156 



EEPORT 1882. 



of corrections above described to tlie various methods investigated. It is 

 shown in fig. 1, Plate I. 



Gay-Lussac's method was also applied a third time to the thermo- 

 meter. On this occasion a much longer thread 44 m.m. (4°) in length 

 was used. The method of transference was used in finding the correc- 

 tions, and the observations with the thread 2° long were used (for the 

 sake of example) to obtain some secondary points between those found 

 by the longer thread. 



The points determined are shown in fig. 1 , Plate I. 



Hallstrora's and Thiesen's methods were applied to find the corrections 

 of ten principal points, Miirek's of five, Rudberg's of twelve. In all 

 these the method of transference was applied. Bessel's method was also 

 applied, the principal points being 2° apart. The calculations were per- 

 formed twice, as above stated. 



(12) The following Table contains a statement of the number of 

 thread lengths measured in the application of each of these methods. 



Table III. 



The difference in the amount of labour required by the different 

 methods is not to be measured by the number of observations alone. 



In the case of the methods of Gay-Lussac and Thiesen the calculations 

 are extremely short and easy ; those of Hallstrom and Rudberg are not 

 lengthy, but they lack the symmetry of the two just named, and are there- 

 fore less simple in application. The longest of these methods, that of 

 Thiesen, may be completed in a few hours, but the calculations and curves 

 which Bessel's method requires demand an amount of time which must 

 be measured by days rather than hours. The operation of reducing the 

 thread lengths to scale divisions, and performing the work for two full 

 approximations, requires about four days' constant attention. 



It is on the other hand true that the same extreme accuracy of 

 measurement is not necessary, and thus in the example given each thread 

 was measured once only, instead of twice as in the case of the other 

 methods. This is justified partly by the result which previous experience 

 had shown to be probable, viz. that the errors made under such circum- 

 stances are small. Only one of the 138 measures gives an apparent error 

 as great as 0°01, and the mean is, as has been stated, 0°-0024. The 



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