merhods elirloyed in calibration of mkkcdiual thermometers. 179 



Bessel's Methol» 

 (As modified hij A. von Oettingeii). 



(29) For a full theoretical discussion of this method, reference must 

 be made to von Oettingen's work, ' Ueber die Correction der Thermometer 

 insbesondere ilber Bessel's Kalibrir-Methode ' (Dorpat, 1865), which has 

 been frequently cited. It will be sufficient here to describe the method, 

 and to refer to some points in which it seems open to criticism. 



A scries of equidistant points are selected, extending over the whole 

 length of the thermometer-scale. The first of these should be at or near 

 the lowest point on the scale, and if (as in the examples here given) ten 

 threads are used, the tenth should be near the middle of the scale. Hence, 

 if the distance between any two consecutive points is taken as the number 

 of entire degrees or of half-degrees, which is most nearly equal to -^^ of 

 the whole scale, the conditions will generally be fulfilled with sufficient 

 accuracy. A mercurial thread is then measured in terms of scale-divisions, 

 when the lower end coincides in turn with as many of the initial points 

 as its length will allow, and this operation is repeated with ten threads 

 of different lengths. 



The conditions which these threads must fulfil as to length are — that 

 when the lower end of the shortest is brought to the first initial point, 

 the upper end shall not reach the tenth initial point (practically, several 

 threads should satisfy this condition), and that when the lower end of the 

 longest is brought to the tenth initial point, the upper end shall be at, or 

 nearly at, the top of the scale. 



The longest thread will thus be measured at ten initial points, and 

 some of the shorter threads will be measured at more. A convenient 

 arrangement is to take the shortest thread about ^, and the longest 

 about ^, of the whole length of the scale. 



Observations other than those in which the end of the thread lies at 

 one of the ten initial points nearest to the bulb are, in the ensuing calcu- 

 lations, treated differently from the rest, and will be called the additional 

 observations. 



Tables XIX. and XX. give the thread-lengths obtained in the case of 

 Thermometer C from the first ten initial points and from the additional 

 observations respectively. For the reasons given above, the lower ends 

 of the threads were not coincident with, but only very close to, the initial 

 points. The error introduced by this fact will be discussed hereafter. The 

 initial points are given in Column 0, the thread-lengths in Columns 

 I. to X. 



Tables XXI. and XXII. are obtained from II. and III. by adding the 

 thread-lengths to the initial points, and thus give approximately what 

 would be the readings for the upper ends of the threads if the lower ends 

 coincided exactly with the initial points. 



These tables give the direct results of the measures. It remains to 

 deduce from them the scale-errors, and it will be convenient to follow 

 von Oettingen's notation closely. Let Vj. be the mean of the numbers in 

 the ¥^ column of Table XXI., H^ the mean of the numbers entered in 

 Columns I. to X. of the same table. Let M be the mean of all the 

 numbers entered in Columns I. to X. of Table XXL, which is obtained 

 by taking the mean either of the ten V^'s, or of the ten H,.'s ; and, lastly, 



n2 



