METnOUS EMPLOIED IN CALIBRATION OF MERCURIAL THERMOMETERS. 149 



by means of a thread of about one-third the whole length of the tube, 

 ■which is measured in the positions (see figure, p. 178) A rf) cZ e, e B, 

 C/, and C g . The process can then be carried further, as described in 

 the detailed account of this method. 



The fourth class of correction methods also comprises one only — ^viz., 

 Bessel's — which may be called a distributed point method. 



In this all the threads are measured with their lower ends at certain 

 ■selected points, but as their lengths are not multiples of the distances 

 between these points, but are within wide limits arbitrary, the cori-ections 

 are determined at numerous points more or less irregularly distributed 

 over the scale. 



In von Oettingen's modification of the method the corrections are 

 finally calculated by drawing correction curves through the points deter- 

 mined by each thread, and taking the means of their ordinates. Pro- 

 fessors Thorpe and Riicker have introduced some changes into von 

 Oettingen's method of correcting the lower and upper parts of the scale. 

 An example of both systems, and a full discussion of the method are 

 given in Part II. Although too detailed to be introduced here it may be 

 said that the examples given prove that Professors Thorpe and Riicker's 

 alterations increase the rapidity with which the method approximates to 

 the true correction curve. 



All the methods above mentioned (with the exception of Handl's) 

 have been tested by the Committee, and as the results are probably suSi- 

 cient for the practical purpose in view, they have not extended their inves- 

 tigation to several others which have been proposed by various writers. 



They may, however, refer to the plans suggested by Egen (' Pogg. Ann.' 

 Bd. XI. s. 529), Rowland ('Proceedings of the American Academy of 

 Arts and Sciences,' Juno 1879), and Pickering (' Physical Manipulation,' 

 PartIL, p. 75). 



(6) Many of the methods of correction theoretically require that one 

 or both ends of the thread should occupy definite positions in the scale. 

 It is impossible, unless the tube is uniform or is perfectly corrected, 

 to establish this coincidence at both ends, inasmuch as a thread which 

 would comply with the condition in one part of the scale would fail to 

 fulfil it in others. In the case, too, where the theoretical position of one 

 end of a thread is indicated by a scale mark, the breadth of this is often 

 so considerable that it is difficult to observe with accuracy the position of 

 the end of a thread which is concealed by it. 



Sometimes it is impossible, and often it is inconvenient, to bring 

 the thread end into its theoretical position. In cases where errors 

 might be introduced by this failure to comply with the exact conditions 

 of the method, they may be allowed for in two slightly diflerent ways. 



The first plan is that of farther approximation. The corrections for 

 the extremities taken out from the correction curve are applied to the 

 measured thread lengths, and then, by repeating the calculations with the 

 corrected values, farther corrections are obtained, which must be added 

 to those previously found. A second approximation is thus worked out 

 in Part II. in the second example of Gay-Lussac's method (p. 166). 



In some cases, however, if the threads are not measured in their 

 theoretical positions, it is convenient to avoid the necessity for a second 

 approximation by the preliminary use of a correction curve drawn by any 

 simple method. Let the thread end be situated at M, and let the cor- 



