1863.] 285 IChase, 



motion is greatest ; it therefore presses ngainst the lagging air, and 

 the barometer rises. From 12h. to ISh. the earth moves away from 

 the air, and the barometer falls ; while from 18h. to 24h. the .in- 

 creasing velocity of the air urges it against the earth, and the 

 barometer rises. 



If the force of rotation at each instant be resolved into two com- 

 ponents, one in the direction of the radius vector, and the other 

 parallel to the earth's orbit, it will be readily perceived that when- 

 ever the latter tends to increase the aerial pressure, the former tends 

 to diminish it, and vice versa. Let B = the height of the barometer 

 at any given instant; M=the mean height at the place of observa- 

 tion; — 90° = the hour angle; C= the earth's circumference at 

 the equator; ^ = 24 hours; ^=^ the terrestrial gravity; Z= the lati- 

 tude ; and a simple integration gives the tjjeoretical formula, 

 r sin. 0. cos. 0. COS. I 2c-\ 



^=<i+ s ,tO-* 



This formula gives a maximum height at 9h. and 21h., and a 

 minimum at 3h. and 15h. The St. Helena observations place the 

 maximum at lOh. and 22h., and the minimum at 4h. and 16h., an 

 hour later in each instance than the theoretical time. This is the 

 precise amount of retardation caused by the inertia of the mercury, 

 as indicated by the comparisons with the water barometer of the 

 Royal Society of London. 



Aerial currents, variations of temperature, moisture, and centri- 

 fugal force, solar and lunar attraction, the obliquity of the ecliptic, 

 and various other disturbing causes, produce, as might be naturally 

 expected, great differences between the results of theory and ob- 

 servation. But, by taking the grand mean of a series of observa- 

 tions, sufficiently extended to balance and eliminate the principal 

 opposing inequalities, the two results present a wonderful coinci- 

 dence. 



According to our formula, the diiferences of altitude at 1, 2, and 

 3 hours from the mean, should be in the respective ratios of -5 *866, 

 and L The actual differences, according to the mean of the St. 

 Helena observations, are as follows : 



c 



* -- represents the effective ratio of an entire day. But there is in each day 

 a half day of acceleration, and a half day of retardation, and the ratio for each 



half day is — s-^ = 



2-4 gr- 



