56 



Mr. P. E. Chase on the Barometer 



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

 whenever 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 observation; — 90°= the hour-angle; C= the 

 earth's circumference at the equator; t = 24< hours; g= the 

 terrestrial gravity ; /= the latitude : and a simple integration 

 gives the theoretical formula 



- R _ M /, sin cos 6 cos / 2C\* 

 V + * ~W~ " *gF) * 



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

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

 maximum at 10 h and 22 h and the minimum at 4 h and 16 h , 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 baro- 

 meter of the Royal Society of London. 



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

 trifugal 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 observation. But by taking the grand mean of a 

 series of observations, sufficiently extended to balance and elimi- 

 nate the principal opposing inequalities, the two results present 

 a wonderful coincidence. 



According to our formula, the differences of altitude at 1, 2, 

 and 3 hours from the mean, should be in the respective ratios of 

 •5, *866, and 1. The actual differences, according to the mean 

 of the St Helena observations, are as follows : — 



Differences of Barometer. 



Ratios. 



Difference of time 

 Before lh 



lh. 



•0166 



•0159 



•0122 



•0135 



•0136 



•0131 



•0161 



•0150 



2h. 



•0298 



•0266 



•0202 



•0239 



•0248 



•0215 



•0287 



•0265 



3h. 



•0365 



•0298 



•0243 



•0297 



•0284 



•0227 



•0348 



•0286 



lh. 

 •455 

 •534 

 •502 

 •455 

 •479 

 •577 

 •463 

 •524 



2h. 

 •816 

 •893 

 •831 

 •805 

 •873 

 •947 

 •825 

 •927 



3h. 



After lh 



Before 7h 



After 7h 



Before 13h 



After 13h 



Before 19h 



After 19h 





Mean 



•0145 



•0252 



•0293 



•495 



•860 



1 





9? 



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 lor each half day is o ~4~ F* 



