366 ON PHYSICAL DATA 



all values of .v less than -p^ — p , providing that 

 the two curves represented by the equations 



P , P 



&"2 1 "3 



P — P 



have not a common tangent at the point A = p°p 



This condition may be determined by differen- 

 tiating the above equations. 



<y ^ 3P 2P, 



dx a^ 3? 



dy 3P, 2P3 



dx ~ ^ '^ x' 



.-, 3P + 2P, X = 3P2 + 2P3 X 

 or 3P + 2P, . |i=^ = 3P, + 2P3 . ^^ 

 3PP.-3PP3-1-2P,P2-2P,P=3P2P,-3P2P3+2P3P,-2P3P 



PP,-PP3=P,P,-P,P3 



or (P,-P3)P=(P,-P3)P2 

 or P=P, 



