ON THE ARSOLUTE EXPANSION OF MERCURY. 23 



level in tin- gauge could not lie read nearer than O'OOl cm. was an important limitation 

 of accuracy at low temperatures, when the difference of level was small. But at 

 temperatures l>etween 200 C. and 300 C., where the difference of level was 40 to 

 60 cm., the possihle errors in the measurement of the length and temperature of the 

 hot columns became more important, and the order of accuracy was limited in a 

 different way, namely, as a fraction of the whole quantity measured. For low 

 temperatures, the differences between the observed and calculated values of the 

 expansion itself were the best criterion of accuracy ; but for high temperatures, the 

 corresponding differences tatween the observed and calculated values of the coefficient 

 of expansion appeared to l>e a better guide in the selection of an equation. The 

 formula obtained by the method of least squares was accordingly nuxlified from this 

 point of view, but the modifications required were so slight as to Ix; almost within the 

 limits of expei imental error. 



The following formula was finally adopted to represent the value of the mean 

 coefh'cient u a< between C. and t" C. in terms of the volume at 0. : 



= [1805553 + 12444 (*/100) + 253'J (</100) a ]x 10' 10 ..... (8) 

 The value of the fundamental coefficient uiuo given by this formula is 



oai, w = 0-0001820536. 



It is, unfortunately, impossible to represent the results satisfactorily over the whole 

 range by a linear formula for the mean coefficient, of expansion, because the rate of 

 increase of the mean coefficient is more than twice as great at 300 C. as at C. 

 But for approximate work the following simple formula for the mean coefficient may 

 be sufficiently exact to be of use : 



,,0, = (18006 + 2<)xlO~ 8 



This formula gives results which are practically correct at 100 C. and 200 C., and 

 which do not differ from formula (8) by so much as 0'05 C. at 50 C. and at 150 C. 

 But the value of the mean coefficient is about 1 in 400 too low in the neighbourhood 

 of C. and 300 C. 



For convenience of comparison with the above formula (8), the observations of 

 Series I. and II. (which were reduced to 20 C. in the first instance, and expressed in 

 terms of the volume at 20 C.) are here reduced to C., and expressed in terms of 

 the volume at C., by multiplying the values of V,/V [namely, l+a,x(-20)] 

 given in the tables, by the value of V 31 /V (( (namely, 1 '0036 1632), given by the formula 

 of comparison. This reduction will not introduce any error in. the comparison of the 

 observed results with those calculated by the formula. 



