4IO THE GRAMMAR OF SCIENCE 



after the interval. Hence the fraction of the individuals 

 with organ 5 who have died is the ratio of d$ ~n^S to 

 d^. Now let us reduce the vertical distances of the poly- 

 gon 2, c, b, g, 14 to yth of themselves, so that the new 

 polygon just falls as 2, f, c, /, 14 inside the old polygon 

 I, d, a, h, I 5. Then we have for the death-rate (d^ ~7i^S) 



-^ds=ids-y^/S)/dS, but /S=dS-d/. Hence the 

 death-rate 



= {'^5-f(^^5-^/)}-^5 



m m df 

 71 n as 



= a constant part i — ^/ijn, together with a part propor- 

 tional to df-^d^. 



Now if we have chosen ni so that the new polygon 

 2, f, c, 2, I ^ just touches the original polygon i,d, a, b, 15, 

 there will be one point c at which there is no intercept 

 between the two polygons, or the whole death-rate will be 



the constant part i — — , or be non-selective. This point 

 will not necessarily, or even generally, fall at the mode as 

 in our figure ; it can, however, always be determined by 

 reducing the polygon 2, e, b, g, 14 until it just falls 

 inside touching the old polygon. For example, the two 

 polygons might have touched at /, and j'k would then 

 have been the frequency after selection of the organs of 

 size k, for which there was no selective death-rate. These 

 are accordingly the organs best fitted to survive under the 

 given environment. Here we may notice several points : — 



{a) The individual best fitted to survive is neither of 

 necessity in the mode either before or after selection, he 

 is simply the individual for whom the death-rate takes its 

 non-selective value. 



{h) While the value of in can generally be found, that 

 of n is unknown, hence we do not get the absolute value 

 of either the selective or non-selective death-rates, or even 

 the proportion of the two. 



