40 Arrangement and Formation of the Series. [CHAP. u. 



subject is impossible at the present stage. For one thing, it 

 would involve too much employment of mathematics, or at 

 any rate of mathematical conceptions, to be suitable for the 

 general plan of this treatise : I have accordingly devoted a 

 special chapter to the consideration of it. 



The main reason, however, against discussing this argu 

 ment here, is, that to do so would involve the anticipation of 

 a totally different side of the science of Probability from that 

 hitherto treated of. This must be especially insisted upon, as 

 the neglect of it involves much confusion and some error. 

 During these earlier chapters we have been entirely occupied 

 with laying what may be called the physical foundations of 

 Probability. We have done nothing else than establish, in one 

 way or another, the existence of certain groups or arrange 

 ments of things which are found to present themselves in 

 nature ; we have endeavoured to explain how they come to 

 pass, and we have illustrated their principal characteristics. 

 But these are merely the foundations of Inference, we have 

 not yet said a word upon the logical processes which are to 

 be erected upon these foundations. We have not therefore 

 entered yet upon the logic of chance. 



12. Now the way in which the Method of Least Squares 

 is sometimes spoken of tends to conceal the magnitude of 

 this distinction. Writers have regarded it as synonymous 

 with the Law of Error, whereas the fact is that the two are 

 not only totally distinct things but that they have scarcely 

 even any necessary connection with each other. The Law of 

 Error is the statement of a physical fact ; it simply assigns, 

 with more or less of accuracy, the relative frequency with 

 which errors or deviations of any kind are found in practice 

 to present themselves. It belongs therefore to what may be 

 termed the physical foundations of the science. The Method 

 of Least Squares, on the other hand, is not a law at all in the 



