448 Prof. A. M. Mayer's Researches in Acoustics, 



infinitely small compared with the entire amplitude of dis- 

 placement." It is evident that the compressions and dilatations 

 which may exist in any body depend entirely on the differ- 

 ences in the phases of the vibrations constituting the sonorous 

 wave ; and when the body has a depth equal to half a wave- 

 length, it can embrace the maximum amount of condensation 

 and rarefaction. But condensation and dilatation alone produce 

 lateral action on the walls of a straight canal traversed by sono- 

 rous vibrations ; and hence, if the length of the canal be but a 

 small fraction of the wave, then there exists throughout the 

 canal but little difference in phase, and therefore but little 

 lateral action. Now the united lengths of the scalar is but a 

 small fraction of the mean length of the sonorous waves which 

 traverse it ; for if we take, as above, 4§ metres as the mean 

 length of the waves which are propagated through the scalse, 

 and 59 millims. as the length of the united scalse, it follows that 

 the latter is only ^ of the mean wave-length. Now if we ima- 

 gine the scalse straightened and forming one continuous tube 

 with a free communication existing at the helicotrema, then the 

 mean wave traversing them will cause only ^ of the lateral 

 action which this same wave would produce if the scalse had the 

 length of half of the wave ; and it follows that the whole liquid 

 of the scalse would vibrate forward and backward almost as an 

 incompressible mass, approaching in character to the oscillations 

 of a solid piston in a cylinder ; therefore the action against the 

 walls of the ductus cochlearis would be very slight. But now 

 consider the change in effect on the ductus which takes place 

 when it, together with the scalse, is wound up into such an as- 

 cending spiral as exists in the ear. The molecules of the liquid 

 in the scalse thrown forward and backward by the vibrations of 

 the stapes, tend to move in straight lines ; but the now curved 

 form of the scalse causes them to press against the outer or peri- 

 pheral part of the upper wall (membrana Reissneri) of the ductus 

 cochlearis and against the outer part of the lower wall (mem- 

 brana basilaris) when the stapes moves inward ; and when it 

 moves outward this action of compression is relieved from the 

 two opposite walls of the ductus. But these actions produced 

 by the stapes on the two walls of the ductus are opposed to each 

 other; and since they take place simultaneously and with about 

 the same intensity (by reason of our assumption of the free com- 

 munication of the scalse), the rods of Corti and the hair-cells will 

 not vibrate, but will only experience compressions and dilata- 

 tions like the fluid in which they are immersed. Therefore there 

 appears to me a physical basis for the opinion that either there 

 is no communication between the scalse, or, if the helicotrema 

 exists, that it must be a very constricted passage. Indeed, if we 



