244 VARIATION, DISTRIBUTION, AND EVOLUTION OF THE GENUS PARTULA. 
to be offset in part by discrepancies in the other, on the law of chances. Hence, we 
may deal with the three series in the above order, without reviewing all of the steps 
in the process, which is precisely the same as in the cases of rubescens and affinis. 
First, assuming that banding is recessive, the empirical proportions of DD, DR, 
and RR mates of the cestata individuals prove to be 31:85:41, which are signifi- 
cantly probable; the correction of the first and third class figures is $, again a 
probable fraction in view of the great number of adults that bear only one young 
snail apiece. When these data are used to test the correspondence between theory 
and observation in the case of the plain parents, the expected numbers in the group 
bearing plain young only and in the group bearing both plain and banded young 
are 185:263, as compared with the empirical figures of 197:251; the difference 
amounts to 12 in 448, or 2.7 per cent. 
Making the assumption that absence of bands is recessive, and inverting the 
tables, the numbers of DD, DR, and RR prove to be the improbable figures 31:85: 
332. Pursuing the analysis further, in the alternative series, expectation and 
observation differ to the extent of 19 in 157, or 12.1 per cent. ‘There are two 
reasons for regarding the former assumption as the more tenable, when the funda- 
mental hypothesis is made as to the Mendelian order of inheritance. 
Next, the sinistral series may be taken by itself, when, under the first assump- 
tion as to the recessiveness of banding, the proportions of DD, DR, and RR prove 
to be 11:39:20, with an indicated correction of %. Theory and observation, in 
the independent test, differ by 5.5 per cent. Supposing plainness to be recessive, 
the three genetic classes would be as 20:27:115, which are improbable propor- 
tions; it is true that expectation and empirical determination differ by only 2 in 
70, or 2.8 per cent, which, however, only partially offsets the unnaturalness of the 
proportionate relations specified. 
Turning now to the fuller dextral series, and proceeding first on the basis of 
the dominance of the plain pattern, we find that DD, DR, and RR are as 20: 47: 20, 
and that the independent test gives a departure of observation from theory of 
only 3 in 286, or 1.05 per cent. When the contrary supposition is made as to the 
relative values of plainness and banding, the analysis breaks down, because the 
expected numbers of RRX RR is 77 per cent of 286, or 220, which exceeds the actual 
number of banded parents with only banded young, viz, 169. 
In brief, the Tenaire material is very complex, and the results are not entirely 
consistent, but there is a preponderance of evidence (1) that the phenomena are 
Mendelian, and (2) that the absence of bands is dominant to their presence. 
Maara VALLEY. 
The colony is quite as complex as before, while there are additional difficulties 
due to small numbers. The numbers of plain and banded snails are as follows: 
Plain. Banded. 
Whole population 91/203 =44 p.ct. 112/203 =55 p. ct. 
Sinistral population 57 /133 =42.8 p. ct. 76 /133 =57 p. ct. 
Dextral population 36/ 72=50 p.ct. 36/ 72 =72 p. ct. 
