METHOD OF VARIATIONS. 57 



it was conducted. Thus Dr. Joule clearly proved that 

 rarefaction produces as much heat as cold, and that only 

 when there is a disappearance of mechanical energy will 

 there be production of heat h . What we have to notice, 

 however, is not so much the result of the experiment, as 

 the admirably simple manner in which a single change in 

 the apparatus, the separation of the portions of water 

 surrounding the strong air vessels, is made to give indi- 

 cations of the utmost significance. 



Collective Experiments. 



There is an interesting class of experiments which 

 enable us to observe an indefinite number of quantitative 

 results in one act. Generally speaking, each experiment 

 yields us but one number, and before we can approach 

 the real processes of reasoning we must laboriously repeat 

 measurement after measurement, until we can lay out a 

 pretty complete curve of the variation of one quantity as 

 depending on another. Now we can sometimes abbreviate 

 this labour, by making one quantity vary in different 

 parts of the same apparatus through every required 

 amount. Thus in observing the height to which water 

 rises by the capillary attraction of a glass vessel, we may 

 take a series of glass tubes of different bore, and measure 

 the height through which it rises in each. But if we 

 take two glass plates, and place them vertically in water, 

 so as to be in contact at one vertical side, and slightly 

 separated at the other side, the interval between the 

 plates varies through every intermediate width, and the 

 water rises to a corresponding height, producing at its 

 upper surface a hyperbolic curve. 



The absorption of light in passing through a coloured 

 liquid may be beautifully shown by enclosing the liquid 



h 'Philosophical Magazine,' 3rd Series, vol. xxvi. p. 375. 



