Use q/'Lissajous' Figures to determine a Rate of Rotation. 349 

 / }f\ _ n^ 2p-l 



2p 

 _ n" 2p-l 



-Im^ + n^J' 2p 2p-2"'^'^\ 



~ 2mp \_m^ + n^] ' 2p(2p-2) ... 4.2 2^p\p \p 



{2Kfp ___^p__ r n^ 'Y_ (fp 



' "]2^''2^~ 2mp{\'py ' Im^ + n^A ~ 2mpQpf ' 





» 1 / C* C^ \ 



{\2r ^-(\sy 



Q. E. D. 



N.B. — The symbols used for the constants throughout this 

 Appendix have no connexion with those in the main paper, 

 except that m is the same in both. The value of the C of the 

 Appendix, expressed in terms of the symbols used in the 



paper, is 



47r/(:n/u-Vo\/S -f- L. 



XLI. On the Use of Lissajous' Figures to determine a Rate of 

 Rotation, and of a Morse Receiver to Measure the Periodic 

 Time of a Reed or Tuning-fork. By Prof. J. Vikiamu 

 Jones, M.A.* 



IT is sometimes of importance to determine with great accu- 

 racy the angular velocity of a rotating body at a given 

 instant. For instance, in measuring an electrical resistance 

 in absolute measure by the British Association method or the 

 method of Lorenz, the rate of rotation of the revolving coil or 

 disk must be known with full accuracy at the time when the 

 reading of a galvanometer-needle is taken. 



The method I have to bring before the Physical Society in 

 this note consists in obtaining, by means of Lissajous' figures, 

 equality of period between the rotating body and a reed main- 

 tained in vibration electrically, and then subsequently deter- 

 mining the vibration-period of the reed. 



* Communicated by the Physical Society : read March 23, 1889. 



