ON ERRORS OP OBSERVATION. 131 



unknown, and the variations do not follow any dis- 

 tinguishable rule, their effect upon general results 

 differs in nothing perceptible from that of the observer's 

 own errors, with which they are mixed up in the par- 

 ticular results of observation. 



Before any trials are made, that is, before any thing 

 is known of the character of the observer, of the instru- 

 ment he uses, or the perceptibility of the phenomenon, 

 we can have no reason to suppose that any one observ- 

 ation is more likely to exceed the truth than to fall 

 short of it. When any observation is greater than the 

 reality, the error is called positive ; when less, negative. 

 The hypothesis, therefore, of an equal presumption for 

 positive and negative errors, is one with which we must 

 commence ; and it follows from the supposition that 

 the average is the most probable result of a number of 

 discordant observations. The sum of all the observations 

 will be affected by the balance of all the errors, but 

 will be without error itself if the amount of the positive 

 errors be equal to that of the negative ones. This last 

 supposition, though not probable in itself, is never- 

 theless more probable than any other, and the odds are 

 very much in favour of its being nearly true. Now 

 whatever may be the error of the sum of observations, 

 say 100 in number, the average, or the hundredth part 

 of the sum, contains only the hundredth part of that 

 error; and the presumption that such an average is 

 very near indeed to the truth, greatly exceeds the pro- 

 bability in favour of any one of the observations. 



But before we proceed further, it becomes necessary 

 to ask what laws of error can be absolutely determined, 

 and shown in the nature of things to exist? And 

 first, what do we mean by a law of error ? Let A B 

 be a length to be measured * or estimated, subject to 

 error of observers and instruments ; and let the greatest 

 possible errors be B K (negative), and B L (positive) ; 

 so that the result of measurement may be any thing 



* The second figure is an enlargement of part of the first. 

 K 2 



