Mr. J. Bishop on the Pitch of the Tuning-Fork. 349 



it, the plane of the magnetic meridian. This done, we must put 

 b = 0, and afterwards allow s and ft to increase indefinitely in 



such a manner that the ratios - = sin y and -3 =T may preserve 



s s 



constant values. The quantity T will then represent the inten- 

 sity of the constant magnetic force, and 7 the angle between the 

 direction of this force and the axis of rotation. In this case the 

 current curves reduce themselves to the system of circles repre- 

 sented by the equations 



r= const., z/= const., 



all of which lie in planes parallel to that of the magnetic meri- 

 dian. The constant current-density within each current-curve 

 will be 



^nkKT sin y . \, 

 if 



be the radius of the current- circle. With respect to its external 

 action, the current-system deports itself like a magnet whose 

 axis coincides with that of y, or, in other words, is perpendicular 

 to the plane of the magnetic meridian. Worthy of notice is the 

 analogy which exists between this result and the one deduced by 

 Poisson from his magnetic theory of rotation-magnetism in his 

 memoir " Sur le Magnetisme en mouveinent"*, as well as the 

 one found by Green f, in the case where a sphere of imperfect 

 electric conductibility is supposed to rotate under the influence 

 of a constant electrostatic force, or where a sphere consisting of a 

 magnetizable substance endued with coercive force rotates under 

 the influence of a constant magnetizing force. 

 Berlin, March 1864. 



XLII. On the Influence of the Pitch of the Tuning-Fork on the 

 Mechanism of the Human Voice. By John Bishop, F.R.S.% 



ALL those who have paid attention to acoustics know that 

 what is denominated pitch in musical science refers to a 

 certain definite number of vibrations or undulations of the air, 

 and also that, for musical purposes, a tuning-fork has been con- 

 structed to yield a note or sound termed C, which we may assume 

 as the fundamental note in the diatonic scale, or gamut. 



Since, then, the pitch of the tuning-fork determines that of 

 all the other notes, both in music, musical instruments, and 



* Mem. de V Acad, des Sciences, vol. vi. p. 497. 



t Journal fur die reine und angewandte Mathematik, vol. xlvii. p. 187- 



% Communicated by the Author. 



