162 



DEPARTMENT OF THE NAVAL SERVICE 



the order of the calculations. Tlie example here used was a tish from one of the New- 

 foundland samples, belonging to the lOO-t year-class ; the values for the different incre- 

 ments (t) for the specimen in question are shown in the first column of the table. 

 The second column gives the corresponding average values for all Newfoundland fish 

 investigated; the third the deviation of the specimen from these averages; the fourth, 

 the standard deviations for these averages in question; the fifth, deviations of the 

 specimen divided by the respective standard deviations (i.e., deviations of the speci- 

 men expressed in units of the corresponding! standard deviations) ; the sixth, these 

 deviations squared; and finally, the sum of these squares is shown at the foot. The 

 second half of the table is drawn up in a manner exactly corresponding to this, the 

 specimen being here compared with the averages for the 1903 year-class from the Mag- 

 dalen islands. The resulting sums of the squares are, it will be noticed, highly dissi- 

 milar; that for the comparison with the Magdalen islands averages being more than 

 ten times the figures resulting from comparison with the averages for the fish to 

 which the specimen actually belonged. 



It will be interesting to refer to table 48 showing the method of comparison 

 between growth values for a single herring and the corresponding average figures for 

 the herring of two different waters, according to the principle of " least squares." 



Table 48. — Example showing the growth of a single herring compared with average 

 growth of the herring from Magdalen Islands and Newfoundland by the 

 method of least squares. 



Individual herring, to be tested. . 

 Average from Newfoundland san 



pies 



Deviations from Newfoundland 



averages 5 



Standard deviations for Newfound 



land samples cr 



8 

 ~~ Newfoundland 



Gf- 



Averages for Magdelen Islands 

 samples. ... 



Deviations from Magdalen Islands 

 averages 5 



Standard deviations for Magdalen 



Islands samples tr 



5 



c-r 



tia 



8 

 0-7 

 1 

 25 

 0-40 



016 



0-7 

 1 

 21 

 0-48 



0-23 



Resulting s an of fz\ ■ For comparison with Newfoundland averages 27. 

 Resulting sum of /"_ | • For comparison with Magdalen Islands averages 28'5. 



The specimen here dealt with was one of twent.y others selected for examination 

 by this method. Ten of these were taken from one of the Magdalen islands samples 

 among the 1903 year-class, the requisite standard deviations for this year-class having 

 been previously computed; the remaining ten were selected from fish of the 1904 year- 

 class in one of the Newfoundland samples. In order to ensure the obtaining of an 



