242 ON THE MEAN RESULTS OF OBSERVATIONS, 



that which is greater in amount. For the purpose of comparing 

 their magnitude, I have taken the differences of the successive 

 daily means, for the decimation, the atmospheric pressure, and 

 the temperature, as deduced from the observations of the year 

 1843; and have calculated the square-root of the mean of the 

 squares of these differences. The results, which may be taken as 

 the measures of the irregular changes from day to day, are the 

 following : 



Mean Fluctuation from Day to Day. 



Magnetic decimation, . . . Fluctuation = 1/-04. 



Atmospheric pressure, ... =0 -214. 



Atmospheric temperature, . . = 3'07. 



Similarly, if we take the differences of the yearly means corre- 

 sponding to the successive hours of observation, and combine them 

 in the same way, we obtain the mean two-hourly fluctuations, 

 arising from the regular diurnal change. These numbers are the 

 following : 



Mean Fluctuation in two Hours. 



Magnetic declination, . . . Fluctuation = 2' f 04. 

 Atmospheric pressure, ... =0 -0065. 



Atmospheric temperature, . . 1'46. 



These numbers, compared with the twelfth part of the former, 

 serve to measure the relative magnitude of the regular and irregu- 

 lar changes to which the elements are subject in the same time. 

 We thus find that, in the case of the magnetic declination, the 

 irregular change (which is less than -^th part of the regular) may 

 be safely neglected ; and we have only to attend to the diurnal 

 changes, and to the irregular changes of short period. The daily 

 means are, therefore, to be deduced from one of the combinations 

 of Art. 10, giving the preference to that which contains the great- 

 est number of individual results. 



In the case of the atmospheric temperature, the irregular change 

 (which is less than one-fifth part of the regular) is small ; and we 

 must attend chiefly to the latter. The mean of the day is, there- 

 fore, to be inferred from one of the combinations of Art. 10, giving 

 the preference to those of Art. 11, whoe epoch is noon. 



In the case of the atmospheric pressure, on the contrary, the 

 irregular change (which is triple the regular) is the more import- 

 ant. The mean of the day is, therefore, to be deduced from any 



