, if at a wrong position on the scale of quotients, changes 

 its speed of moving towards its right position with a speed 

 proportional to its distance from it : its motion therefore is of 

 an harmonic nature. In either case the movement of the 



