﻿124 Mr. A. Sharp on an Harmonic Analyser.^ 



to be analysed is drawn on a flat sheet of paper and placed 

 on a drawing-board. The carriage FF, which forms the base 

 of the instrument, is supported by an axle with two equal 

 wheels w 1 and a third wheel w which roll on the paper, the 

 direction of motion of the carriage being OX. A disk d x 

 mounted on a vertical spindle is driven by a pair of bevel 

 wheels by the axle w 1 w v A long key on the upper surface 

 of this disk fits into a groove on the under surface of a disk 

 d 2 , which is thus free to move in a straight line relative to 

 disk d x . A groove on the upper surface of disk d 2 at right 

 angles to that on its lower surface has a key from the lower 

 surface of disk d 3 resting in it. Thus the disk d 3 always 

 turns with disk d ± , although any point on disk d 3 may be 

 made the centre of rotation ; the three disks being kinema- 

 tically equivalent to Oldham's coupling for the transmission 

 of motion between two parallel shafts. The keys and grooves 

 would be replaced, in an actual instrument, by wheels and 

 rails, in order to diminish frictional resistance. 



The tracing-point P is mounted on a smaller carriage /, 

 which is free to run in the direction OY relative to the main 

 carriage F. This smaller carriage carries also the rolling 

 wheel W which rolls on the disk d 3 . The rolling wheel W 

 should be spherical in form, and of as small diameter as 

 possible, so that its surface of contact with the paper on disk 

 d 3 approximates to a point. The friction between wheel W 

 and disk d 3 is great enough to prevent any relative sliding. 

 As the tracer P moves over the curve (fig. 1) the point of 

 the wheel W will describe on the disk d 3 the curve Opp'R 

 (fig. 2). To ensure that, as the tracer P is moved in the 

 direction OY, the wheel W will roll on the disk d 3 the same 

 distance and not displace it relative to disk d v a wheel "W of 

 the same diameter as W is mounted on the same spindle 

 and rolls on a fixed portion of the carriage FF. If W be 

 compelled to roll, W must roll on the disk d 3 an equal 

 amount. 



The actual shape of the curve Opp'R (fig. 2) is of no im- 

 portance, the initial and final points being all that are required. 

 A needle or pencil n may therefore be carried at any con- 

 venient part of the carriage /, and the initial and final posi- 

 tions and R marked by it. The direction of the initial 

 line OR will be recorded on the disk d 3 by making two marks 

 with the needle n as the tracer P moves along the line OY 



(fig- !)• 



The gearing must be such that the disk d 3 turns once 



while the tracer P describes one complete period of the curve. 



If now pairs of equal wheels w 2 w 2 , w 3 tr 3 , ... of diameters 



