314 



Royal Society.. 



■with a bulb of the same dimensions as those intended to be sup- 

 plied to the Admiralty, and filled with the alcohol. This thermo- 

 meter was marked S. 9 E. Comparisons were then made between 

 the readings of this instrument and those of a standard mercurial 

 thermometer, through as large a range of temperature as was found 

 practicable. The comparisons above the freezing-point were taken 

 in water, in the apparatus described in my former report ; those 

 below 32° were taken in freezing mixtures of ice and salt or chloride 

 of calcium. The following Table contains the results of two series 

 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 comparisons between a Standard Mercu- 

 rial Thermometer, and a Spirit Thermometer with an arbitrary 

 scale of uniform capacity. 



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 T is 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 B=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 



