PAPER BY PROF. HELMHOLTZ. 87 



Both these values are positive where the west wind prevails; both 

 negative where the east wind prevails. 

 The equation (4e) can also be written 



Jp ir Oi ^2 L ^1 — 6^2 J 



In order that this may be positive at all latitudes, the following iu- 

 equality must be satisfied 



or, 



Ordinarily this will be the case, since in general 6 increases simulta- 

 neously with p and from a definite value at the pole to a finite value at 

 Ihe equator. Similarly ili'' also increases with p, and from zero at the 



pole to cjf^ p^ at the equator, so that -^ also increases from zero at the 



u 



pole to a definite positive value at the equator. We will therefore des- 

 ignate this case as the normal case. Exceptions can only occur under 

 special conditions within limited zones. 



lu the normal case as we progress along the same level, the warmer 

 TTi lies on the side of the greater p; that is to say, on the side towards 

 the equator, and equally on the side of the greater r if we progress 

 toward the celestial pole ; that is to say, p and r increase toward the 

 same side of the boundary surface, and this surface must be so inclined 

 that the tangent of its meridian section intersects the celestial sphere 

 between the pole and the point of the horizon lying immediately be- 

 neath it. Near the equator, where the pole rises very little above the 

 horizon, this gives an inclination to the boundary surface such that it 

 makes a very small acute angle with the horizon. 



In accordance with this, equation (4a) shows us that under those cir- 



(It 

 cumstances t— is negative along the boundary surface itself. 



Therefore the normal inclination of the bounding surface is in an 

 ascending direction toward a point situated beneath the celestial pole. 

 If on the other hand exceptional localities should exist at which 



oo,-p^-\- ^'^;~_^f' <^ ^^^^ 



d.Y 

 then in such cases according to equation (4a)— i- will be positive ; that 



is to say, the boundary line will ascend to higher levels as we depart 

 from the earth's axis. 



Since moreover equation (4(Z) shows that as we proceed in the direc- 

 tion of a line drawn to the pole, the warmer air must lie higher, there- 



