ON THE MEAN KESULTS OF OBSERVATIONS. 241 



complicate the problem, inasmuch as a different process is required 

 for their elimination. 



In the reduction of the magnetical and meteorological obser- 

 vations made at the Observatory of Dublin, the civil day is adopted ; 

 and the observations being made at the odd hours of Dublin mean 

 time, very nearly, the epoch of the mean of all the twelve results is 

 mean noon. But in the case of deficient observations, the epoch of 

 the mean, inferred from the remaining observations, may deviate 

 one or more hours from noon ; and its amount, therefore (as com- 

 pared with the mean reduced to noon), is affected by an error equal 

 to the change which the observed element undergoes in that time. 

 In the case of the atmospheric pressure, this error is often very 

 considerable, and much exceeds that due to the changes of whose 

 elimination we have hitherto spoken. 



The law of the changes here referred to being unknown, we 

 can only deal with them on the assumption that their course is 

 uniform throughout the space of a day ; and this assumption will, 

 probably, seldom err much from the truth. Upon this principle, 

 the effect of the irregular change will be eliminated by taking the 

 mean of two or more results equidistant from noon (that is, the mean 

 of a forenoon and afternoon result corresponding to the hours x and 

 12 - x y or any combination of such means) ; and we have only to 

 consider in what manner this process can be combined with the 

 elimination of the regular diurnal change. 



Let the mean of the four equidistant observed values commenc- 

 ing with the n th hour be denoted, for brevity, by IV ; then the 

 epochs of the means IVi, IV 3 , IV 5 , are 10 A.M., noon, and 2 P.M., 

 respectively ; so that the two conditions are satisfied by the com- 

 binations 



| (TV, + IV.), and IV 3 . 



In like manner, the means of any three equidistant observed values 

 being denoted by III,,, the epochs of the means IIIi, Ills, Ills* 

 III 7 , are 9 A. M., 11 A.M., 1 P. M., and 3 P.M. respectively ; so that 

 both conditions are satisfied by the combinations 



i (III, + III 7 ), and | (III 3 + IH 5 ). 



12. When, from the number and disposition of the blanks, none 

 of these combinations can be had, and therefore both changes (regu- 

 lar and irregular) cannot be eliminated, we must attend chiefly to 



