532 Mr. J. Lannor. [May 11, 



From these equations x may be eliminated by means of the equa- 

 tions found for V 



K, df dt 



df da dh 



where P = ^-+?L+. 



dx dy dt 



There result equations of the type 



(V-K, *y = f (!45 w-guK, * 



\ rf*V 4jr(r\ K, cfc/ dx 



Thus, finally, 



_ K ------ . 



V ^d?) \dz\dz dx) Jy\dx dy)} 



The three eqaations of this type are equivalent to only two inde- 

 pendent equations. 



They show that all displacements fgh for which the condensation 

 P is zero are propagated with the constant velocity K!"*, whatever be 

 the form assigned to 0(r). For, write 



df , dg , dh' 

 so that ^L + _*- + = 0; 



dx dy dz 

 this is possible, for to determine S we have simply 



-P = v'S, 

 so that S = V/4*r. 



These equations will then determine the mode of propagation of 

 J'g'h' subject to this condition of no condensation, because S disap- 

 pears from them. The propagation of S or V/4*- has already been 

 considered. 



For a system of non -condensational waves of this kind, propagated 

 along the axis of x, all the quantities must be functions of x ; there- 

 fore / must vanish ; that is, the displacement must be perpendicular 

 to the direction of propagation. These waves are therefore waves of 

 transverse displacement. 



