﻿new Harmonic Analyser. 115 



If the integration is performed with regard to y we get 



nA n = I sin nddy, nB a =- I cos nOdy, 



both taken over the whole continuous curve from A' to B". If 

 the integration be continued from B" to A' on the line parallel 

 to the axis of x nothing is added to the integral, because here 

 dy vanishes. 



For the Analysers now to be described this extension of 

 the integration should always be made in order to eliminate 

 certain errors of the instrument. 



These new integrals are of a very different form from the 

 old ones, and require accordingly a different mechanism. As 

 the tracer of the instrument follows the curve, each dy has to 

 be multiplied by sin nO or cos nd. In other words, we have 

 to decompose the dy for each element of the curve into two 

 components at right angles to each other, of which the one 

 makes an angle 6 with the axis of #, and then add all com- 

 ponents of each kind to get A n and B n . 



Originally I did this by aid of a pair of registering-wheels 

 such as are used in Amsler's well-known planimeter, the axes 

 of the two being at right angles. If such a wheel moves 

 along a straight line of length p, making an angle nO with its 

 own axis, it will register not p but p cos nO, whilst the second 

 wheel at right angles to it gives p sin nO. 



A model of this instrument was made in 1889. 



The curve is wrapped round a horizontal cylinder. Parallel 

 to this a carriage runs on a rail carrying the tracer which 

 moves along the upper edge of the cylinder. It also carries 

 a vertical spindle which has the two registering-wheels at- 

 tached to it. These roll on a horizontal platform. If, now, 

 this spindle is made to turn through an angle nO when the 

 cylinder has turned through an angle 0, and if the tracer is 

 made to follow the curve, then the two registering-wheels 

 will give the coefficients A n and B n . For the details of the 

 construction I must refer to Prof. Dyck's Catalogue, p. 213. 



§ 5. The next improvement is due to Mr. A. Sharp, of 

 the Teaching Staff in the Guilds' Central Technical College. 

 Having used my model, he brought me a design in which the 

 principles explained were realized in a different manner. 

 Among the alterations introduced one struck me as being of 

 importance. It consisted in an inversion of the motion, the 

 curve being drawn on the drawing-board and the instrument 

 made to move over it whilst the registering-wheels rolled on 

 the paper. 



It seemed to me that we had now all the elements needed 



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