188 



SCIENCE. 



[Vol. VII., No. 16a 



mentum, corresponding to that of a uniform velocity 

 of ten miles per day for all the strata. We can only 

 judge of the force of the winds, as exerted upon the 

 surface of the ocean, by the amount of momentum 

 produced in a given time ; and, from the small amount 

 of momentum produced in so long a time, this force 

 must be very small. 



Let us now examine the effects of gravity as called 

 into play by the gradients of the strata of equal 

 pressure, arising from unequal upward expansions 

 due to differences of temperature. Referring to my 

 notes upon this subject, I make the following extracts 

 from a larger table, in which the temperatures and 

 the upward expansions are given for three stations at 

 the given depths in the first column : — 



Depths 



IN 



Equator. 



Lat. 23°. 2 N. 

 Long. 3x°.7 W. 



Lat. 37°.9 N. 

 Long. 41°.7 W. 



FATHOMS. 



Temp. 



Expan. 



Temp. 



Expan. 



Temp. Expan. 







25°. 5C. 



5.1ft. 



22°. 2C. 



7.8ft. 



21°. 1C. 



8.5ft. 



50 



17 .7 



3.9 











100 



13 .1 



3.2 



19 .4 



5.8 



17 .5 



6.7 



200 



8 .1 



2.8 



14 .8 



4.6 



15 .9 



5.2 



300 



5 .7 



2.4 



11 .4 



3.6 



15 .6 



4.0 



400 



4 .6 



2.0 



x .7 



2.8 



12 .7 



3.0 



560 



3 .8 



1.8 



6 .5 



2.3 



8 .2 



2.3 



600 



4 .0 



1.6 



5 .4 



2.0 



5 .3 



1.9 



700 



3 .9 



1.4 



4 .8 



1.8 



4 .8 



1.7 



800 



3 .9 



1.2 



4 .1 



1.6 



3 .4 



1.6 



9:0 



3 .4 



1.1 



4 .0 



1.5 



3 .2 



1.5 



1000 



2 .7 



l.» 



3 .5 



1.4 



3 .2 



1.4 



1500 



2 3 



0.6 



2 .6 



0.9 



2 .7 



0.9 



The temperatures are the means of six soundings 

 of the Challenger expedition, as given by Dr. Croll ; 

 and the upward expansion, computed from Dr. 

 Hann's formula for the density of sea-water, is that 

 arising from the differences of temperature at the 

 different depths, and that of the maximum density 

 of sea-water in the polar regions. The temperatures at 

 the bottom of the stations, ranging in depth from 

 2,500 to 2,700 fathoms, were a little less than 2 C . 

 The upward expansion of the surface at the equator 

 is a little greater than that of Dr. Croll (4.5 feet), 

 ■ Stained by means of Muncke's tables, but the differ- 

 ence is of no consequence. 



It is seen that the temperatures and upward ex- 

 pansions diminish rapidly n^ar the surface, and that 

 ^he !a* f er are small in the lower depths. Supposing, 

 for simplicity, that the pradic-uts are uniform from 

 th i equator to the latitude of maximum density . say' 

 5,<»00 miles from the equator, then the average gra- 

 dient of the whole mass of the ocean, down to the 

 depth of 2,500 fathoms, is about 1.5 feet in 5,000 

 miles, instead of 5.1 feet, as at the surface. The 

 force, therefore, down this average gradient, of the 

 whole mass, is to that of gravity about as unity is to 

 18,000,000. It is readily found, from computation, 

 that this force down this small gradient would give 

 to the whole mass, in four days, a velocity of ten 

 miles per day. According to Zoppritz, the whole 

 action of the winds in 239 years produced only this 

 amount of velocity on a surface stratum of 100 metres 

 in depth, say one-fiftieth part of the whole depth. 

 To produce an amount of momentum, therefore, 

 equal to that of the whole ocean, with a velocity of 

 ten miles per day, would require nearly 12,000 years. 

 Comparing, now, four days with 12,000 years, we get 

 an approximate idea of the relative strengths of the 

 two forces, for these must be inversely as the times 

 required to produce a given amount of momentum. 



The force of the winds upon the ocean, therefore, in 

 comparison with the gravitation force, is almost in- 

 finitely small, if Zoppritz's results are to be accepted. 

 But I have never accepted these, and therefore 

 regard this simply as a very strong argumentum ad 

 hominem on the subject to anyone who accepts 

 them, and also maintains that the winds have any 

 sensible effect in causing ocean-currents. Of course, 

 a very small force, with time enough, will produce 

 any given amount of momentum ; and so the winds, 

 in time, could have caused an amount of motion 

 equal to that observed in the ocean, if no other forces 

 had been in operation ; but with other forces many 

 times greater, causing both vertical and horizontal 

 circulations, of course the effects of the infinitely 

 small force would be entirely lost. 



In the flowing of rivers down a gradient, knowing 

 the gradient and the mass, we have a measure of the 

 force required to overcome the friction ; and thus, 

 from the known depth and velocity, it is easy to 

 obtain approximately the value of the friction-con- 

 stant. From any considerations of this kind I have 

 never been able to obtain a friction- constant nearly 

 so small as that assumed by Zoppritz, and therefore 

 think it is many times too small as applied to rivers 

 or ocean- currents. 



If we assume that the winds can cause the given 

 amount of momentum iu one year, instead of 12,000, 

 we still have their force upon the ocean nearly 100 

 times less than the gravitation force ; and I think 

 good judgment in the matter would decide that a 

 year, at least, would be required for the slight action 

 of the gentle winds blowing over the ocean to give 

 an amount of momentum equal to that of the whole 

 mass, with a velocity of ten miles per hour. I cannot 

 think, therefore, that the effect of the winds is more 

 than one-hundredth part of that of the gravitation 

 force. 



Professor Davis seems to think that the gravitation 

 force is too small, even allowing it a long time to act, 

 to move the whole mass of the ocean. But the 

 greatest tidal gradients with reference to the result- 

 ants of gravitation and lunar forces, are little, if 

 any, greater than that of fifteen feet in 5,000 miles ; 

 yet these move the whole mass of the ocean to the 

 bottom back and forth twice a day, causing regular 



tions and depressions of the surface, now high 

 water, and six hours after, low water. The maxi- 

 mum tidal velocities for all depths amount to a 



ity of nearly a mile per day. I do not think a 

 quarter diurnal reversal of the directions of the 

 winds would give rise to reversed velocities of that 

 amount to a stratum of the depth of ten metres ; and 

 so the effect of the winds would be about 150 times 

 less than that of the tidal forces, which are about 

 the same as those of the gradients arising from the 

 differences of temperature. 



The regular gradients from the equator to the 

 polar regions must be regarded as the initial ones, 

 and consequently the forces arising from them, as 

 the forces which overcome the inertia of the water 

 before the final motions have been fully established. 

 But the directions of the initial motions are very 

 much modified by the deflecting forces of the earth's 

 rotation, and the distribution of the temperature dis- 

 turbances somewhat changed. An interesting exam- 

 ple of this kind is indicated by the temperatures of 

 the last two stations of the preceding table, from 

 which it is seen, that, in the region of the Sargossa 

 Sea, the high temperatures extend down to greater 



