ON ERRORS OP OBSERVATION. 129 



have not been accurate, it is still reasonably probable 

 that the average of their guesses would be nearly true ; 

 the limits of error would certainly be larger. It is the 

 object of the present chapter to show how the theory of 

 probabilities must be applied to the detection of the 

 most probable result, when various observations are 

 discordant with each other. 



Error, as used in this part of the subject, merely 

 means discordance of which the cause is unknown. In 

 the different branches of physics, in their application to 

 the arts, &c. c., that which we signify by the pre- 

 ceding word may arise from various causes, the chief of 

 which are here enumerated. 



1 . From some law of nature not known to the 

 observer. Thus before the discovery of the aberration 

 of light, all the small yearly changes which the places 

 of stars receive from that cause, only appeared in the 

 form of embarrassing differences between the observ- 

 ations of different months. Those who used astro- 

 nomical instruments might suspect the existence of 

 some unknown motion in the heavenly bodies; they 

 might think it extremely improbable that their improve- 

 ments in the art of observing should permit purely 

 casual discrepancies of so large an amount as those 

 which occurred : but still, so long as no account of the 

 magnitude of these possible results of law could be 

 given, those who observed could in no manner dis- 

 tinguish them from the imperfections of the instru- 

 ments, or of the human senses. But had it been 

 shown that these discrepancies were always the same at 

 the same time of the year, for any one star, they would 

 then have ceased to be errors, and would have become 

 the objects of prediction, as soon as one year's observ- 

 ations had been registered. The physical cause might 

 or might not have been subsequently discovered, without 

 altering the state of the question : the certainty of a 

 phenomenon is all that is required to remove it from 

 the domain of probability. 



2. From the personal constitution of the observer ; 



K 



