January 2, 1891.] 



SCIENCE. 



9 



refrained from taking any notice of it. But now that this last 

 memoir has recently been brought to the attention of English, and 

 especially of home, readers, justice to himself requires that this 

 matter shall not be allowed to remain unnoticed any longer. 



The question of the cause of the high j)ressure in the subtropical 

 zones, according to the old theory, is one of the relation between 

 kinetic and potential enei-gy ; that is, between velocity and press- 

 ure. As the air of the upper part of the atmosphere moves toward 

 the poles, it is supposed to become crowded and checked in its 

 motion, and the kinetic energy changed to pressure. But the 

 question arises as to why this takes place up to a certain latitude 

 only, that of maximum pressure, and not all the way up to the 

 poles; for the maximum velocities of the upper poleward-moving 

 currents must be a little above this latitude, and the converging 

 of the meridians increases up to the pole. As long as kinetic 

 energy is changed to pressure, this must be increased; and so the 

 greatest pressure must be at the pole, and not down at a low lati- 

 tude. But it may be shown that the whole effect is so extremely 

 small, that it is not worthy of any consideration practically. 



The following general expression of the relation between press- 

 ure and velocity is taken from " Recent Advances in Meteorology," 

 p. 194 : — 



h s- - si 



(1) log P„ — log P = iy4oi (1 + .oo4t) + 360940(1 + .004r)' 

 in which P is the barometric pressure in millimetres of any part 

 of the air with corresponding velocity s; P„ equals 760 millime- 

 tres, being taken as the value of P at the earth's surface, and the 

 corresponding value of s equals s^ ; h is the difference of altitudes 

 corresponding to P„ and P; and - is the temperature by the Centi- 

 grade scale. If M, V, and x are the meridional, longitudinal, and 

 vertical velocities respectively at any given point, we have 

 (3) s= = u- + v^ + x^. 



The numerical constants in (1) are adapted to common loga- 

 rithms, and the expression is strictly applicable to the case only in 

 which r is constant and in which friction may be neglected. 



The first term in the second member of (1), depending upon h, 

 arises from gravity. Where only small portions of air are con- 

 sidered, or strata of very small depths, the part of the pressure 

 depending upon h is so small in comparison with the whole at- 

 mospheric pressure, that it may be neglected, and the expression 

 may then be put into the following form : — 



(3) 



P.-P=' 



206 (1 + .004r) 



This is substantially the same, in different measures and nota- 

 tion, as that of Kaemtz {Lehrbuch der Meteorologie, vol. i. p. 150), 

 when used at the earth's surface, where p' = 760 millimetres. 



In the application of the preceding expressions it is necessary to 

 know the value of s^ corresponding to Pg ; but this js known in a 

 few special cases only, since we do not have a complete solution 

 of the dynamic problem of the general circulation, in which the 

 condition of continuity and the frictional conditions are taken 

 accurately into account. It is also necessary to know the stream- 

 lines, since P and P„ must be in the same stream-line. 



It IS evident from the observations of the cirrus clouds at Zi-ki- 

 wei (latitude 31° 13' north) that the velocity of the poleward- 

 moving curi-ent of the upper part of the atmosphere at this latitude 

 cannot be more than about two metres per second, or four 

 miles and a half per hour (see Popular Treatise on the Winds, 

 etc., p. 133). Let us now suppose that there is a perpendicular 

 wall on the parallel of 35° extending all around the globe, and 

 reaching up to the top of the atmosphere, and that the whole 

 upper half of the atmosphere has a motion, from some cause, 

 directly against this wall, with a velocity u. The current in this 

 case will pass directly down to the earth's surface, where, near the 

 wall, we must have sensibly s„ = 0. Supposing, now, that 

 Pg = 760 millimetres when the whole atmosphere has no meridi- 

 onal component of velocity, and that A Pq is the effect of the 

 upper current : we get from (1), in this case, 



u" 

 (4) log (760 + A Po)= log 760 + 360940(rTT004;)- 



Putting u — 3, and r = 0, this gives a P(, = .0194 millimetres, 

 or about .00076 of an inch of barometric pressure. The increase 



of barometric pressure in the high-pressure belt, above the 

 normal pressure, is about 0.3 of an inch. So the old theory, 

 even upon the extreme supposition that the whole kinetic energy 

 of the upper current is converted into pressure in the high-pressure 

 belt, accounts for only about the ;f J^ part of the observed increase 

 of pressure in this belt. When we consider, then, how small a 

 part of the kinetic energy of the upper current is changed to press- 

 ure, and that the most of it passes on to higher latitudes, how 

 extremely small must we suppose the effect from the old theory 

 to be ! 



Where there is friction, of course some of the kinetic energy is 

 changed into heat, and so the pressure is accordingly diminished; 

 and a little greater velocity would be required to cause the same 

 increase of pressure. 



In what precedes we have supposed the kinetic energy to have 

 its origin from some other source than a pressure gradient; but in 

 the interchanging motions between the equatorial and the polar 

 regions, toward the pole above, and the contrary below, this is 

 not the case, but the pressure must decrease from the equator to 

 some middle latitude where the velocity ti and kinetic energy are 

 the greatest, and then increase from that to the pole, where it is 

 and the pressure the greatest. The preceding formula is appli- 

 cable in this case at the equator and the poles, since s„ =0; and, 

 putting u = 2 metres per second, we get A Pq = .0194 millimetres, 

 as before. If vve suppose P„ to be in the latitude where ti^ = u, 

 that is, where the velocity of the return current is the same as the 

 maximum velocity u above, then, instead of u^ in (4), we have 

 u'^ _ itl = 0, and hence we get A Pq in this case equal 0; that is, 

 there is no change of pressure here arising from the interchanging 

 motion between the equator and the pole. The pressure, there- 

 fore, is a little greater at the equator and the poles than at the 

 latitude where m is a maximum, which, on account of the con- 

 vergency of the meridians, and the narrowing of the intermeridi- 

 onal spaces, toward the poles, is between the middle latitude and 

 the equator, and perhaps near the parallel of 35°. Instead, there- 

 fore, of an excess of barometric pressure here of about 0.3 of an 

 inch, there should be a very slight depression, if there were no 

 other forces to cause this excess. And this is very evident from a 

 very simple manner of considering the matter : for as long as the 

 air, in moving from the equator, is acquiring increased velocity, 

 there must be a descending pressure gradient ; but, as soon as there 

 is a decrease of velocity, there must be an ascending gradient to 

 cause it. The same is true in the lower strata of the atmosphere, 

 where the air returns from the polar to the equatorial regions. 

 The oscillations of the air-particles between these regions are similar 

 to those of a pendulum, in which the force from both sides acts in 

 the direction of the middle point. 



With regard to the effect of descending currents, to which Dr. 

 Hann ascribes the local high barometric pressures of the middle 

 and higher latitudes, already referred to, the formula (4) can be 

 applied in this case also. We have only to substitute for u the 

 vertical component of velocity x. This being done, we can readily 

 compute what the value of x must be to give A Pq equal to any 

 assignable value. Let us suppose it is requii-ed to find wiiat value 

 X must have to give A P,, = 35 millimetres ; that is, an increase of 

 barometric pressure of about one inch. We can, in this case, 

 assume «„ — 0, at least in the middle of high-pressure area. The 

 formula in this case gives a; = 71.3 metres per second, or about 

 160 miles per hour, if we put r = in the formula. For a higher 

 temperature this velocity must be greater. 



If any one is disposed to doubt this result given by the formula, 

 let him take the experimental result obtained by Mr. Dines and 

 others, that a velocity of about seventeen miles per hour gives a 

 pressure of one pound per square foot upon a plate exposed at 

 right angles to the current. But the pressure of the whole atmos- 

 phere, corresponding to 30 inches of mercury, is about 3,100 

 pounds. The pressure corresponding to one inch, therefore, is 70 

 pounds. As the pressure is as the square of the velocity, we must 

 have .-« = 17 X V 70 = 143 miles per hour, to give a pressure equal 

 to one inch of barometric pressure. This result is less than that 

 obtained theoretically, because it is well known that the experi- 

 mental pif ssure upon a small plate is greater than the theoretical, 

 on account of tlie effect of friction of tlie air which passes around 



