254 Mr. J. Y. Buchanan [May 8, 



the same signification as in Table I. H ( = Y - z;) represents the 

 volume of pure ice included in U. It will be seen that H, the volume 

 of real ice present at t, suffers a sudden diminution at - 21° '72, and 

 then continues to diminish, at first slowly, and then at an increasing 

 rate, until liquefaction is complete. 



In Fig. 1, curve B represents the variation of apparent volume 

 IT with temperature t, the salt being active ; while the straight 

 line B a represents the variation of Y with t, the salt being inert. 

 The fine B a represents the dilatation of pure ice, on the basis of a 

 constant coefficient of dilatation (V 00016. As chloride of sodium is, 

 by nature, inert at temperatures below the cryohydric point, the 

 straight line l e \^ part of the curve B, as well as of B a. Between 

 -25° and -21° '72 the ice expands uniformly at the same rate, 

 whether it is pure or contains salt. We have in c the first singular 

 point of the curve, and it occurs in all the curves of expansion of ice 

 contaminated by chloride of sodium. When the temperature of the 

 ice rises to - 21° " 72, the inertness of the salt is exchanged for activity ; 

 and, if the requisite supply of heat is available, 5*498 c.c. of ice are 

 melted, producing 5 • 040 c.c. water, under a contraction of • 458 c.c. 

 While this amount of ice is melting, the temperatm-e remains constant, 

 but the volume U contracts. Graphically, this is represented by a 

 straight line {c e) parallel to the axis of volume. Therefore the curve 

 of volume of the ice l^etween - 25° and the point where the tempera- 

 ture begins to rise above - 21° • 72 is represented by two straight lines 

 1) r and c e which meet each other in an acute angle at c. When the 

 temperature rises above -21' "72, anothei', generally acute, angle is 

 formed at^, so that tins portion of the curve of volumes takes the form 

 of the letter Z. 



Between -25° and -21° '721 the coefficient of dilatation is 

 0" 00016. At the point ^, corresponding in Table II. to the tempera- 

 ture -21° '721, the cryohydric point has l)eeii reached on a rising 

 gradient, but no melting has taken place. Melting is supposed to 

 begin only when the temperature has reached - 21° • 72 exactly. Then 

 there is a contraction of * 458 c.c. with no change of temperature, so 



that, at this stage the coefficient of dilatation is - — - — = - oo. 



When the temperature rises above -21° "72, the apparent volume U 

 increases with the temperature, but at a gradually diminishing rate 

 until, at - 7° • 0, the increase of volume due to simple expansion of the 

 ice is exactly balanced by the contraction due to induced melting. At 

 this temperature the coefficient of expansion changes sign, and, between 

 - 7°*0 and -0°*1, at which the ice has practically all melted, the 

 coefficient of expansion is negative. Therefore the eoeffleient of 

 thermal expansion of this ice ehang-es sig-n three times when 

 it is warmed from a temperature below the cryohydric point 

 of solution of chloride of sodium to that at which liquefac- 

 tion is complete. 



