298 THE MECHAXICS OF THE EARTH's ATMOSPHERE. 



temperature variation of oue degree gives a pressure variation of 1,3 

 millimetres. 



If however the amplitude of the temperature variation is not uniform 

 throughout the whole height, but diminishes with the height so that it 

 diminishes by one-half for each ascent of 1,000 metres, then a tem- 

 perature variation of ten degrees at the earth's surface gives a varia- 

 tion of pressure at the same level of only 2.4 millimetres. 



In respect to the whole-day wave for continental tropical regions one 

 could be satisfled with this result. The agreement, however, is only 

 accidental. The twelve-hour wave of pressure at sea still remains 

 entirely inexplicable. Even on the land oue should expect that the 

 amplitudes of the whole-day and half-day waves of pressure would have 

 the same ratio as the corresponding temperature amplitudes, since e 

 remains unchanged when we put i L and ^ Q in place of L and O. 



The computation would hold good for a cylinder of great diameter 

 equally as for a plane; even under certain restrictions it would also 

 hold good for a mass of air within a circular boundary. But it can 

 only be applied to the atmosphere when the air is divided into a num- 

 ber of zones by vertical walls parallel to the circles of latitude. The 

 zones in the neighborhood of the latitude of 50° would have enormous 

 variations of pressure, and there also two neighboring zones would 

 have opposite phases; the amplitudes diminish thence toward both 

 the pole and the equator. 



From the great differences in pressure that are thus obtained for dif- 

 ferent zones, we see the necessity of reducing to calculation the condi- 

 tion of the air over the whole sphere without any partition walls. I 

 pass over the formuhe for the sphere at rest in order to report upon 

 that part of the computation that apparently offers useful results for 

 the elucidation of the hSilf-day wave of pressure. First, I will present 

 some passages quoted already by Hann from a memoir of Sir William 

 Thomson's. 



After speaking of the disproportion between the whole and half day 

 Tariation of the temperature on one hand and the pressure on the other, 

 Thomson says:* " We must consider the atmosphere as a whole and 

 investigate its vibrations with the help of the formulae that Laplace has 

 developed for the ocean in the Mecaniqne Celeste, and which, as he has 

 shown, are also applicable to the atmosphere. When in the calculation 

 of the tide-producing force, one introduces the influence of temperature 

 instead of attraction, and develops the oscillations corresponding to the 

 whole day and half day terms of the temperature curve, it will proba- 

 bly be found that in the first case the period of the free oscillations de- 

 parts more from twenty-four hours than in the second case from twelve 

 hours, wherefore for a relatively small amount of tide-producing force. 



* " Ou the thermo-dyuauiic acceleratiou of the earth's rotation," Proc. E. S. Edin- 

 bimjh, 1682, vol. XI. Sir William Thomson. "Mathematical aud Physical Papers," 

 Loudon, 1890, vol, iii, page 344. 



