1 28 Mr. J. J. Waterston on the Expansion 



respective temperatures if they had retained the character of a per- 

 fect liquid. Do the numbers in this column indicate any quan- 

 titative law of divergence ? This has been tested by tabulating the 

 differences of these numbers in column 5, and the reciprocals of 

 these differences in column 6. These reciprocals have been- laid 

 off as ordinates to the temperatures in fig. 13 (PI. IV.). It will 

 be observed that the points range in the straight line s s nearly. 

 This line meets the axis of temperature at — 47 0, 8. Let w repre- 

 sent a number in column 4 at temperature/. The values of -r- are 

 given in column 5, and of -7- in column 6. Pig. 13 represents 

 -7— oc(/-f 47*8). If this were a governing law, we should have 

 w qc log (£ + 47*8), which affords the numerical equation 



{*^} -<«»-•. 



in which log c = 8*94037. The numbers in column 7 have been 

 computed from this equation : on comparing them with those in 

 column 4, it will be remarked that it exactly represents the curve 

 of observed expansion below 100°, but that above that the ob- 

 served volumes gradually depart from it and enter the curve of 

 normal liquid expansion at about 190°. The curve of column 7 

 crosses the normal at 159°, and at this temperature the observed 

 volume is *0036 above the point of intersection, an amount 

 which represents 3°. 



§ 23. It may be that the equation for column 7 is only to be 

 considered as empirical ; yet it may be remarked that if it ex- 

 presses a physical law, that law is very simple, and has reference 

 to a limiting temperature, as do also the laws of saturated vapour 



and normal expansion. The equation -7- qc (£ + 47*8) means 



that the absolute increment of divergence from the normal liquid 

 volume increases with a descending temperature in the inverse 

 ratio to the distance of that temperature from the limiting point 

 —47*8. The normal law of expansion is, that the proportionate 

 increment of volume at a given temperature increases in the 

 inverse ratio of the distance of that temperature from the upper 

 limit7=411°-6. 



§ 24. Since the law of liquid expansion has all the appearance 

 now of being general, and assumes the character of the quanti- 

 tative exponent of perfect liquidity, it may be as well, before con- 

 cluding this paper, to describe the method of projecting on a 

 general chart the line which represents both the vapour and 

 liquid condition of a body throughout its range of temperature. 



