as an Indicator of the Earth's Rotation, fyc. 57 



The mean of the above differences varies from the theoretical 

 mean less than -5 oVo °f an mcn - If we take the mean of the 

 ratios instead of the ratios of the means of the observed differ- 

 ences, the coincidence is still more striking. 



Difference of time 1 h. 2 h. 3 h. 



Means of observed ratios -498625 -864625 1-000000 



Theoretical means -500000 -866025 1-000000 



The calculated time for the above-observed means differs less 

 than 20" from the actual time. 



Observed means -498625 -864625 1-000000 



Theoretical difference of time . 59' 48" 119' 40" 180' 



Observed difference of time... 60 120 180 



The varying centrifugal force to which the earth is subjected 

 by the ellipticity of its orbit, must in like manner produce 

 annual tides. The disturbing elements render it impossible to 

 determine the average monthly height of the barometer with 

 any degree of accuracy, from any observations that have hitherto 

 been made. We may, however, make an interesting approxima- 

 tion to the annual range, still using the St. Helena records, which 

 are the most complete that have yet been published for any sta- 

 tion near the equator. Comparing the mean daily range as de- 

 termined by the average of the observations at each hour, with 

 the mean yearly range as determined by the monthly averages, 

 we obtain the following results : — 



Approximate 

 Year. Daily range. Annual range. Ratio. solar distance, 



"in. in. m. 



1844 -0672 -1650 2-4553 137,0/0,000 



1845 -0646 -1214 1-8793 80,300,000 



1846 -0670 -1214 1-8120 74,650,000 



3)-1988 3)-4078 3)6-1466 



•0663 ~ 7 1359 2-0489 95,446 000 



Mean -0663 _jl290 1*9457 86,056^000 



2)-1326 2)-2649 2)3-9946 



•0663 -1324 1-9973 90,702,000 



The approximate estimates of the solar distance are based on 

 the following hypothesis : — 



Let e = effective ratio of daily rotation to gravity. 



a = arc described by force of rotation in a given time t. 

 r = radius of relative sphere of attraction, or distance 

 through which a body would fall by gravity during 

 the disturbance of its equilibrium by rotation. 

 A= area described by radius vector in time t. 



