ON THE MEAN RESULTS OF OBSERVATIONS. 243 



combination whose epoch is noon, giving, however, the preference 

 to one of those of Art. 11, in which the diurnal change is also 

 eliminated. 



13. I now proceed to consider the reduction of the monthly 

 means, in the case of deficient observations. 



For the purpose of determining the regular diurnal variation 

 of any magnetical or meteorological element, it is necessary to take 

 the mean of an adequate number of separate results corresponding 

 to each hour of observation, so as to eliminate the irregular and 

 accidental changes. The results usually so combined are those 

 of each month. Their number is, in general, sufficient for the 

 purpose above mentioned ; while, on the other hand, the course 

 of the diurnal change is sufficiently different from one month to 

 the next, to demand a separate determination. 



But in the case of deficient observations, the monthly means of 

 the results corresponding to each hour will not exhibit, in general, 

 the true course of the diurnal change without a correction. If a 

 result be wanting at one hour of a day, in which all the results 

 are much above the mean, it is obvious that the monthly mean 

 corresponding to that hour will be too small, as compared with the 

 means of the other hours ; while, on the other hand, it will be too 

 great when all the results of the day in question are beloic the 

 mean. The error will be greater, the greater the variation of the 

 element observed from day to day. In the case of the atmospheric 

 pressure, it is so considerable, that the uncorrected monthly means 

 afford no approximation to the law of the diurnal change, in the 

 case of deficient observations. 



The remedy which first suggests itself, in such a case, is to 

 omit all the results of a day in which one or more are wanting. 

 This process is inartificial and unsatisfactory. The weight of the 

 mean is diminished in the proportion of the number of observa- 

 tions combined ; and it is therefore important to employ all the 

 observed results in its deduction, provided we can obtain a 

 correction. Such a correction is easily found. 



14. Let x denote the observed value of any element, at any 

 hour on any day ; and let a denote its mean value for that day ; 

 then 



x = a + K, 



in which is the magnitude of the diurnal variation corresponding 

 to the hour in question. Let there be n days of observation to be 



R2 



