METHODS EMPLOYED IN CALIBRATION OF MERCURIAL THERMOMETERS. 157 



other justification of the course adopted is that, as will immediately 

 be showD, an error of measurement in Bessel's method is of relatively 

 little importance. 



(13) This question is fully discussed in Part II. The following 

 Table may, however, be given here. If e is the probable error of a 

 single thread measurement, and me the probable error of a collection, 

 the numbers in the Table are the values of m^, when ten principal points 

 have been found, and are therefore proportional to the squares of the 

 probable errors, or to the reciprocals of the combination weights of the 

 corrections of the scale obtained by the method to which they refer. 



The probable errors of all thi-ead lengths are taken as the same, though 

 measures on long threads are less reliable than those on short, on account 

 of their greater mobility, and the greater value of the temperature correc- 

 tions with respect to the error of reading. In the case of Rudberg's and 

 Bessel's methods the numbers can only be considered as approximations. 



Table IV. 



To make the result of this table more obvious, the numbers have been 

 plotted down and curves drawn through them in the following figure. 

 The curves serve only to connect the points given by the same method. 

 At these points their ordinates are proportional to the squares of the 

 probable errors of the corrections. The enormous differences between 

 them will be at once appreciated. Care, however, must be taken to avoid 

 drawing false conclusions. The numbers have no reference to any 

 approximate assumptions. They refer only to the methods as exemplified 

 in this Report, e.g. for Bessel's and Thiesen's methods, with 10 threads 

 and so on. Had Thiesen's method been applied to determine five 

 points only, instead of ten as was actually the case, the ordinates would 

 have been doubled. This points to a fundamental distinction between 

 such a method as Thiesen's and Gay-Lussac's. Gceteris paribus, the larger 

 the number of points corrected by the former, the more accurate is the 

 correction of each, whereas in Gay-Lussac's method the reverse statement 

 holds good. 



The extreme irregularity of the Hallstrom carve depends on the want 

 of symmetry of the method. The extraordinary accumulation of the errors 

 at the seventh and ninth points is sufficient to condemn it as presented 

 by Pfaundler. 



