1913-14.] Principia Atmospherica. 79 
Section III. — Propositions. 
Proposition 1 . — To define the conditions for the persistence of the existing motion of the 
atmosphere. 
Proposition 2. — To show that the rate of increase of pressure-difference per kilometre 
of height is 34 - 2 L ( ^ ^ ) ; and hence that the distribution of pressure in the strato- 
& 6 \ d p) * 
sphere is the dominant factor in the circulation of the air at the surface ; that the inter- 
mediate layers between 4 kilometres and 8 kilometres exert little influence upon the 
distribution of pressure. 
Proposition 3.- — To show that the wind velocity across the slope of pressure at any level 
is proportional to 0 ; and thence to show how to utilise observations of the pressure 
and temperature to calculate the wind velocity at any level. 
Proposition 4. — To show that the wind velocity generally increases with height until the 
substratosphere is reached, and falls off with increase in height in the stratosphere. 
Proposition 5. — To show how the distribution of pressure and temperature in the 
upper air can be calculated from the observations of structure represented by a sounding 
with a pilot balloon, and thence to account for the local distribution of rainfall when an 
upper current from the north-west crosses a lower current from the south-west. 
Proposition 6. — To account for the average general circulation over the Northern 
hemisphere in the four-kilometre level as set out in Lemma 2. 
Section I. — Axioms or Laws of Atmospheric Motion. 
The time has arrived when it seems possible and desirable to formu- 
late the laws and principles which can be effectively employed at the 
present day in the explanation of many of the recognised phenomena of 
the structure and circulation of the atmosphere, and to illustrate their 
application. These laws and principles are the result of observations some- 
times suggested or controlled by theory. They are of the nature of 
axioms or inductions, about the validity of which a good deal of discussion 
is possible. Into that discussion I do not now propose to enter. The 
axioms really depend for their justification upon their effectiveness in 
explaining observed facts. They are set out as follows : — 
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. 
The line of argument in favour of this law, which cannot strictly speak- 
ing be either verified or contradicted by any available process of observa- 
tion, is as follows : The condition specified in the law is the condition of 
