Id 20 



Number of pairs drawn 



Fig. 2 Examples of the form of graphs for the distribution of the probabilities 

 of the various possible numbers of pairs, in certain cases. The figure is designed 

 to illustrate the variety of forms of such graphs, and to show how little they resem- 

 ble, in many cases, the 'normal curve.' The ordinates are probabilities; the ab- 

 scissas are numbers of pairs, from 1 to 10. The graphs are drawn, like the usual 

 polygons of variation, by connecting the tops of the ordinates representing the 

 probabilities. 



The line A-B-C-D-E shows the probabilities for the different possible numbers of 

 pairs obtainable when 20 specimens are drawn from 1000 (500 pairs). From 3 up 

 to 10 pairs (D to E) the probabilities are so small that they do not show in a figure 

 drawn to this scale, so that the line representing them coincides practically with 

 the line. 



The remaining graphs (numbered 10 to 20) show all those obtainable when any 

 possible number of specimens is drawn from 20 (10 pairs). The numbers adjacent 

 to the graphs shov/ the number of specimens drawn; thus the graph numbered 10 

 shows the probabilities for the various possible numbers of pairs (0 to 5) when 10 

 specimens are drawn from 20. As the figure shows, the graphs for 17 and 18 are 

 straight lines; those for 19 and 20 are points. 



These graphs (10 to 20) are identical with those to be obtained when the numbers 

 to 10 are drawn from 20, save that in the latter case: (a) they stand in the re- 

 verse order, the graph for 1 being the same as that for 19, the graph for 2 the same 

 as that for IS, etc. ; (b) all would begin at the left on the line, so that they would 

 be crowded together. Otherwise they have the same form, slope, and dimensions 

 as tho.se shown, for drawing 10 to 20. 



408 



