186 



of experiments ; the numbers in the first two columns are differences 

 from the freezing-point; those in the first being Fahrenheit's de- 

 grees ; and in the second and third columns, the arbitrary scale divi- 

 sions of the spirit thermometer S. 9 E. 



Table, containing results of co?nparisons between a Standard Mercu- 

 rial Thermometer, atid a Spirit Thermometer with an arbitrary 

 scale of uniform capacity. 



First Series. 



Second Series. 



Standard 



Spirit 



S. 9 E. Ob- 



Standard 



Spirit 



S. 9 E. Ob- 



mercurial 



thermometer 



served minus 



mercurial 



thermometer 



served minus 



thermometer. 



S. 9 E. 



calcvdated. 



thermometer. 



S. 9 E. 



calculated. 



+69-95 

 +66-93 

 +53-15 

 + 40-53 

 +20-83 

 + 17-80 

 -18-44 

 -36-15 

 -43-14 



Scale div. 

 +209-5 

 + 199-7 

 + 156-7 

 + 118-2 

 + 60-1 

 + 51-0 



- 50-5 



- 98-0 

 -117-9 



Scale div. 

 + 0-2 

 -0-1 

 -0-3 

 -0-3 

 +0-2 

 -0-1 

 + 0-9 

 -hl-2 

 -0-2 



+ 65-76 

 +60-04 

 +52-04 

 + 37-72 

 +24-05 

 + 16-01 

 -16-38 

 -29-00 

 -36-33 

 -44-72 



Scale div. 

 + 196-4 

 + 178-3 

 + 153-5 

 + 1103 

 + 69-8 

 + 46-7 



- 44-8 



- 79-7 

 -100-2 

 -123-0 



Scale div. 

 +0-2 

 0-0 

 -0-1 

 + 0-2 

 + 0-4 

 +0-8 

 +0-9 

 +0-4 

 -0-5 

 -11 



To deduce the law of expansion from these comparisons, the num- 

 bers were arranged in equations of the form 



AT + BT=-N=0, (1.) 



where Tis the number of Fahrenheit's degrees from 32°, N the cor- 

 responding number of divisions by thermometer S. 9 E,, A and 

 B being the constants whose value is to be ascertained : the con- 

 stants depending on higher powers of T than the second, were not 

 considered. 



The values of A and B were obtained from the equations by the 

 method of least squares, and were as follows : — 



From first series A=2-8203 B=0-002455 



From second series A=2-8377 ...... 6=0-002221 



The mean of both series giving . . A=2-829 B = 0-002338 



The numbers in the columns " Observed minus calculated," are 

 obtained by taking the difference between the observed readings of 

 the spirit thermometer, and the numbers calculated from the mean 

 values of A and B just stated. 



Having determined upon the adoption of the law of expansion 

 stated above, the graduation of the spirit thermometer was proceeded 

 with as follows. 



The process of calibrating the tubes was the same as for the mer- 

 curial thermometers ; as in these, also, the freezing-point and a tem- 

 perature of 90° or 95° were determined with reference to short 

 scales on the stems ; the distances OF, OH (figure, page 184) were 

 also measured ; and by comparing these measurements with _the 



