PHYSICS. 453 



couibustion continues even after ex])ansion has progressed considerably. 

 The heat cousunied was distributed as follows: Indicated work, 17 per 

 cent.; exhaust, 15^ per cent.; water jacket, 52 per cent. ; loss by radia- 

 tion, &c., 15.} per cent. The enj>ine was rated at ten-horse power, and 

 the cost of operating' it is jiiven as 8.^ cents ])er liorse-i)ower per hour. 

 {Vaji NostraricVs Mag., February, 1884, xxx, 89; Science, April, 1884, 

 in, idG.) 



2. Expansion and Change of State. 



Thorpe and Eiicker have apjdied the theory of Van der Waals to 

 the establishing of an inii)ortant relation between the absolute tem- 

 perature of boiling- of a liquid, the volume at this temperature, and a 

 constant, which they have determined to be 2, or very near this number. 



Mendelejeff had already established the formula ^=1 — It for the ex 



pansion of liquids, in which 7c is a modulus varying with the liquid. 

 This author now shows that if the dilatation of gases be expressed by 



Vt =1 4- «^j and that of liquids by Vt= — =-, then 2ti= y— , and put- 



ting a equal to 2, we have =- = 2i + 273, in which either li or t being 



k 



given the other can be determined. (J. Gliem. Soc, April, 1884, xlv, 



135; J. Soc. Phys. Ghim. Rnsse, xvi, 232; Nature, August, 1884, xxx, 390.) 



I)e Heen, assuming that the molecules of a liquid attract each other 



in the inverse ratio of the seventh power of their distance, and that the 



work done by the molecular forces during expansion through 1° in 



temperature is a constant for the same liquid, has given the formula 



dY 



-— _= aV^"'^^ as true for the volumes of all liquids. In this formula « 



dt 



represents the expansion coefficient at 0°. The author has compared 



the values of -^ calculated by this formula with those deduced from 

 dt 



the empirical formulas of other authors, especially Kopp and Is. Pierre, 

 and finds a satisfactory agreement. (J". Phys., December, 1884, II, in, 

 549.) 



Thoulet has suggested a very simple method of determining the vol- 

 ume expansion-coefficient of solid substances in small fragments. For 

 this purpose he uses a solution of mercuric iodide in potassium iodide, 

 of si)ecific gravity from 2.75 to 2.85, the coefficient of which has been 

 accurately determined hj Golds(5hmidt. The solid is ])laced in the 

 solution, and water is added until it remains in equilibrium, having the 

 same density as the liquid. The temperature and density are noted. 

 A small quantity of the concentrated solution is now added, and the 

 solid rises to the surface. The density is again noted. Then the tem- 

 ])erature is slowly raised, the liquid expanding more than the solid, 

 until the temperature is reached at which the solitl is again in equilib- 

 rium. Noting the hnal density of the liquid and its temperature, the 



