106 MESSRS. WALTER ROSENHAIN AND P. A. TUCKER. 



question. A practical difficulty lies in determining the proper boundaries of these 

 areas on the side not bounded by the observed curve. In the present instance the 

 areas have been closed by lines drawn in free-hand in such a way as to coincide as 

 nearly as possible with the limits of the recalescence, these limits being graphically 

 estimated on the general lines laid down in the paper cited above. While this is 

 obviously only a rough approximation, the errors involved are probably much smaller 

 than those which are unavoidably introduced by variations in the rate of cooling as 

 from one curve to another of the same series. These variations in the rates of cooling 

 have been approximately allowed for in each estimation, but the rates of cooling from 

 which this was done are the average rates during that particular experiment, and 

 probably differ considerably from the rate at which cooling actually took place during 

 the course of the recalescence. The weights of the specimens of metal were accurately 

 known in each case, and these have been allowed for in making the estimations of the 

 heat equivalents of the recalescence peaks. The actual areas of these peaks were 

 obtained by plotting the cooling-observations on a large scale, and measuring the areas 

 of the peaks by means of a planimeter. The area so found was divided by the weight 

 of the cooling body and multiplied by the inverse of the rate of cooling. The resulting 

 approximate values of the quantities of heat evolved have been plotted for the three 

 most complete series of curves, and are shown in figs. 9, 10, and 11. Fig. 9 refers to 

 the eutectic arrest-points in the derived differential curves of Series A, and for the 

 alloys lying between 18 and 25 per cent, of tin the points fall on a straight line, i.e., 

 the heat evolved by the solidification of a gramme of eutectic appears to be constant 

 for these alloys. The good agreement of this result with theoretical expectations 

 serves to show that under favourable conditions the method of approximation yields 

 reasonably satisfactory results. If TAMMANN'S method of extrapolation be applied to 

 this curve, we find that the zero of the eutectic falls at about 17 per cent, of tin, a 

 result which agrees well with other lines of evidence, except that in the present set 

 of curves the limit is shifted slightly towards the tin side of the series, because as 

 has already been pointed out the rates of cooling used in the experiments were not 

 sufficiently slow to allow of the attainment of complete equilibrium. 



When the same process of approximation is applied to the study of the recalescences 

 which occur in the solid alloys at a lower temperature, the conditions are not so 

 favourable and the results consequently much less concordant. In the alloys contain- 

 ing the larger proportions of lead the temperature at which the heat-evolution occurs 

 varies considerably from one alloy to another, and this introduces large corrections 

 derived from widely differing rates of cooling. It is therefore not surprising to find 

 the points in the curves of figs. 10 and 11, which refer to the cooling- curves shown in 

 figs. 2 and 6 and 7 respectively, lie somewhat irregularly. In fig. 11 the points 

 relating to alloys with 14, 16, and 18 per cent, of tin, which are marked with a small 

 circle, refer to cooling-curves taken from specimens which had previously been 

 quenched. Their erratic position is probably due to this difference in treatment, and 



