SEA-FISHERIES LABORATORY. 279 



harmonic sine and cosine formula, but the labour of this 

 would be very great, and the results not at all reliable 

 when only a few cruises in the year are made. It is, 

 however, possible to deduce a "factor" by means of 

 which the temperatures may be corrected in a simpler 

 manner. Daily temperature readings are made at the 

 Carnarvon Bay Light Vessel, which is not far away from 

 Stations 5, 6, and 7, and is situated practically in the 

 fairway of the Channel. From the known variability in 

 sea-temperature at this point during the small periods 

 in question, the corresponding variability at the three 

 hydrographic stations may be deduced by supposing the 

 changes to be parallel ones at both places. There is 

 every reason for supposing that this is the case. 



If the daily temperatures obtained from the light- 

 ship be plotted, it will be. seen that those observed during 

 a period of (say) 25 days may be regarded, without 

 significant error from our point of view, as an " element " 

 of the curve. That is, they may be regarded as lying 

 about a straight line, and since the inclination of this is, 

 of course, the same at all points, the rate of variability of 

 the temperature function may be calculated. Let the 

 straight line be a + bx, we have to determine the con- 

 stant a and the coefficient b, the latter representing the 

 rate of variation of temperature. The mean temperatures 

 for every two or three days during each period of time 

 covered by the quarterly cruises have, therefore, been 

 calculated, and " moments of inertia " have then been 

 obtained (see Elderton " Frequency Curves and Correla- 

 tion, 1906) by Pearson's method. In the notation of 

 the work cited m , which is simply the sum of the mean 



temperatures, is equal to / (ab + x)dx, while m u which 

 J L% 



is the "first moment" is equal to / x(ab + x)dx. We thus 



J L 2 



