6 EQUAL TRANSMISSION OF PRESSURE. 



the angles which a plane perpendicular to AC makes with 

 the planes, ABD and BCD, respectively ; then we have 



^ABD-costf = jf^ -BCD-cosy. (1) 



But ABD- cos |3 = BCD -cosy = the projections of the 

 areas ABD and BCD on a plane perpendicular to AC ; 

 therefore (1) becomes 



P = Pi- 



And similarly it may be shown that the pressures on the 

 other two faces are each equal to p or p r As the tetrahe- 

 dron may be taken with its faces in any direction, it follows 

 that the pressure at any point is the same in every direc- 

 tion.* 



COR. Hence the lateral pressure of a fluid at any point 

 is equal to its perpendicular pressure. 



SCH. This property constitutes a remarkable distinction 

 between fluids and solids, the latter pressing with their 

 whole weight in the direction of gravity alone. This prop- 

 erty of fluids can be conceived to arise only from the ex- 

 treme facility with which the particles move among one 

 another. It is not easy to imagine how this can take place, 

 if the particles be supposed to be in immediate contact; 

 they are therefore probably kept at a distance from one 

 another by some repulsive force. 



8. Equal Transmission of Fluid Pressure (1) Let 



AH be a tube of uniform bore, and of any shape whatever, 

 tilled with a liquid, and closed at its 

 extremities by two pistons A and B, 

 which fit the bore exactly, but yet 

 can move along it with perfect free- 

 dom : and let the interior of the tube 

 be perfectly smooth, so a< not to offer the least resistance to 



* $90 Beeant'B HydromwbanicB, p. 4. 



