124 Mr. R. Moon on the Theory of Pressure in Fluids. 



But if one of the quantities P p P 2 is constant — for instance, if 

 we have 



V+ \/V 2 + 4Rp 2 = 2«, 



where a is constant, we shall have 



or 



which gives us 



n <*dp dp 9 



a value which, it will be found, satisfies both the equations of con- 

 dition (14). 



In this case equations (8«), from which (o 1} &> 2 are to be de- 

 rived, become 



= dv s> 



9 



0=A-{v(«+j)-«}^ • • • (15) 



.-. (o { = v-] — , and equations (13) become 



.+ .=*!_. ^ — *h 



where a) = const, is the integral of (15). 



If we put u — v-\ — , the three equations which determine the 



circumstances of the motion, i. e. the pressure, density, and ve- 

 locity, become 



p=- - + xM, 



^^I^X'W-^J, y . . (16) 

 1 C du , f a "1 



might assume p= a function of p only — an assumption which is open to all 

 the objections which in my former paper have been shown to apply to the 

 law of the received theory, viz. p = o'y. 



