184 VARIATION, DISTRIBUTION, AND EVOLUTION OF THE GENUS PARTULA. 
its special value for a particular biological problem. Inthe first place, all individuals 
may be united into a single series, when the figures for the mean value and standard 
deviation will define the variety as it occurs in the whole area of its occupation. In 
this case, colonies which are numerously represented in the collections will affect 
the general average far more than series that comprise only a few snails or a single 
specimen. Yet the valley collections were made during approximately equal 
lengths of time, and the varying abundance of rubescens in the several associations 
indicates the biological fact that shells of different sizes and shapes do not occur 
with equal frequency. Furthermore, errors due to inequalities in the number of 
hours devoted to field-collecting balance one another to some extent when all of the 
series are grouped together. Hence, from one point of view, the description of the 
variety on the basis of all specimens grouped together is the best. The figures are 
given in table 118. 
Tasie 118.—Partula otaheitana rubescens. Summary description. 
Mean VALUE. 
Shell. Aperture. Length aper- 
ture + length 
shell, propor- 
Tooth, index. 
Length. Width. Proportions. Length. Width. Proportions. tions. 
Combined series, all mm. mm. p. ct. mm. mm. p. ct. p. ct. 
WEN B.c 00600000 20.6411 .0266) 11.5942 .0154) 56.1709 .0478| 10.4608 .0134| 7.9475+.0100) 76.0105 = .0539| 50.6772 .0337| 1.5578+.0171 
Combined series, 13 
tabulated valleys. .| 20.6388 .0267) 11.5932+.0155| 56.1650+.0478) 10.4606+.0134) 7.9470+.0100) 76.0060+ .0539) 50.6710 .0337] 1.5598 .0172 
Average of all val- 
levaAtyDesmemeeiee 19.8452 11.3392 57.0354 10.2033 7.7924 76.4789 51.3247 1.1838 
Average of 13 tabu- ; 
lated valley types. .| 20.1510 11.4312 56.7029 10.2122 7.8356 76.2401 50.9880 1.5083 
| 
STANDARD DEVIATION, 
Combined series, all 
WOUIEBs.coccc0000c 1.4900 .0188| 0.8643+.0109| 2.6769+.0338) 0.7491+.0095| 0.5618+.0071) 3.0180+.0381} 1.8865+.0238] 0.9603=.0121 
Combined series, 13 
tabulated valleys..} 1.4905+.0189 -8659=.0109| 2.6743 .0338 .7493+.0095| .5622+.0071) 3.0154+.0381) 1.8862+.0238| .9619+.0122 
Average of all val- 
leyaty;pDeSmeseeeecre .6503 .3755 2.0447 -3225 -2842 2.1485 1.2823 -2817 
Average of 13 tabu- 
lated valley types. . .6756 .4738 2.4466 4312 -3550 2.6671 1.5832 .3515 
In the same tabulation, the several mean values and standard deviations are 
averaged, each colony being accorded the same weight as another, irrespective of 
the number of individuals giving the basis for any single constant. Thus, the 
Oopu colony includes 272 shells, while only a single specimen was obtained in 
Apirimaue. The summary gives the average of the typical conditions for the 
several valleys—for all 18, and for the 13 which have been analyzed in detail. 
When the facts are treated in this manner the figure for a given character (as for 
example, shell length) differs from the average for the series taken as a whole; in 
this particular instance the reason is that the colonies which are numerously repre- 
sented in the collections have larger shells than those which include only a few 
