182 



of temperature being, nearly, the curve of sines. In this case, 

 then, the mean of the temperatures at any two homonymous 

 hours is, nearly, the mean temperature of the day. This fact 

 has been long known to meteorologists. 



The coefficient as is small in all the periodical functions 

 with which we are concerned in Magnetism and Meteorology ; 

 and therefore the daily mean values of these functions will 

 be given, very nearly, by the mean of any three equidistant 

 observed values. To show this, the author gives the four 

 following groups of results, obtained by combining three 

 eight-hourly values of the magnetic declination, the atmos- 

 pheric pressure, and temperature. The results combined, m,, 

 Ms, Ms, &c., are the yearly mean values corresponding to the 

 hours 1, 3, 5, &c., reckoned from midnight, as deduced from 

 the observations made in the Magnetical Observatory of Dub- 

 lin in 1843. The mean of all the values, corresponding to the 

 twelve hours of observation, is denoted by a. 



Means. 



Declin. 



Pressure. 



Temperature. 



3 (m, + Mg + Mn) - a 

 3 (^5 + Wi3 + M21) - « 



^(M7 + Ml5 + M33)-a 



+ 0'-5 



-0-3 



-0-1 



0-0 



+ •0005 

 + •0005 

 -•000 5 

 -•0005 



+ 0''-l 



0-0 



-0-3 



+ 0-2 



It appears, then, that three equidistant observations are 

 sufficient to give the daily mean values (and therefore also 

 the monthly and yearly mean values) for each of these ele- 

 ments. In choosing the particular hours for a continuous 

 system of observations, we should select those which corre- 

 spond nearly to the maxima and minima of the observed ele- 

 ments, so as to obtain also the daily range. This condition is 

 fulfilled, in the case of the magnetic declination, very nearly, 

 by the hours 6 a.m., 2 p.m., 10 p.m.; and if we add the 

 intermediate hours 10 a.m., 6 p.m., we shall have, nearly, 

 the principal maxima and minima of the other two magnetical 

 elements, the maximum of temperature, and the two maxima 



