﻿130 Prof. Perry on Harmonic Analysers. 



Journal. We have found them of practical value, but I do 

 not know whether they are of such general value that they 

 ought to be printed. 



It is well known that l xJ Q (x) . dx=xJ 1 (x), and hence if 

 Jo 



we write <f>(r) for firJi(fjur), and y for our arbitrary function 



/(r), the required integral I rf[r) .Jo(fir) Ar is 



Jo 



The part between the square brackets is usually 0, but 

 however that may be, we see that we can evaluate the 

 integral by the machine. A curve is drawn representing 

 f(r) from r=0tor=aona sheet of paper which is wrapped 

 round a roller, a need not be equal to the whole circum- 

 ference of the roller and the scale of r is unimportant. Of 

 course the ordinate y or f(r) lies parallel to the axis of the 

 roller. It is the measurement of y in inches which my 

 instrument analyses, as my planimeter is graduated in square 

 inches. A table whose upper surface is in a plane tangential 

 to the roller carries the usually fixed part and rolling wheel 

 of an Amsler planimeter. On turning through an angle 6 a 

 handle which drives a shaft on which a properly shaped cam 

 is keyed, the table is displaced in its own plane towards the 

 roller, through the distance x Ji(#), 6 being proportional to 

 w y and at the same time the roller is driven so that the paper 

 moves circumferentially through a distance proportional to x. 

 For this particular kind of problem a few different but 

 definite trains of gearing might be used to connect the 

 handle and the roller, but for general purposes I would 

 prefer variable friction gearing to give any relative speeds 

 that may be necessary. In my model now being constructed 

 I am using two disks, one of which rests on the other at a 

 point which may be altered, radially. As in Prof. Henrici's 

 instrument, the tracing-point of the planimeter is held against 

 a straight edge, so that it can only move along the tangent- 

 line of roller and table whilst following the curve on the 

 roller. 



If fi is a root of J (/xa)=0 as in the well-known drum- 

 head problem, a being the radius of the drum-head, — in the 

 first operation to find A lf the gearing must be adjusted so 

 that when the whole curve on the roller passes under the 

 tracing-point of the planimeter, a graduated circle on the 



