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Part III. — Eighteenth Annual Report 



VII.— ON THE MACKEREL OF THE EAST AND WEST 

 COASTS OF SCOTLAND. 



By H. Chas. Williamson, M.A., B.Sc. 



The present research was undertaken with a view of determining 

 whether or not racial differences existed between the mackerel of the 

 West and East Coasts of Scotland. The method employed is that of 

 separating local forms by the averages of the size, or numbers of certain 

 characters. This method, first employed by anthropologists in the 

 examination of the races of man, has been applied by Heincke* to the 

 division of the herring into local forms. 



The principles upon which the division of a species into races is carried 

 out, and certain of the theories bearing upon the formation of the local 

 form or race, will be found detailed in Heincke's work. 



All the characters of an individual are variable. If, then, we find that 

 the mean of the variations of a certain character in one group differs from 

 their mean in a second group, we are entitled to regard this as a racial 

 distinction betAveen the two. It is necessary to select a number of 

 characters, e.g., the number of the vertebrae, the numbers of fin-rays, 

 measurements on the body, etc., as tests by which the groups may be 

 compared. The greater the number of individuals in each group, the 

 more nearly correct will be the mean (or average). Since, however, we 

 cannot examine all the members of a race we cannot get the true mean 

 directly. By experiment and observation we get a mean which is more 

 or less approximate. From this observed mean we may get two values 

 between which the true mean lies. This is obtained from the Probability 

 curve. One of these two values is obtained by subtracting and the other 

 by adding the probable error of the mean to the observed mean. The 

 two values are represented by the formulas M — r, and M-\-r, where M is 

 the observed mean and r is the probable error. In order to " get a result 

 which is almost absolutely correct, in place of r, five times r is subtracted 

 and added, viz,, M — 5?*, and -M+5r. According to Heincke there are 

 999 chances to 1 that the true mean lies between these limits. The 

 interval between these values is known as the fluctuation of the mean. 

 If now we find that the fluctuations of the means of a character in two 

 groups do not overlap, w r e are entitled to conclude that the true means 

 are different from one another, and therefore so far as this character is 

 concerned the two groups are of distinct races. 



The Mean, the Probable Error of the Mean, the Standard Deviation are 

 obtained from the following formulae, which have been taken from 

 Davenport's "Statistical Methods," Chapman & Hall, 1899. 



The Standard Deviation, o- = \ \/ n 2 (d 2 f)— (2 d) 2 



The Probable Error of the Mean, r = -6745- Z 



n 



n = number of variants ; d = deviation from the mode : 



The Standard Deviation o- is a measure of the range of Variation. 



As bases of comparison between the mackerel of the East and West 

 Coasts, the following characters were selected : — 



* " Naturgeschichte des Herings," Berlin Otto Salle, 1898, text, 1 Halite. 



