438 Mr Engledow and Mr Udny Yule, The determination of 
to be expected from this ratio, and from the ratio 1:3:3:1, 
The results obtained were 
Ratio 1:3 x? = 2:0974 P=0:554 
puedes, 2G ve SOILS) P=0574 
It will be observed that while the calculated ratio does give the 
better agreement, the difference is slight. In both cases results | 
equally or more divergent from expectation would occur nearly as | 
often as not owing to mere fluctuations of sampling. The result | 
is an illustration of the now recognised fact that a considerable — 
alteration in the coupling-ratio may mean but a small alteration 
in the closeness of fit. 
Two other cases have been tried and gave the following results. 
Collins (loc. cit., p. 579) gives the following data for the characters 
coloured aleurone and horny endosperm in maize. 
Coloured-horny 1774 
Coloured-waxy 263 
White-horny 279 
White-waxy 420 
We find p=0°3891 or a ratio 3509: 1. For this value of the | 
ratio x? is 0°60435 or P =0°947, the calculated frequencies 1782, | 
270, 270, 414 being in very close agreement with those observed. 
For the 3: 1 ratio, x? is 9°106 or P = 0-028, and the divergence is- 
therefore one that would only be likely to occur once in some 
36 trials owing to the fluctuations of random sampling. 
Finally we took the data given by Bateson, Saunders and 
Punnett in the Fourth Report of the Evolution Committee (p. 16) 
for coupling between dark axils and fertility in sweet peas. Here | 
we find p=0'4745, which is equivalent to a ratio 18608 : 1, as 
compared with the ratio 15:1 suggested in the Report and a | 
value “about 20:1” by Collins. The relative merits of the | 
ratios are apparent from the following: 
Ratio 18°608 : 1 x? = 3:'7539 P=0°294 
ests al v= 59226 P=0116 
0c 72=38975 P=0275 
The ratio 15:1 is clearly much the poorest of these three: a worse 
fit is only likely to occur, owing to fluctuations of sampling, some. 
12 times in 100. A worse fit than that given by 20 : 1 may occur 
some 27 times in 100, and a worse fit than that given by our 
calculated ratio some 29 times in 100. The figures again shew, | 
however, how great differences may be made in the coupling-ratio 
assumed without creating an impossible discordance between 
assumptions and fact. The mere agreement of the data, within 
the possible limits of fluctuations of sampling, with the frequencies | 
7 
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