6 THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



to use the general terms liquid, gas, and fluid when neglecting the re- 

 sistance, compressibility, elasticity, and viscosity as in dealing with 

 these ideal substances, and to reserve the terms air, water, etc, for use 

 when dealing with actual natural fluid phenomena where slight com- 

 pressions and expansions and resistances occur. 



The relation between elastic pressure, volume, and temperature, as 

 deduced by Boyle, Mariotte, Gay-Lussac, and Charles, that characterizes 

 a gas, and the equation for which the Germans call the " Zustands- 

 Gleichung" in common with other equations of condition, I have pre- 

 ferred to speak of as the equation of elasticity or the characteristic equa- 

 tion of a perfect gas. 



In view of the remarkable want of uniformity existing in English 

 and American works in respect to the notation for total and partial 

 differentials I have decided to make such alterations in the original 

 notations of these papers as shall make the whole series consistent with 

 the elegant and classical notation that is rapidly being adopted in Ger- 

 many, and that will, 1 hope, eventually be accepted by ail English and 

 French writers. In accordance with this I shall always ex])ress the 

 total differential by <?, as first introduced into geometry by Leibnitz for 

 the infinitesimal difference; the small increment or variation by 6, as 

 introduced by Lagrange; the \a,v go, finite difference by J, first used by 

 Euler; the partial differential by ^, (" the round d,") as used bj- Jacobi. 

 Occasionally the dotted variable x will indicate the rate of variation 

 with regard to the time, or the fluxion as first introduced into mathe- 

 matical physics by Sir Isaac I^ewton, a notation which has lately been 

 extensively revived in England by those devoted to classic authority. 



Evidently the problems here treated by elegant mathematical meth- 

 ods are not always precisely the problems of nature. The differences 

 between the conclusions of Kayleigh, IMargules, and Ferrel as to the 

 diurnal and semi-diurnal tides due to heat, or the differences between 

 Ferrel, Oberbeck, and Siemens on the one hand and nature on the other 

 as to the general circulation, show that by the omission of apparently 

 minor local and periodical irregularities we have constructed for our- 

 selves problems that still differ from the case of the earth's atmosphere, 

 although they may more closely represent the conditions of such a 

 planet as Jupiter. 



I have to acknowledge the assistance of my friend, Mr. G. E. Curtis, 

 in copying a portion of the formuhie for these translations, and renew 

 the expression of my hope that a coming generation of American meteor- 

 ologists may prosecute to further conquests the mathematical studies 

 begun by Ferrel and perfected by our European colleagues. 



Cleveland Abbe. 



February, 1S91. 



I 



