PHYSICS. 453 



combustion continues even after ex])ansiou has i)rogressed considerably. 

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

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

 tion, &(i., 15d ])er cent. The engiue was rated at ten-horse power, and 

 the cost of operating it is given as 8f cents per horsepower per hour. 

 ( Van Nostrandh Mag., February, 1884, xxx, 89 ; Science, April, 1884, 

 III, 49G.^ 



2. Expansion and Change of State. 



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

 the establishing of an important relation between the absolute tem- 

 perature of boiling of a liquid, the volume at this temperature, an<l a 

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



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



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

 This author now show^s that if the dilatation of gases be expressed by 



1 11 



Vt =1 + at, and that of liquids by Vt=^ — ^ , then 2ti= -^— , and put- 



1 — kt k a 



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



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

 135; J. Soc. Phys. Chim. Busne, xvi, 232; Nature, August, 1884, xxx, 396.) 

 De 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 



~-= «V2-^3^ as true for the volumes of all liquids. In this formula a 

 at 

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



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



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

 and finds a satisfactory agreement. {J. Phys., December, 1884, II, iii, 

 549.) 



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

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

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

 of specific gravity from 2.75 to 2.85, the coefficient of which has been 

 accurately determined by Goldschmidt. The solid is placed 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- 

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

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

 rium. Noting' the final density of the liquid and its temperature, the 



