Method of reducing Experimental Results. 101 



But Mr. Lupton has not done this ; and without some such 

 process of trial and error, which might occupy years, it is 

 difficult to see how any evidence bearing on this question of 

 breaks, which is the pivot of the whole controversy, can be 

 obtained by the method which he advocates. If we decide 

 with Mr. Lupton to represent a certain arbitrarily selected 

 series of results by a continuous function, any break which 

 may occur within the range of the function will necessarily 

 be smoothed out. This is " excessive smoothing " * with a 

 vengeance. It seems clear therefore that in any satisfactory 

 investigation as to the real existence of breaks some method 

 differing from that favoured by Mr. Lupton must be 

 employed. 



Now with a bent lath the process of trial and error alluded 

 to above can be carried out to almost any extent ; i. e. any 

 number of continuous curves of great though not excessive 

 generality can be compared with the experimental points 

 until those are discovered which fit best. The test for a break 

 consists not only in the good fitting of the lath throughout 

 each of the two groups formed by several consecutive points 

 on either side of the break, but also in the impossibility of 

 getting it to fit to an extent in harmony with the experi- 

 mental errors when a group of points is chosen which in- 

 cludes the break. In such a case two different continuous 

 curves meeting at the break must be drawn, if the experi- 

 mental values are not to be departed from to an unwarrant- 

 able extent. 



It is obvious that breaks, if sufficiently slight, might get 

 smoothed out by this process, and that the method is far more 

 likely to cause such disappearances than to introduce a break 

 where it does not really exist ; a consideration which explains 

 why a particular break might be undetected in one or more of 

 the different series of experiments dealt with by Mr. Pickering. 

 The extent to which the process of trial and error was carried 

 by him may be gathered from the following quotation. 

 " Drawings on several different scales, and with several 

 different points as origins, were made in all cases, and the 

 labour entailed in the treatment of the results has by far 

 exceeded that of the determinations themselves " f . 



Mr. Lupton's preference for a process " which will give 

 the same result in all hands " irresistibly suggests a com- 

 parison between a barrel-organ and a violin. The latter is 

 undoubtedly the superior instrument, and yet it can neither 

 be denied that in the manipulation of the violin " a strong 



* " Nature of Solutions," p. 104. 

 t " Nature of Solutions," p. 68. 



