374 On a Simple Form of Harmonic Analyser. 



a quantity which (as the elements are small) approximates to 



i 



2tt 



yd (sin 6). 



Thus the planimeter-reading after this procedure gives us 

 the first cosine coefficient. I need not enter at length into 

 the mode of getting the others. For the second coefficient 

 one would have to shift the tracer. P 12° at a time instead of 

 6°, and so on. 



In my case I actually used steps of 6°, as above; and there 

 were three scales on E F G going by steps of 6°, 12°, and 18° 

 respectively for the first three terms, the separation of the 

 scales helping to avoid confusion. The results were good : for 

 example, in one test the actual coefficients were 4*82, 1*09, "009: 

 the instrument gave 4'86, 1*08, *01. The chief objection to 

 such a non-automatic integrator is of course that one is liable 

 to forget to shift the planimeter pointer at some stage of the 

 proceedings. The chief advantage is that your curve need 

 not be drawn to any particular base-length. Whatever the 

 base, it is only necessary to divide it into the proper number 

 of equal parts, and erect the ordinates at the centres of these 

 elements. 



Suppose we wished to make the arrangement automatic. 

 We might substitute for the harmonic motion of P along S S a 

 circular motion round the centre of S S. This merely amounts 

 to giving P another harmonic motion (perpendicular to S S) , 

 a proceeding which adds nothing to the planimeter-reading 

 if the integration be continued completely round the curve. 



But this is not an easy motion to obtain mechanically. The 

 difficulty is obviated at once if we remove the card ABCD 

 altogether and fix the pole of the planimeter in the drawing- 

 board. If we give P the same circular motion as before we 

 have the " disk " analyser, which I described in the first 

 part of this paper. The area of the curve analysed is added 

 to the integral given by the planimeter, but that is all. 



Evidently in the instrument of fig. 4 we ha\e only taken 

 a special case in making the scales scales of sines. We might 

 have used scales graduated proportionally to x n and got 

 moments. Any other integral could be obtained approxi- 

 mately if a proper scale could be drawn. 



