100 BIOLOGY OF DEATH 



and in that event one would be qnite as fully justified 

 (or really unjustified) in concluding that the dx 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) J — {mx) 



qx = a + T;r <* 



TO 



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^ , of the life table, rather 

 than the dx which we have hitherto been discussing. But 

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

 diately converted into dx 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 liologically 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 dx 

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

 excessive infant mortality aJising from perfectly clear 

 biological causes, identical with the human dx 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 dx line owed its 

 origin to any fundamental heterogeneity in the material, 

 or differentiation in respect of the forces of mortality. 



