256 



difference, divided by Carnot's function, which is y if the tempera- 



ture is measured on our absolute scale. Hence if a film such as a 

 soap-bubble be enlarged, its area being augmented in the ratio of 

 1 to m, it experiences a cooling effect, to an amount calculable by 

 finding the lowering of temperature produced by removing a quan- 

 tity of heat equal to 



dT 



from an equal mass of liquid unchanged in form. 



For water T=2'96 gr. per lineal inch. 



Work per square inch spent in drawing out a film =5 '92, say 



dT 1 

 gramS ' "" ==T) or thereab uts. 



/f 300 

 Suppose J-B-J. -_^ | then the quantity of heat to be removed, 



to produce the cooling effect, per square inch of surface of augmen- 

 tation of film will be $ ^ . Suppose, then, 1 grain of water to be 

 drawn out to a film of 1 6 square inches, the cooling effect will be 

 J}$Q of a degree Centigrade, or about -^j. The work spent 

 in drawing it out is 16 X 6 = 96 grains and is equivalent to a 



96 1 



heating effect of __^=__. Hence the total energy (reck- 



oned in heat) of the matter is increased -^ + -^ of a degree Cen- 

 tigrade, when it is drawn out to 1 6 square inches. 



IV. " On the Logocyclic curve, and the geometrical origin 

 of Logarithms." By the Rev. J. BOOTH, LL.D., F.R.S. 

 Received April 15, 1858. 



In a paper read before the Mathematical Section of the British 

 Association during its meeting at Cheltenham in 1856, and which 

 was printed among the reports for that year, I developed at some 

 length the geometrical origin of logarithms, and showed that a tri- 

 gonometry exists as well for the parabola as for the circle, and that 

 every formula in the latter may be translated into another which 

 shall indicate some property of parabolic arcs analogous to that 

 from which it has been derived. 1 showed, moreover, that the 



