ON BIOLOGICAL MEASUREMENTS. 289 



E. Failure to Make the Most Suitable Biological Analysis. (See also No. 6.) 



8. A further example of failure to analyse data in the best way owing to lack of 

 the most suitable preliminary biological method (the statistical method being wholly 

 adequate) is afforded by a paper by Pearl, Gowen and Miner (1910, Maine Agric. 

 Exp. Sta. Ann. Re}).), who in calculating the influence of bulls on the milk-production 

 of their female descendants takes as a measure of the bulls performance : daughter's 

 yield minus mother's yield. This clearly gives an undue advantage to bulls mated to 

 cows of low milk-yield. The error here has practical consequences, since the market 

 value of the bulls would be altered in relation to the verdict of the scientist. 



9. As Klatt (1919, Biol. Zentralb. 39, 406) points out, failure to realise that other 

 relations than that of simple proportionality may, and usually do, hold between the 

 size of an organ and the size of the whole organism vitiates many discussions as to 

 the relative size of organs in different types within one group. The usual plan is to 

 express relative organ-size as a percentage of total size. Since, however, a frequent 

 relation of organ to body is not y = ax, but y = ax b , this is of no value. Parrot 

 (1894, Zool. Jahrb. (Syst.) 7) had arranged a series of birds in a scale according to their 

 percentage heart-weights. Klatt, having previously found that the heart-weight (h) 

 of warm-blooded vertebrates was related to the body-weight (w) according to the 

 exponential formula h = a.w b where a varied considerably, but b was always close 

 to 0-83, re-analysed these figures, and was thus enabled to calculate the real relative 

 heart-weight, which is given by the size of the fractional constant a in the above 

 formula. Thus, for instance, the stork has a moderately low percentage heart-weight, 

 but this is due to its large absolute size. When the value of a is calculated by the 

 correct method, its true (physiological) relative heart-weight turns out to be one of 

 the three highest in the list. 



10. In general, measurements reveal the fact that in many groups there are no 

 final fixed proportions of parts (e.g. many Crustacea), and that the only quantitative 

 constants which are of value are not percentages but exponents. This is true 

 even of certain Mammals (' Monograph of the Voles and Lemmings living and extinct,' 

 M. A. C. Hinton, vol. i, 1926). 



D'Arcy Thompson (' Growth and Form,' chapter ii) gives an historical and 

 critical account of many similar cases where absolute size must be taken into con- 

 sideration in assessing the functional meaning of particular relative sizes of parts. 



A. General Considerations. 



1. Identification. 



The material under investigation should be examined by exact taxonomic methods 

 and care should be taken that the series of specimens dealt with are, so far as possible, 

 correctly identified. The advice of an expert in the group under consideration should 

 be sought if necessary. 



2. Characteristics or the Population Sampled. 



The examination of a sample only supplies direct information respecting the popu- 

 lation as sampled by the methods of collection employed, or, in other words, the 

 population from which such a sample may be regarded as fairly drawn at random. 

 This may often differ materially from : — 



(i) the whole population living at the time of capture, owing, for example, to 

 selection of sex, age or size by the methods of capture ; 



(ii) the average population ordinarily living in the same habitat, owing, for 

 example, to seasonal or other periodic fluctuations ; and 



(iii) the populations of different habitats in the same region. 



The results of the examination of a sample should therefore be supplemented 

 with all possible care by information designed to specify the population sampled, 

 even though such specification is undoubtedly often difficult. The aim should be 

 that any significant (see Section D) discrepancies between samples obtained by 

 different investigators should be assignable to their true causes, whether ago, six, 

 local variation, time, season, method of capture, &c. 



These should always be specified where possible, but in every investigation special 

 points will need to be considered. 



1927 U 



