﻿120 On a new Harmonic Analyser. 



shaft, and this motion will be communicated to each of the 

 registering-wheels. It will be seen at once, if q denotes the 

 radius of the sphere, the point of contact of the sphere and 

 the wheel E, 1 is at a distance g sin n6 from the axis of the 

 sphere, that therefore the turning communicated to this wheel 

 will be proportional to dy sin n6. Similarly the other wheel 

 will turn proportionally to dy cos n6. If the tracer moves 

 through the whole curve, these two wheels will therefore 

 register numbers proportional to A„ and B n . The dimensions 

 are so chosen that the readings give nA n and nBn in centi- 

 metres. 



It will be seen that now one spindle does the work of two 

 in the old instrument. There is, further, no slipping of any 

 kind in the integrating apparatus. 



Another improvement is that the wheelwork for turning 

 the spindles is done away with. Each spindle is turned 

 directly by the silver wire, and thus any slackness in the 

 wheels is done away with. 



It has also been possible to introduce an arrangement to 

 set all spindles to zero after the wire has been tightened. 



Lastly, the readings are taken with much greater ease as 

 the registering apparatus is well exposed to the eye. 



In order that the instrument may work accurately it is 

 necessary that the point of contact of the sphere with its cylinder 

 should lie in the geometrical axis of the spindle. But it is 

 practically impossible to secure this. This point will there- 

 fore describe a small circle on the cylinder and this will turn 

 the sphere about some horizontal diameter, and therefore also 

 the registering-wheels. It is of importance to eliminate the 

 error thus introduced. This is done by bringing the tracer 

 back to the starting-point A on the curve by moving it from 

 B to A (figs. 1, 2) parallel to the axis of as. The sphere will 

 hereby repeat the motion which produced the error, but in 

 the opposite sense, and therefore completely cancel it. 



§ 8. The first instrument of this kind has been made for 

 Prof. Klein at Gottingen. It contains one spindle, as in 

 fig. 3. Going once over the curves it gives therefore one pair 

 of coefficients. To get more, disks of different diameter 

 have to be used to drive the spindle. Of these six are pro- 

 vided. Since then two further instruments have been finished; 

 one with five spindles, which goes to Moscow, the other, with 

 three spindles, for Prof. Weber in Zurich. The experience 

 gained in the making of the Gottingen instrument has 

 enabled Coradi to introduce a number of small improvements, 

 with the result that the carriage runs in the Moscow instru- 

 ment, where it has to drive five spindles, as easily as in the 

 one for Gottingen with only one spindle. 



