244 ON THE MEAN RESULTS OF OBSERVATIONS. 



combined ; then, summing the n results, dividing by , and denoting 

 the mean values by x, , and f , 



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* = S n a-a + Sn-it. 



And dividing by n - 1, 



8a -a f a- a' 



a + 



r- = - , 

 n-1 n-1 



whence 



a'-a 



x + = - a 



n-1 



The correction, therefore, is + j. 



Similarly, if ^> results be wanting, we find 



Set -pa . 



x + = a + c, 



-|i 



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

 the deficiencies occur. Hence, the correction to be applied to the 



observed mean, x, deduced from the n -p values, is + =". 



n-p 



15. The preceding correction depends, as might have been 

 anticipated, on the difference of the daily means, for the days of 

 deficient observations, and the mean daily mean. "With the view 

 of determining its probable amount, I 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 observations of the year 1843 ; and have calculated the 

 square root of the mean of the squares of these differences, or 



the values of the expression li L =Ll. The values of this 



quantity, which may be denominated the mean daily error, are 

 the following : 



