240 ON THE MEAN EESULTS OF OBSERVATIONS. 



by the addition of a known correction ; and the hours of observa- 

 tion should therefore be chosen chiefly, if not exclusively, with 

 reference to the diurnal range of the observed elements. 



10. The next question which presents itself for consideration, 

 with respect to the daily means, is one which affects more nearly 

 the reduction of the observations hitherto made at Dublin. In the 

 extended system prescribed by the Council of the Royal Society in 

 1839, and followed at the Magnetical Observatory 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 observations so frequent, and extending over so con- 

 siderable a time, blanks must unavoidably occur ; and the question 

 which presents itself here is in what way are the daily means ta 

 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 number of ob- 

 servations 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 of four, or into four 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, 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 re- 

 sults, or from two groups of three ; of which the latter combination, 

 containing six results, is to be preferred. When three results are 

 wanting, the mean of the day can be inferred (in general) only 

 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 subject. But there are also irregular changes of 

 longer duration (as, for example, those produced in the atmo- 

 spheric pressure by the passage of the greater aerial waves), which 



