ON Till: AMSOLITK F.XI'ANSION OF MKKCURY. ) 



were taken with the cold column at a temperature in the neighbourhood 



of 20 < '. It makes a different ..... t' more than 1 in 500 in the fundamental coefficient 



a ....... 'ding as we assume HKHNA KIT'S value 0'0001795, or WULLNEK'S value ()'00()J814, 



for (In- mean coefficient l>etween d ( '. and 20 C. in reducing the observations. The 

 uncertainty is greater at lower temperatures. REGNAULT states that he solved his 

 formula by a method of successive approximation, but the approximation would 

 evidently be unsatisfactory at low temperatures, and his calculations cannot be 

 reproduced so as to make his results fit with his observations. REGNAULT himself 

 was conscious of this difficulty, and endeavoured to avoid it by cooling the cold 

 column with melting ice, but he appears to have abandoned this method on account 

 of difficulties of manipulation. The apparatus employed in the present investigation 

 was better suited for the purpose than REGNAULT'S, and a special series of observa- 

 tions was successfully taken with the cold column in ice, and at 10 C., for the 

 accurate determination of the coefficient at low temperatures. But the majority of 

 the observations were taken with the cold column at the atmospheric temperature, 

 t>ecause this procedure, besides greatly facilitating the manipulation, made all the 

 other corrections as small as possible, and in particular rendered the correction 

 depending on c?H practically negligible, so that it was in most cases unnecessary to 

 measure the length of the cold column at each observation. 



It is easily seen that a formula precisely analogous to (5) applies to the reduction 

 of the observations to any convenient standard temperature t , other than C., 

 namely, 



//), ...... (6) 



where O a 2 , oi, denote the mean coefficients between ? and t a , t r respectively expressed 

 in terms of the volume at t . Formulae (2) and (5) may be regarded as special cases 

 of this more general formula in which / is replaced by t\ and by C. respectively. 



The majority of the observations in the first series with the cold column at the 

 atmospheric temperature in the neighbourhood of 20 C., were reduced to a standard 

 temperature of 20 C. in the first instance, because the value of the coefficient at 

 20 C. in terms of the volume at 20 C. could be inferred with considerable accuracy 

 from the observations themselves, and the difference (ti 20) was comparatively small. 

 The correction term (^ 20) oiH 2 was of the order of 3 per cent, at most, and was 

 itself known with certainty to 1 in 2,000. If the observations had been reduced 

 directly to C. by REGNAULT'S formula, this correction would in some cases have 

 exceeded 30 per cent., and would have been most uncertain, since the mean coefficient 

 from C. to 20 C. could be obtained only by extrapolation. The corrections 

 involved in deducing h' from h, were of the order of 2 or 3 parts in 10,000 only, and 

 could not give rise to any similar uncertainty. 



With the apparatus above described, the expansion of mercury is obtained under a 

 mean pressure of 2 '5 atmospheres, but the result will not differ from the expansion 

 under a pressure of 1 atmosphere except in so far as the compressibility of mercury 



VOL. ccxi. A. C 



