148 REPORT — 1882. 



(5) Methods of calibration and correction may be divided into four 

 classes; 



The first contains what may be called the step hij step method, which 

 is due to Gay-Lnssac.^ In it a thread of mercury is measured in a posi- 

 tion A B, then shifted to B C, so that the lower end is in the position 

 previously occupied by the upper end, then measured again, and so on 

 for the whole length of the tube. From these measures the corrections 

 for the points B, C, D, &c. can be deduced. 



The second class contains what may be called principal point methods. 

 In these a number of equidistant points are selected on the uncorrected 

 scale, and the corrections for these are determined by means of threads 

 the lengths of which are approximately equal to or multiples of the dis- 

 tance between two consecutive points. 



Several methods are included in this class. 



Hallstrom's^ is a modification of Gay-Lussac's, in which an attempt is 

 made to prevent the risk of the accumulation of ei'rors inherent in the 

 use of very short threads. Two slightly different varieties of Hallstrom's 

 method are described by A. von Oettingen and Pfaundler, of which the 

 latter has been employed by the Committee. If the tube be divided into 

 the parts A B, BO, &c. by principal points, a thread approximately equal 

 to two of these parts is measured with its lower end at each of the points 

 in turn. A second thread nearly equal to three of the parts is measured 

 with its lower end at each of the two lowest principal points, and from 

 these observations the corrections are deduced as desci'ibed in Part II. 



Dr. A. HandP has recently described a method of calibration which 

 appears to differ from those of Gay-Lussac and Hallstrom only in the 

 form of the calculations. 



Another method has been devised by M. Thiesen.^ The scale being 

 divided into n parts by principal points, threads equal in length to 

 1, 2, . . ii — 1 of these intervals are measured with their lower ends 

 coincident in turn with as many of the principal points as possible, and 

 hence the corrections are deduced. 



Mai'ek* has applied the method of least squares to the calculation of 

 the corrections for any number of pinncipal points less than seven. 



By all these methods the corrections can be determined for as many 

 points as may be desii'cd, either by taking the principal points near 

 together, or by breaking up the intervals between them by secondary 

 points. There is, however, one method — Rudberg's" — the essential 

 feature of which is the breaking up of corrected scale intervals into 

 smaller sections. This method therefore constitutes the third class, which 

 may be called that of repeated subdivision. In this method the tube is 

 first divided into two equal parts by measuring a thread of approximately 

 half its volume, when the lower and upper ends are in turn at the 

 extremities of the tube. These portions are then subdivided into three 



' See Pierre, Poffff. Annalcn, Bd. 57, S. 55t, and Ann. de Chlm. et de Phys. s^r. iii. 

 iv. p. 427; Welsh, Proc. Roi/. Son. vi. p. 178, and Phil. Mag. (4) iv. p. 306 ; A. von 

 Oettingen, op. cit. p. 43, Verdet, Cunr.i de Phys-iqiie, i. p. 64. 



2 See Poffff. Ann. Bd. 9,S. 535 ; Muller-Pouillet's Lckrbuch der Physik (Piaundlei) ; 

 A. von Oettingen, oj>. cit. S. 51. 



' Carl's Mepertorium, Bd. xvii. Ht. 5. 



« Ibid. Bd. XV. S. 285. 



» Ibid. Bd. XV. S. 300. 



« Poffff. Annalcn, Bd. 40, S. 574 ; A. von Oettingen, ojf. cit. S. 50. 



' 



