﻿126 Prof. Perry's Remarks on Prof. Henrici's 



instrument, which conies to us from America, and which in the 

 size here exhibited is well suited to Indicator-diagram work, 

 I can say that some of my students instituted a careful 

 comparison between it and the Amsler which they use for 

 Indicator diagrams, and they found that the average error 

 with it was about one third of that with the Amsler. 



We know that in mathematical physics generally the 

 development of an arbitrary function in a Fourier's Series is 

 often of great importance ; but I wish to say that this subject 

 is becoming of greater and greater importance to the practical 

 man — the engineer. 



Thus in alternating-electric-current work, all the disturbing, 

 distracting, dangerous troubles are considerably increased when 

 the currents are not simple harmonic functions of the time. 

 With two-phase or three-phase currents, if the amplitudes are 

 not equal, the rotating magnetic field neither remains of 

 constant strength nor has it constant angular velocity ; and if 

 there are overtones we have extra fields of changing 

 magnitude, which rotate irregularly at two or more times 

 the speed of the fundamental. 



I have long thought that mechanical engineers need such 



instruments as Prof. Henrici has designed, if only to 



familiarize them with the ideas of Fourier. It has for some 



time been my habit, when studying with students any kind of 



reciprocating motion of a piece of machinery, to resolve the 



motion into its fundamental harmonic motion and overtones. 



For example, if one is studying the forces causing the motion, 



one ought to keep in mind that the reciprocating motion 



which (speaking rather vaguely) requires the smallest forces 



or moments of forces to produce it, is the simple harmonic 



motion. The accelerating forces due to an octave are four 



times as great as for a fundamental of the same amplitude. 



The motion of the piston of a steam-engine is, with sufficient 



exactness for practical calculations, a fundamental of amplitude 



r 2 

 r and an octave of amplitude -^, where r is the length of the 



crank and I the length of connecting-rod. 



A special graphical method of study may be discovered and 

 employed for any special motion ; but for applicability to 

 reciprocating motions in general I know of nothing to 

 compare with the method of study which is based on finding 

 the fundamental motion and one or more overtones. 



Again, the difference between one kind of slide-valve 

 motion and another may be exceedingly great, practically, 

 and yet the theories found in books show no difference at all. 

 Indeed, the complete mathematical methods of study are too 



