270 



will be the coefficients of the six ellipsoids used by Mr. 

 Haughton in his former paper. 



2. If the body be incapable of transmitting normal pres- 

 sures, and the vibrations be normal and transversal, and the 

 normal vibration vanish, the general character of the medium 

 will be restricted, and the function V will become a function 

 of the quantities 



dr\ dZ dZ d^ d^ dri 

 dz dy ' dw dz' dy dx ' 



This is the function used by Professor Mac Cullagh, and de- 

 notes a body which can propagate exclusively transverse vi- 

 brations. The equation contains six constants. 



3. If the body be incapable of transmitting tangential 

 pressures, and be restricted to propagate exclusively normal 

 vibrations, the function V will be reduced to a function of the 

 quantity 



_ d^ dr\ dZ 

 dx dy dz ' 



The equations contain one constant. 



These are the equations commonly used in hydrodynamics, 

 and may be shown to signify the perpendicularity of pressure 

 to a given plane ; they are approximately true in the equa- 

 tions of the motion of air. 



4. If the body be only restricted to propagate normal and 

 transverse vibrations, the function V will consist of three 

 parts ; the first denoting exclusively normal vibrations ; the 

 second, exclusively transverse vibrations ; and the third, vibra- 

 tions of a peculiar character. It is to be remarked that, if 

 the original function V were a function of the six quantities 

 used by Mr. Haughton in his former paper, this third portion 

 of the function would disappear. 



All bodies may be placed between two limits, one limit 

 being bodies capable of propagating exclusively normal vi- 



