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



observations. In this case tlie mean of the day may be inferred from observations 

 taken at anij hours whatever, by the addition of a known correction ; and the 

 hours of observation should therefore be chosen chiefly, if not exclusively, with 

 reference to the diurnal range of the observed elements. 



10. The ne.-ct question which presentsitself for consideration, with respect to 

 the daily means, is one which affects more nearly the reduction of the obser- 

 vations hitherto made at Dublin. In the extended system prescribed by the 

 Council of the Eoyal Society in 1839, and followed at the Magnetical .Obser- 

 vatory of Dublin during the four years commencing with 1840, observations 

 were directed to be taken twelve times, at equal intervals, throughout the day, — 

 namely, at the even hours of Gottingen mean time. In a system of observa- 

 tions so frequent, and extending over so considei'able a time, blanks must 

 imavoidably occur ; and the question which presents itself here is, — in what 

 way are the daily means to be deduced in such a case ? 



It has been shown that the effect of the regular diurnal variation may be 

 nearly eliminated, and the mean of the day obtained, by taking the mean of 

 three equidistant observed values. For the elimination of the irregular changes, 

 however, the nmuber of observations combined should be as great as possible ; 

 and in the case of the magnetic elements, in which these changes are often 

 very considerable, this condition is an important one. 



Now it is obvious that the twelve results of any day may be resolved into 

 two groups of six equidistant results, or into three groups oi four, or miofour 

 groups of three. Hence, when one result is wanting in the day, the mean may 

 be inferred either from one group of six results, from two groups of four re- 

 sults, or from three of three. The last of these combinations, containing nine 

 separate results, is, of course, to be preferred. When two results are wanting, 

 the mean may be inferred from one group of four results, or from two groups 

 of three ; of which the latter combination, containing six results, is to be pre- 

 ferred. When three results are wanting, the mean of the day can only be in- 

 ferred (in general) from one group of three ; and when more than three are 

 wanting, that mean cannot be generally obtained. 



11. What has been said above applies to the irregular changes of short 

 period, such, especially, as those to which the magnetic elements are sub- 

 ject. But there are also irregular changes of longer duration (as, for ex- 



