66 The Rev. H. Lloyd on the Mean Results of Observations. 



U-A„^+ -0024 sin (.r + 244^3) + -0089 sin {2x + 144^4) 

 + -0008 sin (3j- + 27°-9) + -0006 sin (4,t + 78'-5) 

 + -0001 sin (5.r + 228^7) + -0002 sin (6.c + 180"). 



The second term in this formula being the principal one, the mean of the pres- 

 sures observed at any two equidistant hours, so far from approaching the mean 

 daily pressure, may recede from it by the greatest possible amount within the 

 Hmits of the diurnal variation. Tlie error committed, in taking the mean of the 

 pressures observed at three equidistant houi's as the mean daily pressure, is, 



very nearly, 



+ -0008 sin {3x + 27^9) ; 



and cannot therefore exceed -0008. It is needless to inquire into the least 

 value of this quantity, which is in all cases less than the probable error. 



8. The law of tlie diurnal variation of tlie magnetic declination is ex- 

 pressed by the equation 



U^Ao = + 3'-29 sin (,i- + 65°-7) + 2'-08 sin (2.r + 224°-5) 

 + 0'-63 sin (3.B + ll"-!) + 0'-30 sin {ix + 237°-5) 

 + 0'-13 sin (5x + 114°-7) ; 



the coefficient of the last term being evanescent. Hence the error to which we 

 are liable, in taking the mean of the declinations observed at any three equi- 

 distant hours as tlie mean of the day, is, very nearly, 



-I- 0'-63 sin (3^ -|- 71°-7) ; 



and cannot exceed 0'-63. This term vanishes, and the mean of the three ob- 

 served values will deviate from the true daily mean, by an amount less than 

 the errors of observation, when 



x = 36°-l, or, ,1 = 96^1; 

 that is, when 



t = 2'' 25'", or, t = 6* 25'". 



Accordingly, the best hours of observation, for the elimination of the diurnal 

 variation of the declination, are 



2' 25"" A.M., 10" 25"" A.M., 6" 25"' P.M.; 

 and 



e" 25-" A.M., 2* 25" P.M., 10" 25'" P.M.; 



