Mr. W. J. M. Rankine on the Conservation of Enei-gy. 347 



According to the experiments of MM. Dulong and Hess, 

 1 litre, or 61 cubic inches of hydrogen, burned in half a litre of 

 oxygen, gives out heat sufficient to raise 3102 grms. of water 

 1° C., or 12"3 lbs. 1° F. The water formed by the combustion 

 is 0-00168 lbs. The ratio this bears to 123 lbs. is 1 to 7345 ; 

 so that the heat given out by the combustion of hydrogen suffi- 

 cient to form 1 grain of water, would raise 7345 grains of water 

 1° F. in temperature. Comparing this with 15,000 grains 

 raised 36,000 degrees, we arrive at the conclusion that the me- 

 chanical value of the electricity required to decompose 1 grain 

 of water is less than ^^^th of the mechanical value of the 

 electricity in the 800,000 charges of the 25-feet battery. Thus 

 eleven charges of this battery represent the integral electric 

 force contained in 1 grain of water. 

 Edinburgh, February 13, 1859. 



LV. Note to a Letter " On the Conservation of Energy." 

 By W. J. Macquorn Rankine, C.E., LL.D., F.R.S. 



To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, 



I BEG leave to add to my letter which appeared in the Philo- 

 sophical Magazine for April, the following remarks rela- 

 tive to the terms " Force,^' " Power," or " Energy," when used 

 in the sense of an unknown secondary cause of physical changes. 



The magnitude of a cause, if measurable at all, can only be 

 measured indirectly by means of the magnitude of its effects. 

 The magnitude of the cause may be a simple quantity ; but the 

 effects by which it is to be measured may be of such a nature, 

 that, to obtain from their magnitudes a proper measure of the 

 magnitude of the cause, factors must be multiplied together, and 

 terms added together. The tests of a proper measure are, first, 

 its " conservation," that is, the invariability of its magnitude 

 by any actions amongst the system of bodies to which it relates ; 

 and secondly, its completeness, or its taking into account all the 

 known relations amongst those bodies. 



To measure the magnitude of the " enei'gy " of gravitation 

 in a system of bodies, not only must the mean attraction be- 

 tween each pair of them be multij)lied by the distance thi'ough 

 which it is capable of acting (giving what I have called the 

 "potential energy"), but the mass of each body must be mul- 

 tiplied by the half-square of its velocity relatively to the centre 

 of gravity of the system (giving what is called " actual energy " 

 or "m viva"), and the results must be added together. The 

 quantity thus measured is not the less a simple magnitude 



2 A2 



