System of Winds on the Earth. 499 



holds good for the displacement of the air rotating with the 

 earth's surface in a meridional direction. To this I cannot 

 agree, but, on the contrary, must deny that the conservation 

 of the moment of inertia comes into play in the motion of 

 the air. 



This law of areas, taken from astronomy, states that a mass 

 which rotates freely about another describes equal areas in 

 equal times. This is due to the acceleration of the rotating 

 mass as it approaches and its retardation as it recedes from 

 the centre of attraction of the fixed mass. The greater 

 velocity acquired by acceleration results in the description of 

 a larger arc in the unit of time, and so leads to the law of 

 areas. According to Ferrel a quantity of air rotating in any 

 latitude with the earth's surface cannot travel in the direction 

 of the meridian with an invariable absolute velocity, and 

 therefore with a constant vis viva as I assume it to do, but its 

 moment of inertia must remain constant, which corresponds 

 to a considerable change of velocity. In order that the 

 moment of inertia may remain constant (which is the case 

 when the linear velocity of the rotating body varies so that 

 equal areas are described by it in equal times), a considerable 

 amount of energy must be expended to produce the alteration 

 in the velocity of the inert mass of air. But there is no force 

 whatever available to perform this work. If the radius of 

 rotation of a rotating solid body is shortened, the force which 

 produces the shortening must overcome the centrifugal force. 

 The sum of the products of all the centrifugal forces into the 

 paths traversed gives the work expended in the acceleration 

 of the rotating mass, and this exactly suffices to maintain the 

 law of areas, that is, in this case the moment of inertia con- 

 stant. But no analogous relations exist in the case of the 

 motion of the air on the earth's surface, where no alteration 

 in the force of attraction is caused by the tangential displace- 

 ment, and no acceleration of the shifting mass by gravitation. 

 Nor is it clear how the neighbouring air-strata can exert a 

 pressure on those to be displaced capable of performing the 

 considerable work of acceleration which the maintenance 

 of the moment of inertia requires. A displacement of tbe 

 whole mass of air of a rotating ring in the meridional direction 

 cannot moreover take place, for the volume of such a ring of 

 definite thickness varies as the cosine of the latitude, and with 

 a polar displacement a corresponding portion of the mass of 

 the ring must either lag behind or return to the equator. 

 But even as regards that portion of the ring actually dis- 

 placed in the polar direction, there is no physical reason for 

 assuming a conservation of the moment of inertia in the case 

 of currents of air; such an assumption would, on the contrary, 



