Royal Society. 313 



of revolutions between the first end of the step / and the point F, 

 and similarly r^ for the step h. We have then 



OF =Rj + Rs + R3 + &c. + R^_j + r, 

 and 0H=Ri+R3+ .... +R,_i + ?-,; 

 whence we obtain r and r^. Let K be the number of degrees 

 equivalent to one length of the caUbrating column, — this being of 

 course constant for each length along the tube on the supposition of 

 equal increments of volume for equal increments of temperature. 

 Also, if we suppose that the capacity of the tube does not vary 



T V 



throughout the length of a single calibrating step, -^ and — will 



R, R 



give the fractional parts of a step by which the points F and H are 

 respectively in advance of the first ends of the steps/ and h. We 

 have then 



and FH = f/j— /+ii— ^)K=T^, the higher temperature— 32°; 

 V R^ R/ 



T 



whence K= ^— . The degree corresponding to the point 



R, R, 



O is 32°— ^/-1 + ^W. The length of one degree for any in- 



R 

 dividual step x is — ?. 

 K 



From the quantities thus obtained, a table may readily be formed 

 showing the value in revolutions of the dividing screw of one de- 

 gree at all parts of the scale, and the graduation may then be pro- 

 ceeded with accordingly. The graduation is carried from — 40° to 

 + 120°or 130°Fahr. 



II. Spirit Thermometers. — In the graduation of mercurial thermo- 

 meters, the practice is to consider the increments of volume to be 

 proportional to increments of temperature. If this were assumed in 

 the case of spirit thermometers, very serious errors would be the 

 result, even within moderate ranges of temperature. Dr. Miller 

 having considered alcohol, as on the whole, the best fluid for ther- 

 mometers intended to measure very low temperatures, I was supplied 

 by him with some which he had himself prepared with great care, its 

 specific gravity being 0"7U6 at 60° Fahr. The first step to be taken 

 was the determination of the law of exjjansion of the fluid in glass, 

 as com])ared with that of mercury. For this ])urpose a tube was 

 calibrated and divided with an arbitrary scale according to Reg- 

 nault's process : its divisions were found, upon verification, to be of 

 exactly ctpial capacity throughout. The tube was then furnished 



