J. F. EXCKE ON THE METHOD OF LEAST SQUARES. 349 



The sum of the squares of these errors will be found, either by 

 immediately squaring each single error, or by means of formula 



(14.) to be 



= 1612-0; also m = 29; 

 consequently. 



whence 

 and 



= ^^" = r-5S8, 



r=ie^.gV2 = 5"'-118, 



A = -^ = 0-093, 

 r 



= -i .- 



r 

 the unit being the Parisian line. 



As m=29, and therefore -7-^ =0-08846, it is an equal chance 



that 



£2 . . will be between 6"'-916 and 8"'-260, 

 r,.. „ 4 '665 „ 5 "571, 



h... „ -085 „ -101. 



Lastly, the most probable deviation, in reference to a single 



one of these experiments, has the weight 29 ; consequently its 



probable error (and in like manner the H belonging to it and the 



mean error) 



the limits of certainty of which are given in the same manner 

 from the Umits of r, and it is an equal chance that the true de- 

 viation lies between 



4"'-136 and 6"'-036. 



The value given by theory, 4"'-6, is within these limits ; there- 

 fore the experiments agree with it. They also agree sufficiently 

 well for their small number with the value of r, according to 

 which half the errors should be less than5"'-118. Of twenty- 

 nine errors thirteen are less than this amount, and sixteen 



