THE METHOD OF LEAST SQUARES. 57 



demonstration. For it is beyond question distinctly conceiv- 

 able, that different laws may exist in different classes of ob- 

 servation ; and that which is distinctly conceivable is a priori 

 possible. So that we cannot prove it to be impossible, though 

 we may be able to show empirically that it is not true. 



You will probably agree with me in thinking that a wrong 

 notion of Laplace's reasoning lies at the root of the reviewer's 

 new demonstration. But we now come to the demonstration 

 itself. The assumption that the law of error is in all cases 

 the same, is, we are told, justified by our ignorance of the 

 causes on which errors of observation depend. The law 

 " must necessarily be general, and apply alike to all cases, 

 since the causes of error are supposed alike unknown in all.' 7 

 Two remarks are suggested by this statement: in the first 

 place, that our ignorance of the causes of error is not so great 

 but that we have exceedingly good reason to believe that they 

 operate differently in different classes of observations ; and in 

 the second, that mere ignorance is no ground for any infer- 

 ence whatever. Ex nihilo nihil. It cannot be that because 

 we are ignorant of the matter we know something about it. 

 Or are we to believe that the assumption is legitimate, inas- 

 much as it in a manner corresponds to and represents our 

 ignorance? But then what reason have we for believing that 

 it can lead us to conclusions which correspond to and repre- 

 sent outward realities? And yet the reviewer at the conclu- 

 sion of his proof asserts, that, on the long run, and exceptis 

 excipiendis, the results of observation " will be found to group 



themselves according to one invariable law." Thus the 



assumption, though "it is nothing more than the expression 

 of our state of complete ignorance of the causes of error and 

 their mode of action," leads us by a few steps of reasoning to 

 the knowledge of a positive fact, and makes us acquainted 

 with a general law, which is as independent of our knowledge 

 or our ignorance as the law of gravitation. 



Let us, however, suppose it to be true that the .law of error 

 is always the same, and that equal positive and negative errors 

 are equally probable. To determine the special form of the 

 law, the reviewer employs a particular case he supposes a 

 stone to be dropt with the intention that it shall fall on a 

 given mark. Deviation from this mark is error ; and the pro- 



