468 DISCUSSION OF BAROMETRIC OBSERVATIONS. 



interesting as showing the impracticability of obtaining actual conver- 

 gence from a series of observations no longer than the present : 



Bo = 29.7194 



Bi= 0.0480 B4 = .0128 B^ = .0135 



B2= .0210 B5 = .0028 Bs = .0059 



Bs = .0271 Be = .0090 Bg = .0115 



The corresj^onding angles are as follows : 



/?i = 141o 3' /?4= 89^56' /97 = 139o 0' 



/?,= 7 40 /95= 5 8 /58 = 186 12 



/?3= 45 50 /5g = 104 26 /Jg = 242 30. 



Mr. E. L. De Forest, in the Analyst for July, 1877, refers to a previous 

 paper of his own in which he has pointed out a simple test of the accu- 

 racy of the adjustment of a series of values subject to accidental variation. 

 The test quoted is in substance as follows : If the original (observed) 

 values be subtracted from the adjusted values, term by term, the result 

 is the series of residual errors. If the terms of this series be pointed 

 off into groups, by inserting a point of division at every change of sign, 

 the most probable number of terms occurring in groups of three or more 

 is ^ N ± .533 V^', where K denotes the whole number of terms of the 

 series, and the expression following the sign i is the probable error. 

 If the number of terms occurring in such groups falls short of ^ IST by 

 more than the probable error, the inference is that the inequalities of the 

 series have not been smoothed out enough; but if it exceed ^ N by more 

 than the ijrobable error, the series has been smoothed too much. From 

 the nature of the periodic function, the adjustment effected by it would 

 be expected to err (if at all) in the latter of these two directions. In 

 fact, when a series of residuals is formed by subtracting the terms of 

 Table II successively from the corresi^onding terms of Table I, the 

 number of terms or signs occurring in groups of three or more exceeds 

 half the whole number of terms by 79, while the probable error, .533 a/366, 

 is only 10.3. Though a closer approximation to a perfect adjustment 

 might probably be derived by the use of the more exact coefficients just 

 obtained, it seems preferable, for the purposes of comparison, to use a 

 different process of adjustment, and hence the method of successive 

 means has been employed. The arithmetical means between each term 

 of the series of Table II and the next succeeding term form the first 

 order of means, the second is derived in the same way from the first, 

 and so ou until the tenth order of means is obtained, which constitutes 

 Table IV. 



