72 The Rev. H. Lloyd on the Mean Results of Observations. 



14. Let a: denote the observed value of any element, at any hour on any 

 day ; and let a denote its mean value for that day ; tlien 



x = a + ^, 



in which § is the magnitude of the diurnal variation corresponding to the hour 

 in question. Let there be n days of observation to be combined ; then, summing 

 the n results, dividing by n, and denoting the mean values by x, a, and |, 



£ =a + |. 



Now, at any particular hour of any day, let one of the results be wanting ; 

 and let a' denote the mean for that day; summing the n — 1 results, 



Sn.i X = S„a - a' + S^i^. 

 And dividing by n — 1, 



S^a -a' ^ a- a' 



X = 



+ ^ =a+^ r + ^; 



71 — 1 - ~ n — 1 



whence 



a' — a 



x + d^ = a+ €. 



n — 1 ~ ~ 



a' 

 The correction, therefore, is + 



n-1 ■ 

 Similarly, i£p results be wanting, we find 



Sa' — pa y 



X -\ i-^ = a + ?, 



n — p 



in which Sa' denotes the sum of the means of the days on which the deficien- 

 cies occur. Hence, the correction to be applied to the observed mean, x, 



deduced from the n — p values, is H — . 



•* w — j9 



15. The preceding correction depends, as might have been anticipated, on the 



diiference of the daily means, for the days of deficient observations, and the 



mean daily mean. With the view of determining its probable amount,! have taken 



the differences between the mean of each day and the mean of the month, for 



the declination, the atmospheric pressure and temperature, as deduced from the 



