78 
Proceedings of the Koyal Society of Edinburgh. [Sess. 
the atmospheric circulation as it presents itself to my mind, arranged in the 
normal scientific form, with axioms which represent inductive laws, with 
postulates or lemmas which represent groups of observed facts, and with 
propositions leading to conclusions which are susceptible of verification. 
Synopsis. 
Section I. — Axioms or Laws of Atmospheric Motion. 
1. The Law of the Relation of Motion to Pressure. 
In the upper layers of the atmosphere, the steady horizontal motion of the air at any 
level is along the horizontal section of the isobaric surfaces at that level, and the velocity is 
inversely proportional to the separation of the isobaric lines in the level of the section. 
2. The Law of the Computation of Pressure and of the Application of the Gaseous Laws. 
The pressure at any point in the atmosphere and at any instant is the weight of the 
column of air which stands upon one unit of horizontal area containing the point. The 
numerical values of pressure, temperature, and density at any point of the atmosphere are 
therefore related by the usual formulae for the gaseous laws. 
3. The Law of Convection. 
Convection in the atmosphere is the descent of colder air in contiguity with air relatively 
warmer. 
4. The Law of the Limit of Convection. 
Convection in the atmosphere is limited to that portion of it, called the troposphere, in 
which there exists a sensible fall of temperature with height. The upper layer of the 
atmosphere, in which there is no sensible fall of temperature with height and therefore no 
convection, is called the stratosphere. 
5. The Law of Saturation. 
The amount of water vapour contained in a given volume of air cannot exceed a certain 
limit, which depends upon the temperature and upon nothing else. 
Section II. — Lemmas or Postulates. 
Lemma 1. — In the stratosphere, from 11 kilometres upwards it is colder in the high 
pressure than in the low pressure at the same level; and in the troposphere, from 
9 kilometres downwards to 1 kilometre, it is warmer in the high pressure than in the low 
pressure at the same level. [W. H. Dines, M.O., 2106.] 
Lemma 2. — The average horizontal circulation in the Northern hemisphere in January 
between 4 kilometres and 8 kilometres consists of a figure-of-eight orbit from west to east 
along isobars round the pole, with lobes over the continents and bights over the oceans. 
The average circulation at the surface is the resultant of the circulation at 4 kilometres 
combined with a circulation in the opposite direction of similar shape due to the distribution 
of temperature near the surface. [L. Teisserenc de Bort, Ann. du Bureau Central Mete'oro- 
logique , 1887 ; and W. N. Shaw, Proc. Roy. Soc ., vol. lxxiv. p. 20, 1904.] 
