ON THE MEAN EESULTS OF OBSERVATIONS. 239 



which coincide, almost exactly, with the best hours for the deter- 

 mination of the mean temperature. 



By taking the mean of the declinations observed at any four 

 equidistant hours, as the mean of the day, the limit of error is 

 reduced to 0'-30. 



9. It appears from the preceding, that any three equidistant 

 observations are sufficient to give the daily mean values (and, 

 therefore, also the monthly and yearly mean values) for each of 

 these elements, with nearly the requisite precision ; and that, by 

 a suitable choice of the hours, the degree of accuracy may be 

 augmented as much as we please. But, in determining the par- 

 ticular hours for a continuous system of observations, this should 

 not be made the primary ground of selection. The error of the 

 daily means being in all cases reduced within narrow limits by 

 the method already explained, we should choose the particular 

 hours which correspond nearly to the maxima and minima of the 

 observed elements, so as to obtain also the daily ranges. This con- 

 dition will be fulfilled in the case of the magnetic decimation, very 

 nearly, by the hours 



6 A.M., 2 P.M., 10 P.M. ; 



which will, moreover, give nearly the maximum and minimum of 

 temperature, and of the tension of vapour, together with the maxi- 

 mum pressure of the gaseous atmosphere* And, if we add the 

 intermediate hours, 10 A. M. and 6 p. M., we shall have, nearly, 

 the principal maxima and minima of the two other magnetic 

 elements. Accordingly, for a limited system of magnetical and 

 meteorological observations, at places for which the epochs of 

 maxima and minima do not differ much from those at Dublin, 

 the best hours of observation appear to be 



6 A.M., 10 A.M., 2 P.M., 6 P.M., 10 P.M. 



The conditions of the problem are altered, if at any place the 

 laws of the diurnal variation have been already obtained from a 

 more extended system of observations. In this case the mean of the 

 day may be inferred from observations taken at any hours whatever, 



* The ternary combination above proposed possesses the further advantage of coin- 

 ciding, nearly, with one of those deduced above, aa the most favourable for the deter- 

 mination of the mean temperature and mean declination. The errors of the resulting 

 means are found by making x = 90 in the third terms of the general formulas ; and we 

 thus find the error of temperature = - 0-07, while that of the declination = - 0'-20. 



