The Rev. H. Lloyd on the Mean Results of Observations. 69 



ample, those produced in the atmospheric pressure by the passage of the areater 

 aerial waves), which complicate the problem, inasmuch as a different process 

 is required for their elimination. 



In the reduction of the magnetical and meteorological observations 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 ob- 

 servations, 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 ehminated 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 - .<•, 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 m/M/ar diurnal change. 



Let the mean oit\xe four equidistant observed values commencing with the 

 n'" hour be denoted, for brevity, by IV„; then the epochs of the means IV,, 

 IV3, IV5, are 10 a.m., noon, and 2 p.m., respectively; so that the two conditions 

 are satisfied by the combinations 



A(IV, -f IV5), and IV3. 



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

 noted by III„, the epochs of the means III,, III3, III^, IIL, are 9 a.m.? 11, 

 1 P.M., and 3 respectively; so that both conditions are satisfied by the com- 

 binations 



i (III, -MHO, and 1(111, -h III,). 

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

 combinations can be had, and therefore both changes (regular and irregular) 



