102 « G. H. KNIBBS. 



6 being the value of x for y = A, that is : — 

 (63)... tan0= --|. 



and the maximum and minimum values of cc, /^ say, are 



given by 



dyjdx = B cos /x — C sin /* == 0, that is 



(64)... tan /*=-5 = - cot 0. 

 C 



In comparing two curves of this type, we must have 

 recourse to such corresponding phases as and p. 



The value of the ordinate at this point, viz. the maximum 



or minimum is 



(65)... y = A + v/JB 2 + C 2 . 



In other cases than that referred to, the determination 

 involves the solution of an equation of the fifth degree, and 

 need not be considered. 



Where there are more divisions than five it will in general 

 be desirable to represent the frequency by an equation of 

 the form 

 (66)... y = a + b sin x -\- c cos x + d sin 2x + e cos 2x. 



The integral of this is 

 (66a).../ ydx = ax — b cos x + c sin x — %dco& 2x + \e sin 2x 



and if it be taken between the limits to - ; - to—; etc... 



6 6 3 



and if y u t/ 2 ... denote the monthly means we have 



y 1 — a+—{- b (cos 30 e - cos 0°) + c (sin 30° — sin 0°) 



TV v 



- id (cos 60° - cos 0°) + \ e (sin 60° - sin 0°)}. 

 As before denoting y k -a by r k ...we get a series of equations 

 of which the first is 



n==b (cos 0° - cos 30°) + c (sin 30° - sin 0°) 



7T 



6 



+ £ d (cos 0° - cos 60°) + \ e (sin 60° - sin 0°) 



Denoting 1 ~bym: — ^ bv * •' an( ^-^ bv &> tne 



equations become 



— ri = wb + | c + d + | Ice, 



