536 



SCIENCE PROGRESS 



obtained by an application of the theorems of probability. It 

 is only the most probable series of frequencies, for each par- 

 ticular one is subject to a certain error capable of being found 

 for each working degree of probability of result. This limita- 

 tion of a numerical conclusion as to organic variability must 

 be noted very carefully. The frequency 50*05, for instance, 

 is obtained for the value of the independent variable, 3. In 

 a series of 200 measurements 3 occurs 50 times, that is, it will 

 form about 25 per cent, of the cases in an indefinitely large 

 series of observations. Now a conclusion expressible numeri- 

 cally in biometric work is only probable, and the degree of 

 probability can be anything we like : it can be as 1 is to 1, 

 as 2 to is 1 , as 3 is to 1 , and so on. We fix the working degree 

 of probability ; say we call the odds that our conclusion is true 



even (that is -, or 1 to 1). Having done so we find the error 



of our value V ; it will be ± E, and that means that any value 

 within the range V ± E is equally probable. The higher the 

 working degree of probability of our conclusion the wider are 

 the limits V ± E. Now so long as the results of the study of 

 organic variability are expressed numerically, with these 

 numerical limits of error, they are valuable, but otherwise 

 one can hardly discuss them. That is to say, an empirically 

 formed frequency distribution such as : 



ng 



*h 



of 67 female crania 



Fig. i. 





