338 J. F. ENCKE ON THE METHOD OF LEAST SQUARES. 



proposition which mil be frequently applied in the sequel, 



viz. : — 



IV. 



If the probability of an error = is to the probability of an 

 error = A, as \ : e~^^ , then for this set of observations we must 

 assume h-=- V p. 



Such a determination of h admits even of combining together 

 observations relating to heterogeneous magnitudes, as for ex- 

 ample angular and linear magnitudes, provided only it be pos- 

 sible to deduce the relative values of h in reference to the re- 

 spective unities. 



An actual exemplification taken from experience may perhaps 

 serve to illustrate this subject further, by showing how very 

 nearly the function 41 A expresses the distribution of the errors 

 in a sufficient number of observations. It is taken from the 

 Fundamenta Astronomic, in which Bessel has given a memor- 

 able example of the consecutive, strict, and elegant treatment of a 

 series of observations. He determines the value of r by a direct 

 observation of the difference of right ascension of the sun, and 

 of one of the two stars, a Aquila and a Canis minoris, as de- 

 rived from Bradley's observations, to be 



r = 0"'2637, 

 and then compares the number of errors which ought, accord- 

 ing to theory, to occur between the limits 0"*0 and 0"'l, 0"-l and 

 0""2, and so on (always increasing by 0*1), with the errors given 

 by actual experience in 470 observations. 



Expressed in units of r, the interval of 0"'l = 0*3792 r. If, 

 therefore, we seek in the second table the value of the integral 

 for the different limits, we find for 



