methods employed in calibration of mebcurial thermometers. 175 



Marek's Method. 

 Thermometer G. 



(27) Thiesen's method supplies, as has already been shown, more 

 equations than there are unknown quantities. Marek has, therefore, 

 applied the method of least squares to measurements made in this way 

 up to and including the case in which the tube is divided into six 

 intervals. 



As the formulte are somewhat lengthy, those only will be given which 

 suflBce for the correction of four points. First, let the tube be divided 

 into five parts by principal points numbered from to 5 (in this case the 

 dashes will be omitted). Let r,„- be the transferred thread-length 

 measured between the ^t*^'* and i"^ principal points of a thread equal 

 approximately to the interval between them, and let the measurements 

 be made as in Thiesen's method, and let threads equal to 1, 2, 3, and 4 

 intervals be measured with their lower ends at as many principal points 

 as possible. 



Finally, let f (0) = f (5) = 0, then 



In applying these formulae to Thermometer C the principal points 

 would be 100°, 108°, 116°, &c. Hence, taking from the tables of thread- 

 lengths given in Thiesen's methods those which are multiples of 8° in 

 length, and which are measured with their lower ends at their principal 

 point, the following values are obtained : — 



r5, = 7-877 . r53 = 16-164 



743=7-874 . 742 = 16-103 



732 = ''■826 . 731 = 16-097 



721 = 7-859 . 720 = 15-935 

 710=7-668 



■whence, from the above formnlee, 

 (0) = 0,<p (1) = 156, <p (2) = 116, <i, (3) = 112, 9 (4) = 62, <[, (5) = 0. 



If it be required to halve these intervals a thread about 4° long must 

 be used, and the calculations are exactly similar to those given in the 

 third example of Gay-Lussac's method. 



Let Pi and Pq be any two of the principal points where corrections 

 ^ (Pi) and ^ (Po) have just been determined. Let 7,, 73 be the trans- 

 ferred thread-lengths of a thread about 4° long, measured with its lower 

 and upper ends near each of them in turn, and then the correction for the 

 point half-way between them is 



M^2-'-l+^(Pl)+^(Po)}. 



