508 



On account of the incommensurability of the times, no periodic 

 return of this or of any other phase can take place, and thus the for- 

 mation of waves or pulsations in a perfectly elastic uniform linear 

 series is impossible ; so that this line of inquiry also fails to give any 

 indications of the velocity with which a vibratory impulse is con- 

 veyed from one end of such a series to the other end. 



When the periodic time of the oscillating body is exactly equal to 

 that of any of the internal oscillations of the system, the extent aug- 

 ments indefinitely with the time during which the action is con- 

 tinued ; a result which would imply that the loudness of a sound 

 should increase with its duration. 



The attempt to pass from a discrete to a concrete system by the 

 method of infinitesimals fails, because by augmenting the number of 

 the parts, we also augment the number of the equations of condi- 

 tion, not one of which can be omitted without vitiating the result. 



The general conclusions are these : — That the observed pheno- 

 mena of sound are inconsistent with the supposition of a perfectly 

 elastic vibratory medium, and that either the viscidity, or some as 

 yet unknown quality of the air, has to do essentially with the pro- 

 duction of those phenomena, so that any analysis in the present state 

 of our preparatory knowledge must be futile. And that the un- 

 dulatory theory of light is altogether conjectural, since far from 

 knowing how one supposed wave would influence another, we do not 

 yet know anything of the manner in which such waves can be formed 

 at all. 



The following Donations to the Library were announced : — 



Transactions of the Royal Society of Literature. Second Series, 



Vol. V. Part 3. — From the Society. 

 Proceedings of the Royal Astronomical Society. Vol. XVII. No. 5. 



8vo. — From the Society. 

 Monatsbericht der Kbniglichen Preuss. Akademie der Wissenschaf- 



ten zu Berlin, 8vo. November — December, 1856. — From 



the Academy, 

 Quarterly Journal of the Geological Society. 8vo. February 



1 857. — From the Society, 

 Journal of the Proceedings of the Linnajan Society. 8vo. Vol. I. 



No. 4. 



