HELMHOLTZ ON THE CONSERVATION OF FORCE. 131 



neglected. It remains therefore to be asked whether the sum 

 of these forces always corresponds to the mechanical force which 

 has been lost. In those cases where the molecular changes and 

 the development of electricity are to a great extent avoided, the 

 question would be, whether for a certain loss of mechanical 

 force a definite quantity of heat is always developed, and how 

 far can a quantity of heat correspond to a mechanical force. 

 For the solution of the first question but few experiments have 

 yet been made. Joule* has measured the heat developed by 

 the friction of water in narrow tubes, and that developed in 

 vessels in which the water was set in motion by a paddle-wheel ; 

 in the first case he found that the heat which raises 1 kilo- 

 gramme of water 1°, was sufficient to raise 452 kilogrammes 

 through the height of 1 metre ; in the second case he found the 

 weight to be 521 kilogrammes. His method of measurement 

 however meets the difficulty of the investigation so imperfectly, 

 that the above results can lay little claim to accuracy f. Probably 

 the above numbers are too high, inasmuch as in his proceeding 

 a quantity of heat might have readily escaped unobserved, while 

 the necessary loss of mechanical force in other portions of the 

 machine is not taken into account. 



Let us now turn to the further question, how far heat can 

 correspond to an equivalent of force. The material theory of 

 heat must necessarily assume the quantity of caloric to be con- 

 stant ; it can therefore develope mechanical forces only by its 

 effort to expand itself. In this theory the force-equivalent of - 

 heat can only consist in the work produced by the heat in its 

 passage from a warmer to a colder body ; in this sense the pro- 

 blem has been treated by Carnot and Clapeyron, and all the 

 consequences of the assumption, at least with gases and vapours, 

 have been found corroborated. 



To explain the heat developed by friction, the material theory 

 must either assume that it is communicated by conduction as 

 supposed by Henry J, or that it is developed by the compression 

 of the surfaces and of the particles rubbed away, as supposed by 



* Philosophical Magazine, S. 3. vol. xxvii. p. 205. 



f It must be remembered that the writer was acquainted with the earlier 

 experiments only of Mr. Joule. — Ed. 



I 



