c2 Records of the Indian Museum. [Vol. XXIII, 



There are 3 changes of sign with % = + 00 y 4 changes with x-o 

 and 6 changes with %= — 00. Hence there is 4 — 3 = 1 real positive 

 root and 6-4 = 2 real negative roots. 



By trial I locate the positive root between and 1, and the 

 two negative roots between o and — 1. 



I try the following successive approximations by Horner's 

 method. 



/( + o-2) =+-0177 /( + 0-I5) =-'03 79 



/( + o*i8) =--oi 17 /( + 0*187) =-'00 09 



/( + 0-188) = + -oo 02 /( + 0-1878) = - -oo 002 



Thus we can take the positive root, p ? = +0-1878 



For the negative roots I try 



/( o) =--oi 19 /(-'5) =-2-27 75 



/(-•25)= --44 88 /(--oi)=- -oo 80 



/( — -i) = + 00 01 



Root is near — *i. I try higher approximations, now retaining 

 eight decimal figures. 



/( — -i) = +o-oo 00 84 36 



/(-•101) = -o-oo 02 54 15 



/(-•1001) = + -oo 00 51 06 



/(-•1003) = — -oo 00 44 78 



/( — -1002) = + 'OO 00 14 65 



Thus />;.= --I002 is another root. 

 Again 



/(-•°5) = + '°° 34 

 /(— -oi) = —-oo 80 



/(-O3) = --00 12 



/( -'04) = + -oo 14 



/(-'034) = --oo 00 97 79 



/(-•0343) = -'oo 00 17 84 



/( - -0344) = + -oo 00 08 69 



Thus pi= -'0344 is the third root. 



It should be observed that if the material is a real mixture of 

 two true normal components, then the mathematical solution 

 would be theoretically unique. In practice, however, a statistical 

 curve may be the sum of two asymmetric curves, and hence we 

 must not be surprised if more than one solution is given by the 

 present method of dissection. Each root of the fundamental 

 nonic gives one distinct mode of dissection. 



ise 1. 

 />. = + oi.s 78 

 Then, P. = - 5'^> 44 



P\ = P\ P = -28-11 01 59 



