238 ON THE MEAN RESULTS OF OBSERVATIONS. 



7. The law of the diurnal variation of the atmospheric 

 pressure is contained in the following equation : 



U-A, = + -0024 sin ( # + 244-3) + -0089 sin (2x + 144-4) 

 + -0008 sin (3a? + 27 -9) + -0006 sin (4as + 78 -5) 

 + -0001 sin (5x + 228 7) + -0002 sin (fa + 180 -0). 



The second term in this formula being the principal one, the 

 mean of the pressures 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 limits of the diurnal 

 variation. The error committed, in taking the mean of the 

 pressures observed at three equidistant hours as the mean daily 

 pressure, is, very nearly, 



+ 0008 sin (3tf + 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 the diurnal variation of the magnetic declination 

 is expressed by the equation 



U- A, = + 3'-29 sin ( * + 657) + 2'-08 sin (2* + 224-5) 

 + 0'-63 sin (3s + 71 7) + 0'-30 sin (40 + 237 -5) 

 + 0'-13 sin (5* +114 7), 



the coefficient of the last term being evanescent. Hence the error 

 to which we are liable, in taking the mean of the decimations 

 observed at any three equidistant hours as the mean of the day, 

 is, very nearly, 



+ 0'-63sin(3tf + 717), 



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

 three observed values will deviate from the true daily mean by an 

 amount less than the errors of observation, when 



* = 36-l, or x = 96-l ; 

 that is, when 



t = W 25*, or t = Q h 25. 



Accordingly, the best three 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.; 



625*A.M., 2*25* P.M., 10* 25* P.M.; 



