57'2 PHILOSOPHICAL TRANSACTIONS. [ANNO 1784. 



mometer-pieces, if a certain degree of my scale be found to correspond with the 

 point d, and another degree of mine with the point c ; then the interval between 

 those 2 degrees on mine must be equal to the interval dc ; and how many of 

 Fahrenheit's that interval is equivalent to will be known from the preceding com- 

 parison. Thus we can find the number of Fahrenheit's degrees contained in any 

 given extent of mine, and the degree of Fahrenheit's with which a given point 

 of mine coincides ; whence either scale is easily reducible to the other through 

 their whole range, whether we suppose Fahrenheit's continued upwards, or mine 

 downwards. 



For obtaining the intermediate thermometer different means were thought of; 

 but the only principle which, on attentive consideration, afforded any prospect 

 of success, was the expansion of metals. This therefore was adopted, and 

 among different methods of measuring that expansion, which either occurred to 

 myself, or which I can find to have been practised by others, there is no one 

 which promises either so great accuracy, or convenience in use, as a gage like 

 that by which the thermometer-pieces are measured : the utility of this gage had 

 now been confirmed by experience, and the machines and long rods, which have 

 been employed for measuring expansions on other occasions, were absolutely in- 

 admissible here, on account of the insuperable difficulties of performing nice 

 operations of this kind in a red heat, and of communicating a perfectly equal 

 heat through any considerable extent. 



To give a clearer idea of this species of gage, which, simple as it is, I am in- 

 formed has been misunderstood by some of the readers of my former paper, a 

 representation of one used on the present occasion is annexed in fig. 14, where 

 abcd is a smooth fiat plate; and ep and gh two rulers or flat pieces, a quarter 

 of an inch thick, fixed flat upon the plate, with the sides that are towards each 

 other made perfectly true, a little farther asunder at one end eg than at the other 

 end fh ; thus they include between them a long converging canal, which is di- 

 vided on one side into a number of small equal parts, and which may be con- 

 sidered as performing the offices both of the tube and scale of the common 

 thermometer. It is obvious, that if a body, so adjusted as to fit exactly at 

 the wider end of this canal, be afterwards diminished in its bulk by fire, as the 

 thermometer-pieces are, it will then pass farther in the canal, and more and 

 more so according as the diminution is greater ; and conversely, that if a body, 

 so adjusted as to pass on to the narrow end, be afterwards expanded by fire, as 

 is the case with metals, and applied in that expanded state to the scale, it will 

 not pass so far ; and that the divisions on the side will be the measures of the 

 expansions of the one, as of the contractions of the other, reckoning in both 

 cases from that point to which the body was adjusted at first, i is the body 

 whose alteration of bulk is thus to be measured, which, in the present instance, 



