METHODS EMPLOYED IN CALIBKATION OF MERCURIAL THERMOMETERS. 161 



either by Bessel's method or by the mean of two good correction curves 

 obtained by Gay-Lussac's raethod with short threads. This last state- 

 ment is proved by reference to fig. 3, Plate I. The mean Gay-Lussac 

 curve and the Bessel's curve are there shown side by side, and it will be 

 observed that at the points where the Bessel's correction differs moat 

 from Thiesen's, the mean curve diminishes the difference. As the Bessel 

 and the Thiesen curves do not differ by more than 0'007, nor the Bessel 

 and the mean Gay-Lussac curves by more than 0°"00o, the latter may 

 certainly be taken as correct to within this limit. 



There seems, too, no doubt that any of the principal point methods 

 will, with Mr. Brown's instrument, and the methods of approximation or 

 transference used as in this Report, give the principal points correct to 

 O^'OOS. Among these the preference is certainly due to Thiesen's. It 

 must, however, be remembered that the points corrected by these methods 

 in this paper are too far apart to enable accurate curves to be drawn. 

 They are suflBciently numerous to enable a comparison between the 

 methods to be made, which is all that was desired. If they are used 

 to determine points nearer together the number of measurements required 

 and the labour of calculation rapidly increase. 



It seems therefore better to use these methods only as auxiliaries to 

 a short-thread Gay-Lussac curve. 



This should be drawn as a first approximation, the length of the 

 thread being a sub-multiple of the distance between the principal points 

 determined by the more elaborate method. The corrections at these 

 points should then be found, applying the method of transference by 

 means of the Gay-Lussac curve, and, finally, the measures made on the 

 short thread should be used to determine secondary between the prin- 

 cipal points. The third standard of accuracy is more difficult of attain- 

 ment. The discrepancies between Bessel's and Thiesen's figures in 

 Table V. prevent certainty that either curve is correct to less than 0°'002. 

 The method of least squares, as applied by Marek, does not seem to 

 produce numbers differing by more than O'OOl from those given by 

 Thiesen's method. The application of such calculations to so small a 

 number of measures is, indeed, of doubtful utility. 



The thread-lengths measured at Kew do not after correction, when 

 treated as above described (p. 159) to discover residual errors in the 

 initial points, anywhere show signs of an error as great as 0°'002. The 

 same statement, however, holds good for Bessel's curve, obtained in 

 this Report with Mr. Brown's instrument, and yet, as has just been 

 shown, it is difficult to feel certain that it is correct to 0°"002. On the 

 whole, therefore, there can be no doubt that this standard of accuracy 

 can be reached only by the most accurate apparatus and most perfect 

 methods. 



The second standard in which the error of calibration is less than the 

 error of an unassisted-eye reading of the thermometer is that which will 

 probably be most generally aimed at. 



For this purpose the Committee, after considerable experience of 

 Bessel's method on the part of some of its members, are (if an instru- 

 ment such as Mr. Brown's or a dividing engine is used) decidedly in 

 favour of the use of less laborious processes. The extreme length of the 

 calculations required by Bessel's method is in itself a serious drawback — 

 an undetected error may vitiate many hours' work. The sanae or a less 

 amount of time spent in obtaining independent correction curves by Gay- 

 1882. . M 



