44 M. G. Van der Mensbriigghe on the Variations 



we shall then have : — 



ciQi= -Aid (S ~|) = -^^^'^^ ' 



Q=-A^^(S,-SO (5) 



Therefore the quantity of heat to be supplied or withdrawn 

 varies proportionally to the fresh surface produced, S2 — Si. 



This theorem can easilj be applied to some well-know^n 

 phenomena, such as the ebullition of liquids and the fusion of 

 solids. 



1. When the temperature of a boiling liquid remains nearly 

 stationary, the liquid is traversed by an infinity of bubbles, the 

 limiting surfaces of which possess a potential energy that in- 

 creases in proportion to their extent ; each bubble therefore 

 grows larger only by cooling the liquid ; so that the mass 

 must be constantly heated to counteract this cooling. To this 

 cause of production of cold must be added further the renewal 

 of the bounding surface of each bubble, which arises from the 

 volume comprised within each bubble becoming saturated with 

 vapour. Accordingly we conceive that the ebullition will be 

 the more active (that is to say, the greater number of bubbles 

 will be formed) the more heat is supplied in the same time. 



I will add that if, for want of air dissolved in the liquid or 

 adhering to the sides of the vessel, all formation of fresh sur- 

 faces within the liquid is rendered difficult if not impossible, 

 the temperature of the mass rises more and more, and far 

 beyond that which corresponds to regular ebullition ; in fact, 

 since the beautiful and celebrated experiments of M. Donny*, 

 we know to what an elevated temperature one can bring a 

 liquid, without maldng it boil, when the air has been expelled 

 from it as much as possible. 



My theory explains with equal clearness the fall of tempe- 

 rature, sometimes considerable, which is always experienced at 

 the time of a sudden explosion of vapour-bubbles in a liquid 

 heated beyond its normal boiling-point ; with respect to this 

 I may refer to the curious experiments of the English physi- 

 cist Professor Tomlinsonj. Thus my formula confirms the 

 idea enunciated long since by Donny, and afterwards verified 

 by Dufour, that, in order to produce regular ebullition, it suf- 

 fices to pass through the liquid a very light current of any gas 

 whatever. 



* " Memoire siir la cohesion desliquides et siir leiir adherence aux corps 

 solides/' Mem. Cow. des Savants etrangers de VAcad. Roy. de BeJg. t. xvii. 



t '' On some Phenomena connected with the boiling of liquids," Phil. 

 Mag. 1875, vol. 1. p. 85. 



