CANADIAN FISHERIES EXPEDITION, lOl'i-lo 273 



altogether. We then obtain the area S of the projection of the closed curve upon the 

 equatorial plane, by pro.iectinjr the curve u]ion the level of the surface of the sea, and 

 multiplying the area a thus obtained by the sinus of the latitude*^ i.e., 



iS = a sin If) ■■' 



Inserting this value for S in -(7), we obtain 



dC da 



dt ^"' dt 



V 



And if, again, we insert in this formula the value for 2 oj, viz., 0.0001458, we obtain 



d C da. ,^^ 



—- = — 0.0001458 -y- sm ^ (8) 



d t d t 



This formula (8) is specially suited to the treatment of measurements of velocity in 

 the sea, as these measurements always give the horizontal components of the velocities; 

 i.e., the projection of the direct velocity upon the level of the sea's surface. 



No measurements of velocity were made during Dr. Hjort's expedition in the 

 Canadian waters, and we have therefore no opportunity of applying the Bjerknes' for- 

 mula for rotation of the earth to observations here in the regular manner above 

 described. We have therefore recourse to another, more indirect application of the 

 same, we can reckon out the velocities which the water should have in order to fulfil 

 the requirements of Bjerknes' equation, with the distribution of density as found by 

 Dr. Hjort. By this means, we obtain indirectly an idea as to the movement of the 

 water within the area of investigation. 



In Bjerknes' equation (6), the first and last terms are small in comparison with 

 the two intermediate ones. As a first approximation, therefore, we may disregard the 

 former and write 



^-'- -dt- 

 or, instead of this, taking the projection of the closed curve upon the level of the sea 



A = 0.0001458 — ^ sin ^ 

 dt 



From which we obtain 



dt 0.0001458 sin <r,' 



(9) 



In this formula, the right side is determined by the distribution of density, and the 

 left by the movement of the water. The right side is known from table 5, which shows 

 A for a large number of closed curves throughout our area of investigation. In con- 

 sequence, therefore i.e., the deformation of these curves, due to the movement of 



d t 



the water, will likewise be known. By this means, we are able to calculate the move- 

 ment of the water from the distribution of density. 



Obviously, however, we cannot by this means obtain the whole movement of the 

 water. We might imagine, for instance, a closed curve composed of water particles in 

 a current, following the current in such a manner that the area of its projection upon 

 the level of the sea's surface would not be altered thereby. This would, then, according 

 to formula (9), contain no solenoids at all. But this does not necessarily imply that 

 the water in whic"h the curve appears, and of which it forms a part, has no great 

 velocity. In other words, the formula (9) gives, not the absolute velocity of the curve, 

 but only its deformation, i.e., the extent to which its one part moves relatively to the 

 other. 



The closed curve should therefore be selected in such a manner as to give the least 

 possible degree of movement in the one part. As equation (9) gives the movement of 



