and Distribution of the Atmosphere, 207 



R cotanX: - — t-— ,or ; which, if the second be the unit 



2co sinX v 



n • i n n -, - m 1 3070 cos X T 



oi time, and the foot the unit of length, is . In or- 



dinary cases the value of this expression ranges from 100 to 

 several hundreds. The tendency to swerve is therefore sensibly 

 the same for motion along a circle of latitude as for motion along 

 a great circle touching it, in the neighbourhood of the point of 

 contact. 



VI. The constraining force on a body moving along a circle 



P 



of latitude is to the body's weight in the ratio — . If the foot 



and second be units, g is about 32*2, and — is ' . Call 



this — . Then if the air between two parallels of latitude is 



m L 



moving east or west with velocity v, the change of pressure is the 

 same in going m feet along a meridian as in rising 1 foot, viz. 

 •00114 inch of mercury. The change of pressure per degree of 

 latitude (365,000 feet), expressed in inches of mercury, is 



x '00114= '0019^ sin X, v being in feet per second. 



The average observed difference per degree is about '01 of an inch. 



5 



This would require v to be about - — - feet per second. 

 ^ sin X i 



VII. For a cyclone, if r denote distance from its axis, and v 

 the component velocity perpendicular to r, centrifugal force 

 computed as if the earth were at rest gives a barometric difference 



l C v 2 



equivalent to rising a height - I —dr. 



The earth's rotation adds to this a difference equivalent to 



Ct 

 rising a height ! - 



%j 



VIII. The following investigation can be employed instead 

 of I., II., III. The earth's rotation co may be resolved into a 

 translation, a rotation about a horizontal axis (at the place con- 

 sidered), and a rotation about a vertical axis. The two former 

 may be neglected. The third is co sin X, which call co r The 

 lateral constraining force is therefore the same for a body moving 

 horizontally in a straight line or in a great circle, as for a body 

 travelling along a radius of a horizontal disk revolving about its 

 centre with angular velocity co r Let r denote distance from 



v dr 



