Nov. 



1871J 



NATURE 



91 



water in a direction contrary to the liquid masses which the 

 soutli-east trade-winds tend to draw from the south Atlantic ; 

 at the same time the north-east trade-winds force the waters 

 of the surface, as Franklin supposed, to take a south-western 

 direclion towards the Carribean Sea. In this sea, and in the 

 Gulf 01 Mexico, where the trade-winds exercise no influence, the 

 water continues its course to the north by the Strait of Florida, 

 and thus gives birth to the Gulf Stream. Rut in order to enable 

 the Gulf Stream to advance from the Gulf of Mexico and the 

 Strait of Florida as far as 30° N. latitude, a difference of level is 

 necessitated, which can be calculated by the help of the general 

 formula; for the movement of water in currents ; by this means 

 we find that the level of the water in the Gulf of Mexico ought 

 to be about 6 feet higher than at St. Augu-tine. If we then ob- 

 serve that in accordance with the density of the water at St. 

 Augustine, the level of the sea ought to be found to be about 

 2i\ feet above the point marked zero, which corresponds to the 

 mean density of i, it follows that the level of the Giilr of M-xico 

 is about 9.1 feet above that point, and that the trade-winds are 

 the means of adding a height of 3 feet to the water of that gulf. 



After this immense curr nt — which, in the Strait of Bemini, 

 maybe compared toa river delivering at the rate of 1,600,000,000 

 culjic feet per second— has passed St. Augustine, it pursues its 

 course to the north-east, as has been said above. In order to 

 accomplish this long passage, if has at its disposal, at the most, 

 an incline of \\ feet ; but it is easy to see that the force which 

 results from this is altogether insufficient to accomplish the work 

 which this movement dem.ands, and it eviden ly follows that the 

 Gulf .Stream ought, during all this curse, to be subjected to the 

 action of another force, to which hitherto our attention has not 

 been drawn. But what is this force of which we have thus taken 

 no notice? Singularly, it is an old acqua'ntance, whose function we 

 have not sufficiently unders'ood. although Kepler was the first to 

 announce its importmce. In fact, the force which impels the 

 Gulf Stream towards the north is simply that which results from 

 the rotation of the Earth ; and it acts not only upon the Gulf 

 Stream, but is, as we shall see, the chief cause of all currents, 

 both a'mospheric and marine. That the daily rotation of 

 the earth should exercise an influence up-m all currents which 

 go from the equator to the pol<-s and viccversd, and that the 

 direction of the trade winds are due to the same cause, are facts 

 well kuiiwn. But though it is agreed that thisro'ation acts upon 

 the currents of the ocean, opimon has hitherto been very much 

 divided as to the importance of the action ; some maintainini; 

 that the rotation of the earth is the chief cause why the t iulf 

 Stream and the polar currents follow respectively the directi^^ns 

 north-east and south-west, while others hold that it cannot cause 

 any change to speak of in the courses taken by the ocean currents, 

 courses wh ch they would continue to follow all the same were 

 there no rotation of the earth. But although there is so much 

 dispute as to this point, every one agrees in acknowledging that 

 we know but Utile about the matter, and in any cise not'.iing 

 certain of the laws which regulate the movements of the ocean 

 a'ld atm isphere ; for we are at pre-ent ignorant whether the 

 atoms of water or air move without resistance, or whether they 

 meet and are subject to the action of certain forces, and we 

 know still le-s about the origin of these foives, their mag- 

 nitude, &c. This ignorance on the suliject of the influence 

 which the rotation of the earth exercises upon the currents 

 is evidently due to th^ impcriect knowledge which we have 

 of the laws which regula'e the movement of fluids in cur- 

 rents ; for if we had been able to ebtabli-.h that such a 

 force ought to be in play, we would, without doubt, .'^oon 

 hive de'ermined the true expression. The thing 's, in fact, 

 very simple ; if we suppose that a section of element cur- 

 rent flows from the equator in the direction of the meridian 

 in a definite channel, that line will turn with the earth with a 



'' TT A* 



speed from west to east = "■,- ^ cos 0, 9 representing the lati- 



S6400 

 tude, and R the'radius of the earth. After a time dt, during 

 which the current in question will arise at latitude d + d 6, 

 it will act upon the sides of the canal as if it were sub- 

 jected to a force which, in the time d /, had communicated to it 



an increase of speed — — — sin. 8 d 6 from west to east, the line 



86400 

 of current being supposed perfectly free. The force which results 

 from the rotation of the earth ciaild then be represented by 



it = ^ sin. fl I ) = sin. e V 



86400 ^d l' 80400 



V being the speed in the supposed channel. But the movement 



not being free, since the material section which we are consider- 

 ing is forced to move in a channel from south to north, it will 

 exercise per unit of ma.ss against the sides of the canal, a pre.'isure 

 1^ directed from west to east. If the section, as we have supposed,' 

 forms part of a current compelled to movecircidrrly in a channel, 

 it is evident that the surface of the wa'er will rise from left to 

 right ; and if we designate the height by what it rises by /;, for a 



breadth of channel = /, we shall have — g —r = '- — ^• 



The trajectory being the same, it is clear that the surface of the 

 current ought to present the same .'■lope, whether it moves in a 

 channel or flows freely in the middle of the sea. But it is no 

 less evident that whatever be the situation of this trajectory on the 

 surface of the globe, the section which in the lime / is found at 

 latitude 6, and after the infinitely small time di, arrives at latitude 

 8 + d 0, ought, under the influence of the rotation of the earth, 

 to move in the same manner as if, the earth being immovable, it 

 had been driven from west to east with a force 



sin. 0. sin. in v 



13750 



where v still represents the speed of the section under considera- 

 tion, and K' the angle which the direction of the trajectory described 

 makes with the eastern part of the circle of latitude. But we 

 cm, in consequence, put aside the rotation of the earth, and 

 consider the latter as immovable if to the other forces which 

 act upon the water, we add the force 1// acting from west to east. 

 If we decompose this into two other rectangular forces, one of 

 them following the direction of the current, which, let us suppose, 



has throughout its course a firll -r-, , we find that its surface 

 •= df. 



ought to present from left to right, and perpendicularly to the 

 direction of the current, an elevation y , whose value is given by 

 the equation 



(I) 



13750 



and that the liquid mass is impelled for.vard by a force 



sin. 8 sin. 





L 13750 d^- 



which, in accordance with my theory, leads to the following 

 equation of the movement of the current : — 

 (2) „ - <■''- 1^^ . 0-01 6 y- + ''. '''0+ f' r, <■ _(. 5in.(;sin.-..o^s.w F-t- r„ ; 



2^ 3 3g H 13750 ig 



where « is the fall of the current in the length A. H its depth, 

 K„ its initial speed, an-i Fits final speed after having run the 

 course L. In short, if, according to the theory, we place for the 

 delivery of the current per second 



(i) 2 = 0-82 V.H.L 



we shall have the fundamental formulas which give the laws of 

 the course of ocean currents over the whole surface of th-' globs ; 

 the angle 9, which is positive in the northern hemisphere and 

 negative in the southern, having its values compreheU'led between 

 o^ and 90', while the angle Zt', following the direction of move- 

 ment, may be found in the 1st, 2nd, 3rd, or 4th quadrant. 



It follows from these three formulas that all the currents of the 

 northern hemisphere, whatever be their direction, have a surface 

 which gofs on rising from left to right, and whose progress, the 

 force resu'ting from the rotation of the earth, accelerates or retards 

 according as they move in the 1st or 3rd, or in the 2nd or 4th 

 quadrant : hence it follows that a movement in one of these la'ter 

 quadrants is possible Only when the current possesses a sufficent 

 fall, or an equivalent force, due, for example, to the action of 

 the wind, the specific weight of the water of the sea, &c. When 

 the current follows the meridian, the inclination of its surface, 

 perpendicularly to its direction, is at the maximum ; but besides 

 this, the rotation exercises no influence upon its course. When 



the current flows at right angles to the meridian, the fall -r = O, 



and the rotation has, in short, no eflfect upon its cour.-e. 



If, then, we consider the Gulf Stream from its exit from the 

 Gulf of Mexico, we see that, in its passage from Bemini to St. 

 Augustine by the Strait of Florida, where it runs directly with, 

 the current is kept up by a dilfeience of level which, as has been 

 stated above, may, for that e.xtent, be estimated at six feet. 

 Throughout this course the current presents from west to east 

 an elevation whose total value is about I 3 feet. 



From St. Augustine to the Bay of New York the Gulf Stream 



