1S5 



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

 tLrou£:hout the length of a sin2:le cahbratins" step, ^ and — vriil 



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 A, We 

 have then 



OF: 



(/-i+I:)k. oh=(.-i^- 



and YK= (h — f-r—^ — —-)k = T,, the higher temperature — 32^ ; 

 T. 



whence K= — , The degree corresponding to the point 



O is S'2- — (^t—l-r:^jK. The length of one degree for any in- 

 dividual step X is 



K 



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

 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 vith accordins-lv. The sraduarion is earned from —40" to 

 --1-20'- or ISO- Fanrr ' 



II. ^^/r/r 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, veiy serious eiTors would be tiie 

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

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

 mometers intended to meniure very low temperatures, I was supplied 

 by mm with some whici; he nad himself prepared vith great care, its 

 specific gravity being 0'7&6 at 60" Fahr, The first step to be tf.ken 

 was the determination of the km: of expansion of the fiuicl in gh=. = s, 

 as compared with that ci mercuiy. For tiiis ])ui-pose a tube was 

 calibrated and oivided vith an arbitrary scale according to Reg- 

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

 exactly equal capacity thriughout. The tube was then fumishea 

 with a buio cf thr same dimensicns as those intended to be sup- 

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

 meter was. mai'ked S. 9 E. Comparisons were then made between 

 the readings of this instrument and those of a standard mercurial 

 thermometer, throuzh as lar2-e a range of temperature as was found 

 practicable. Tne 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 foUowins: Table contains the results of two series 



