452 Lord Rayleigh on a Statical Theorem. 



forces its proper note. The higher octaves of several forks have 

 been thus perceived ; but the forks from Ut 3 to Ut 4 , inclusive, 

 appear to give the best results. 



The fact that sound-pulses sent to the inner ear through the 

 head give the sensation corresponding to the higher octave of 

 that perceived when the fork vibrates the air outside the ear, 

 and therefore that different covibrating parts of the ear are set 

 in action by the vibrations reaching the ear by these two differ- 

 ent routes, is a necessary consequence of my hypothesis of the 

 mode of audition, and was not suspected until my hypothesis 

 pointed it out to me, and was not known until I attempted to 

 test the hypothesis by experiment. I know of no other hypo- 

 thesis that accounts for this fact, which, while it is a necessary 

 consequence of my own views, is directly opposed to those hypo- 

 theses hitherto formed on the mode of audition; for, according 

 to the latter, the covibrating parts of the ear make as many 

 oscillations in a given interval as the tympanic and basilar 

 membranes. 



[To be continued.] 



LIX. A Statical Theorem. By Lord Rayletgh, M.A.. F.R.S* 



IN a paper " On some General Theorems relating to Vibra- 

 tions/' published in the Mathematical Society's ' Proceed- 

 ings ' for 1873, I proved a very general reciprocal property of 

 systems capable of vibrating^ with or without dissipation, about 

 a position of stable equilibrium. The principle may be shortly, 

 though rather imperfectly, stated thus : — If a periodic force of 

 harmonic type and of given amplitude and period act upon the 

 system at the point P, the resulting displacement at a second 

 point Q will be the same both in amplitude and phase as it 

 would be at the point P were the force to act at Q. 



If we suppose the period of the force to be* very great, the 

 effects both of dissipation and inertia will ultimately disappear, 

 and the system will be in a condition of what is called movable 

 equilibrium ; that is to say, it will be found at any moment in 

 that configuration in which it would be maintained at rest by 

 the then acting forces, supposed to remain unaltered. The sta- 

 tical theorem to which the general principle then reduces is so 

 extremely simple that it can hardly be supposed to be altogether 

 new ; nevertheless it is not to be found in any of the works on 

 mechanics to which I have access, and was not known to the 

 physicists to whom I have mentioned it. In any case, I think, 

 two or three pages may not improperly be devoted to the con- 

 sideration of it. 



* Communicated by the Author. 



