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



Case 3. 



p. 2 - -0-03 44 

 Whence p z = +0*17 10 76 



P\ = -4*97 3i 40 

 Thus y' 2 + 4"97 3 1 4o7-'°3 44 = 



7i 



= 



+ # oo 69 075 



7'2 



i-*>s/ component 



= 



-4-98 00 475. 



Mean 



= 



i65°'59 54 mm. 



ft, 



= 



19972 3 



*i' 



= 



176 61 09 



CT i 

 Second component 



s= 



1-32 89 50 



Mean 



— 



1407*24 76 mm 



rc 2 



= 



+ -27 7 



CT a * 



•^~ 



+ l6'5Q 03 2Q 



The second component is real this time, but its frequency 

 being only '277, it is again negligible. The first component gives 

 practically the whole of the distribution. 



It will be seen that first solution (^ = -1878) gives the fre- 

 quency curve as the difference of two normal curves. " The prob- 

 ability curve, with positive area, may possibly be looked upon as 

 the birth population (unselectively diminished by death). The 

 negative probability curve is a selective diminution of units 

 about a certain mean ; that mean may, perhaps be the average 

 of the less fit." ' In our present case, however, the negative 

 component is imaginary. Hence we conclude that the real 

 component is describing the general population with sufficient 

 accuracy. 



In the case of the second solution (/>. 2 = - -1002) the second 

 component, though now additive, is still imaginary. The mean 

 is at 1051-98 mm. This component may be interpreted as repre- 

 senting a "tendency" towards the presence of a small propor- 

 tion of dwarfs. 



This tendency becomes more prominent in the third solution 

 {p. 2 - --0344). We find that the second component, which is addi- 

 tive and real, definitely represents a " dwarf ' ' distribution with 

 an average stature of I407'24 mm. The proportion, however, is 

 extremely small. It is only 0*14% and can be safely neglected 111 

 samples of 200. In larger samples of over a thousand, we should 

 not be surprised to get a few dwarfs. 



1 far as the present analysis goes we must conclude therefore 

 that it is not possible to break up our given curve into two real 



1 -on, Phil. Trans. Roy. Soc, Vol. 1S5 A, 1S04, p. 76. 



