229 



5.355. But Mr Tredgold, arguing that a fractional number was 

 not likely to represent a law of nature ! restored the index 6. His 

 decision has been overturned by tlie Commission of the Academy 

 of Sciences, who have adopted the number 6, as best representing 

 their higher experiments; and last of all, this decision is reversed 

 by the Committee of the Franklin Institute of Philadelphia, who 

 alter other terms of the formula, but reinstate the index 6. 



These formulae are : — 



(6.) F^ = (0.0029 t+iy . . Dr Thomas Young. 



^'■^ ^'^U^^O^'-' • ^^r Southern. 



^'•> ^'=(l6^)' • • • MrCrighton. 



(8.) F,= (2£i|^y- . MrCoriolis. 



(9.) F,= (L+2^y . . Mr Tredgold. 



(10.) F,= (o,7153« + l)^ . . French Academy. 



(11.) F, = (0.00333«+ l/ . . Franklin Institute. 



The author next proceeded to examine the theoretical views of 

 Dr Dalton. From long calculations, and laborious discussions of 

 the experiments and formulae, he has been led to the conclusion 

 that, with certain modifications, these views represent the actual 

 state of our knowledge of this subject better than any of these em- 

 pirical formulae. Dr Dalton finds, that, if the scale of temperature 

 which he considers as the true scale be reckoned from a zero at 

 175° lower than the present scale of Fahrenheit, the progressions 

 of the temperatures being as the square root of the expansions of 

 the mercury, then the progression of the elasticities will be in geo- 

 metrical ratio to those equal or true intervals of temperature. By 

 modifying this hypothesis, so as to reduce it to the following, that 

 the intervals of the common scale are in a geometrical ratio to the 

 intervals of true temperature, reckoned from a point 175° below 

 the present zero, Mr Russell finds that he obtains formulje that 

 perfectly represent the best series of experiments, — so closely in- 

 deed, that the greatest difference between theory and experiment 

 does not exceed ^^g of an inch of mercury from 0^ to 212", and 

 as far as 25 atmospheres does not average half a degree. He 

 also adduces ground for supposing that the theory of temperature 



