100 



SCIENCE. 



[Vol. VIII., No. 182 



with a velocitj' of forty miles per hour to blow over 

 it from one end to the other, we have, no doubt, ap- 

 proximately the conditions under which Dr. New- 

 berry made his observations. Such a wind, then, 

 causes a surface gradient In Lake Erie of four feet 

 in two hundred miles. The first effect of the wind is 

 to drive the surface water from one end of the lake 

 toward the other, and thus to cause a gfradually in- 

 creasing sm-face gradient. The difference of pressure 

 arising from this gradient causes a counter-current 

 in the lower strata of the lake, and the static con- 

 dition with regard to change of gradient takes place 

 when the force arising from this gradient is sufficient 

 to overcome the friction, and maintain a counter- 

 current sufficient to return the water below just as 

 fast as it is driven forward above by the wind. This 

 is required to satisfy the condition of continuity, — 

 a condition which, in all such cases, must be satisfied 

 after the maximum gradient has been reached, and 

 there is no further accumulation of water at the one 

 end or a diminution at the other. 



The force of the wind is applied directly to the 

 surface only, but is communicated to the strata be- 

 low by means of the friction between the successive 

 strata of gradually decreasing velocities with in- 

 crease of depth in the upper strata, and gradually 

 increasing velocities in the contrary direction at 

 depths below the neutral plane which separates the 

 direct from the counter currents. If we assum?, as 

 usual, that fricbion is proportional to the relative 

 velocities between the strata, then, in order to dis- 

 tribute equally the force at the surface to the strata 

 below, it is necessary for these relative velocities to 

 decrease in proportion to increase of depth, and 

 finally vanish ; and consequently the absolute velocity 

 must be comparatively very great at the surface, 

 and diminish, rapidly at first and then gradually less, 

 until the neutral plane is reached, when this velocity 

 vaaishes, and changes sign at lower depths. Since 

 the direct velocities in the upper strata are very great 

 in comparison with those of the retrograde motion 

 below, it is evident that the neutral plane cannot be 

 at any great depth in comparison with the whole ; 

 since where the velocities are least the transverse 

 sectional areas must be greatest, in order that there 

 may be as much flow in the one direction as the 

 other. 



Upon the hypothesis of no frictional resistance 

 from the bottom to the counter-flow below, the rela- 

 tive velocities between the strata would vanish, and 

 the maximum velocity of the counter-current would 

 take place, at the bottom. In this case the force by 

 which the water, held at a certain gradient by the 

 force of the wind, tends to be restored to its level, 

 is an exact measure of the force of the wind. This 

 force, it is well known, is measured by the product 

 of the mass into the acceleration of gravity along 

 the descending gradient. But the mass for the same 

 lake being proportional to the depth, and the ac- 

 celeration proportional to the gradient, a relative 

 measure of the force of the wind is the surface 

 gradient multiplied into the depth. For the same 

 wind, therefore, the gradient is inversely as the 

 depth. 



In the case of frictional resistance to the counter- 

 current at the bottom, as there always is, of course, 

 the maximum velocity of the counter-flow, and the 

 vanishing of the relative velocities, take place at a 

 plane a little above the bottom ; and in this case the 

 static gradient must be such that the force arising 



from it must not only be sufficient to overcome the 

 force of the wind, as communicated by friction to 

 the several strata down to the plane of the greatest 

 velocity of counter-floiv, but likewise to overcome 

 the friction of the bottom, communicated in like 

 manner upward to the strata above, as far as to the 

 plane of greatest velocity of counter-flow, where the 

 relative velocities vanish, and where, consequently, 

 the effect of friction from the bottom must stop. 

 But this is small in comparison with the whole force, 

 and for different depths is proportional to the 

 gradient. We therefore still have, for a relative 

 measure of the force of the same wind, in the case 

 of varying depths, the product of the gradient into 

 the depth, and consequently the gradient inversely 

 as the depth. 



If, then, we suppose the depth of Lake Erie to be 

 increased 60 times, or to the depth of 12.000 feet, a 

 wind with a velocity of 40 miles per hour would cause 

 a gradient of only the one-sixtieth part of the ob- 

 served gradient, or 0.8 of an inch, in 200 miles ; but, 

 on the other hand, if the depth were less, the gradi- 

 ent would be proportionately increased. Hence it is 

 seen how greatly the gradient, and consequently the 

 change of sea-level, belonging to a given wind, de- 

 pends upon depth. But the difference of sea-level, 

 of course, other conditions being the same, is propor- 

 tional to the length. Hence, if we increase the length 

 of the lake 15 times, or to a length of 3.000 miles, the 

 difference of level then would be 15 times 0.8 of an 

 inch, or one foot V^T'ith the depth increased 60 times 

 and the length 15 times, we have approximately the 

 conditions of a section of the Atlantic Ocean extend- 

 ing from New York harbor to the coast of France ; 

 and a westerly wind, therefore, of a velocity of 40 

 miles per hour, would cause the sea-level to be one 

 foot higher at the latter place than at the former. 

 But the average wind blowing across the Atlantic we 

 know is very much less than this, and therefore its 

 effect cannot be nearly so great as this. 



The mean annual velocity of the wind across the 

 Atlantic in middle latitudes is approximately known 

 from the mean barometric gradient. The difference 

 between the annual mean of the barometer at Ice- 

 land and the parallel of 35" is about 10 millimetres ; 

 and this gives a gradient on the parallel of 45*^ which 

 corresponds to a westerly wind of about 8 miles per 

 hour. The relation between wind friction upon water 

 and the velocity of the wind is somewhat uncertain; 

 but it inci'eases at least at as great a rate as the 

 first power of the velocity, and probably at a rate 

 considerably greater. But, assuming it to be as the 

 velocity, then the average westerly wind between 

 America and France causes a difference of sea-level 

 between the two of only 2.4 inches. If wind-friction 

 were as the square of the velocity, it would be only a 

 half-inch. It undoubtedly falls somewhere between 

 these two values, but even by the former the effect 

 of the average wind in causing a difference of sea- 

 level is very small. 



But there is another argument, entirely independ- 

 ent of the observations on Lake Erie, or any absolute 

 wind velocities, from which we deduce about the 

 same conclusions. It is well known from barometric 

 monthlv averages that the barometric gradient be- 

 tween Iceland and the parallel of 35"^ is at least twice 

 as great, on the average, in January as in July. 

 Whatever the absolute velocities of the wind corre- 

 sponding to given gradients may be, we know that 

 they are proportional to the gradients, and conse- 



