with special reference to Right- and Left- Handedness. 511 



In the first place it must be noted that it is not in general 

 possible to satisfy all the five equations (1) — (5) with only three 

 unknowns, viz. 6 and the two ratios p: q : r at our disposal. 

 Probably the simplest method of attempting to satisfy the equa- 

 tions is to assume in the first place a value of d and substitute this 

 value for 6 in (2). This gives a linear relation between p, q and r. 

 Multiply this equation by r and substitute pr = q^ from (1), and 



we are left with a quadratic equation in - . Thus for any assumed 



value of ^ there will be at most two values for p: q:r, and it is 

 an open question whether these values will satisfy the equations 

 (3), (4) and (5). In fact in the one case in which an attempt to 

 apply this method has been made it was found quite impossible 

 to find a value of 6 which would fit into the observed facts, so 

 long as the more frequent of the two classes observed was assumed 

 to exhibit the dominant character. Only after a change in the 

 assumption as to which of the characters was dominant was a 

 good fit obtained, and then the approximation was very close. 



Taking the case of the mode of clasping the hands investigated 

 by Lutz as a test example, equations (1) — (5) assume the follow- 

 ing form : 



pr= q^ (6), 



(p + 2q)(l-e) + re ^ 40 



r(l-e) + (p+2q)d 60 ^^ ' 



R~'4>22 ^ ''' 



R' 56-4 ^^^' 



^' = ^ (10) 



These equations apply when the condition with the left thumb 

 uppermost is regarded as the dominant character. Under the con- 

 trary assumption thefractions in (7) — (10) would have to be reversed. 

 Now if we assume a turn-over of 207oj due to "accidents," 

 from either position, and substitute in (7) 6 = 0*2, we get 



2p -t- 4^- - r = O, 

 or multiplying by r and substituting from (6) 

 2q^ + ^qr — r^=0, 



q - 2 + V6 

 I.e. -i = ^ 



r 2 



* Lutz gives 61 % ,? s and 58 °/„ ? s with right thumb uppermost. We take 

 60 °/o as a mean. 



