SECT. 2] AND WEIGHT 455 



2-1 1. Variability and Correlation 



Enough has now been said about the growth of the parts and 

 organs of the whole considered in isolation, and we must consider 

 the relation between the growth-rate and two other factors, namely, 

 variability and correlation. The population of cells in the metazoal 

 embryo may no doubt be compared with the populations of 

 protozoa in cultures, but, whereas the functions of the whole in the 

 latter case are very limited, those of the whole in the former case 

 are highly complex. In other words, one may enquire to what 

 extent there is variability between different embryos of exactly the 

 same fertilisation age. Closely allied to this question is what is, to all 

 intents and purposes, its converse, namely, at what point in develop- 

 ment is the correlation coefficient greatest, i.e. at what point is the 

 swing of variation among embryos away from the mean least? It is 

 to be regretted that these enquiries have not been very deeply carried 

 on in embryology, but there are some rather significant observations 

 which need attention. 



So far only the mean values for weights and measures of embryos 

 have been under consideration. But obviously no statistical study 

 of these is complete without a consideration of the amount of 

 variability among the individual cases from which the mean value 

 is derived. The variability coefficient is defined as the 



standard deviation 



X 100, 



mean 



the standard deviation being a measure of the spread of points 

 around the mean, i.e. a measure of the point upon the frequency- 

 curve where the change takes place between concave to the mean 

 and convex to it. Fig. 22 showing McDowell's points will explain 

 the meaning of this. It has long been known that the variability 

 coefficient decreases with age in man, and it is always stated that 

 it follows the changing growth-rate quite closely, but some con- 

 fusion has been caused in the past by a doubt as to what manner of 

 representing the growth-rate is being referred to. The fact is, how- 

 ever, that the variability coefficient follows the simple increment 

 curve. Thus, if for absolute growth a sigmoid curve holds good, 

 the greatest daily or monthly increment will occur as we have 

 seen at the middle of the period, and this peak will coincide 

 with a peak in the variability coefficient. This was found to hold in 



