﻿128 Prof. Perry's Remark's on. Prof. Henrici's 



the tracer must be that in which x increases on the real curve. 

 1 here give the results : — 



The values of the arbitrary function to be analysed were 

 really calculated from 



y=10 + 5 sin (^ + 30°) -sin (^x-60°\ 



The result obtained numerically and published in the 

 i Electrician,' using 23 ordinates, was 



y = 9-966 + 5-039 sin (^ +29°-9)- 1-053 rin (^b-55°-3\ 



The result now obtained graphically is 

 y = 10-01 + 5-0096sin(yA- + 30 o -38)-l-0099sin^ar-59 o -2 



It is curious that Prof. Henrici should have based the 

 construction of his first or 1889 instrument on the beautiful 

 idea of the late Prof. Clifford, and not on what I call the 

 Henrici principle. He gives the Henrici principle to explain 

 the later instruments, and does not seem to see that his first 

 instrument is the most beautiful example of its application. 

 I take the Henrici principle to be that jy .sin 0. d0 — (cos Ay, 

 the integrations being for a whole period. Well, in his first 

 instrument, whilst its tracer moves through the distance dy, 

 the ordinarily fixed part of the planimeter now has a dis- 

 placement cos 0, and this is the same as if in the ordinary use 

 of the instrument a curve is being traced whose ordinate 

 is cos 0. 



It is only on the assumption that the Henrici principle 

 applies to his first instrument, that I venture to say that the 

 following analyser is on the Henrici principle. We have at 

 present to develop functions in sines and cosines, spherical 

 harmonics and Bessel functions, because we know that when 

 we have effected such developments we can convert them at 

 once into the solutions of certain physical problems. As 

 time goes on we shall require developments in many other 

 normal forms. I propose to describe a machine which will 

 effect any such development. I mean, that my machine will 



evaluate the integral I f(x) . Q (x) . dec, where y=f{x) is an 



Jo 

 arbitrary function of x and Q(x) is any tabulated function. 

 Following Henrici, we convert the required integral into 



[y**).H(*)]-JH (*).<&, 



