EVOLUTION 451 



bathmic influence (p. 375) which produces this variabiHty ? 

 We can demonstrate the existence of this variabiHty, we 

 can describe it quantitatively, but the why of it is as much 

 a mystery as the why of the law of gravitation. 



Now let us look a little more closely at the conjuga- 

 tion of gametes leading to the zygote, or in the case of 

 animals, the conjugation of spermatozoon and ovum as 

 the gametes are then termed. Let M be the mean of 

 any character or organ in the form of life to which the 

 zygote leads, and z the deviation in the individual 

 resulting from a particular zygote. Let m^, in^, m^ . . . 

 be the means of any number of characters in the 

 spermatozoa of the race, and ;///, ;//./, w/ . . . those of 

 any number of characters in the ova of the race. Let 

 Wj + ,r^, ?;/, + a;,, W3 + A-3 . . . represent these characters in 

 a special spermatozoon, so that it is described by the 

 deviations x^, ;tr.„ x.^ . . . from the racial type ; similarly 

 let 711^ -\-y^, m,^' +y,^, Wg'+Jg • • • represent the characters 

 of a special ovum, so that it is described by deviations 

 Ji> Jg) yo • ■ • from the racial type of ovum. Then 

 M + s for the individual which results from the conjuga- 

 tion of this particular spermatozoon and this ovum must 

 be determined by the values of the characters vi-^+x^, 

 in.^^x^, m.^-^x^, etc., w/+JV ^z^.^'+Jo, ^^^Z+^s. etc. Now 

 if the variations are small as compared with the means, 

 a principle which the mathematician terms the super- 

 position of small quantities, shows us that z may be taken 

 of the form : ^ — 



z = a^ x^ -f- a., A'., -\r a. x,^ -|- etc., 



+ ^,Jl-hA2J2 + ^3^3 + etC. 



Here a^, a,, a, . . . /3p (3.,, ^, ... are numerical con- 

 stants which could only be determined if we were able to 

 measure an indefinitely great number of characters in the 

 ovum and spermatozoon ; and, further, the character z 

 in the individual resulting from the zygote. Actually, of 

 course, this is impossible, but the form we- have given to 



1 This approximate relation is, at any rate, sufficient to illustrate our present 

 discussion. 



