100 BIOLOGY OF DEATH 



and in that event one would be quite as fully justified 

 (or really unjustified) in concluding that the d x line was 

 a homogeneous curve as Pearson is in concluding from 

 his five-component fit that it is compound. Indeed Witt- 

 stein's formula involving but four constants 



n n 



(M x) i (mx) 

 q x = a ~^"^, a 



gives a substantially good fit over the whole range of life. 

 It is, of course, apparent that the formula as here given 

 is in terms of another function, q x , of the life table, rather 

 than the d x which we have hitherto been discussing. But 

 no difference is in fact involved, qx values may be imme- 

 diately converted into d x values by a simple arithmeti- 

 cal transformation. 



But in neither Pearson's, Wittstein's, nor any other 

 case is the curve-fitting evidence, by and of itself, in any 

 sense a demonstration of the biological homogeneity or 

 heterogeneity of the material. Of far greater impor- 

 tance, and indeed conclusive significance, is the fact, to 

 be brought out in a later chapter, that in material experi- 

 mentally known to be biologically homogeneous, a popu- 

 lation made up of full brothers and sisters out of a brother 

 x sister mating and kept throughout life in a uniform 

 environment identical for all individuals, one gets a d x 

 line in all its essential features, save for the absence of 

 excessive infant mortality arising from perfectly clear 

 biological causes, identical with the human d x line. It 

 has long been apparent to the thoughtful biologist that 

 there was not the slightest biological reason to suppose 

 that the peculiar sinuosity of the human d x line owed its 

 origin to any fundamental heterogeneity in the material, 

 or differentiation in respect of the forces of mortality. 



