270 DEPARTMENT OF THE NAVAL SERVICE 



metre. Its breadth is considerably greater, being equal to tlie horizontal distance 

 between the isosteric surfaces. And as it is always bounded horizontally by the same 

 isosteric surfaces, its course may be arrived at by drawing upon a chart the isosteric 

 lines for the level at which the isosteres are situated. This chart will then also give 

 the course and number of all other solenoids in a water layer of one metre's thick- 

 ness at the same level. 



There are thus many ways of drawing up graphic presentments of solenoids. 

 We need not, however, here devote more time to these, but may pass directly to the 

 problem of calculating, in the simplest and surest manner, their number, A. The 

 number of solenoids between two stations in a horizontal water layer of one metre is 

 obviously equal to the difference in specific volume between the two stations at the 

 level in question. Our first task, then, will be to calculate this difference. Let us, 

 for instance, calculate the solenoids between the stations 34 and 35 in section IX. 

 First of all, we note down the depth at which the water samples from each station 

 were taken. This is shown in the first column of table 3. The second column shows 

 the specific volumes for station 34, and the third those for station 35. The fourth 

 column contains the differences between the specific volumes; i.e., the number of 

 solenoids in a water layer one metre thick situated between the two. The signsi 

 before the figures shows the rotary tendency of the solenoids. In the vertical, with 

 greater specific volume, the water will strive to move upwards; where it is less, the 

 tendency will be downwards. The solenoids will thus endeavour to bring about such 

 a rotary movement of the water as should cause it to rise at station 34 and sink at 

 station 35. This is what the signs here show. The signs have thus a certain relation 

 to the order in which the stations appear in the tables. If the stations be reversed, 

 the signs will be changed. 



The next operation is to calculate the number of solenoids in those rectangles in 

 the sea which are bounded by the two stations and the different depths. For this pur- 

 pose, we calculate, from the figures in column 4, mean values for 1-metre water layers 

 at the different intervals of depth. These are shown in column 5. Multiplying by the 

 depth of the intervals in metres, we obtain the desired number of solenoids, as shown 

 in column 6. By this simple and rapid means, it is possible to calculate the number 

 of solenoids between any pair of stations in the. area where observations were carried 

 out simultaneously, or nearly so, however great may be the distance between the 

 stations. The number of solenoids between a station in the Arctic and another at the 

 equator may be calculated as easily as the corresponding value for two stations in the 

 gulf of St. Lawrence. And this is just one of the features which render Bjerknes' 

 circulation theory so useful in discussing the greater phenomena of the sea. 



If the two other pairs of stations in section IX, 33-34 and 35-36, be treated in the 

 same manner, we shall then have obtained all the solenoids in section IX, which can 

 be found from the hydrographical observations there carried out. Fig. 52 shows the 

 number of these, and the areas within which they are found. Here, then, we have yet 

 another method of presenting solenoids. Of the various methods in which this can 

 be done,those shown in figs. 50 and 51 are clearer, but that in fig. 52 is more correct. 



By the method shown in table 3 and fig. 52, we obtain only the solenoids which 

 are found between the hydrographical stations, but not those lying outside. For the 

 latter, the methods shown in figs 50 and 51 are more convenient, permitting, as they 

 do, extrapolation so as to include also the area outside the stations. This extrapola- 

 tion method cannot well be applied to the more exact procedure shown in fig. 52. The 

 extrapolated values might also be of so little value as to leave no reason for preferring, 

 on this account, figs. 50 and 51 to fig. 52. The numerical method shown in table 3 

 should therefore be regarded as the best way of arriving at the number of solenoids. 



On adding up the figures in column 6 of table 3. we obtain the total number of 

 solenoids between station IX 34 and IX 35. The addition may be made either from 

 above or from below. The latter is preferable, the water at greater depths being as a 



