APPENDIX 329 



tions have shown that during this transformation of mechanical 

 work into heat or, vice versa, of heat into mechanical work, a 

 constant, strictly quantitative ratio is observed. A certain 

 amount of mechanical work on transformation gives rise to a 

 definite amount of heat and vice versa. The quantity which 

 expresses this constant ratio is called the mechanical equivalent 

 of heat. It can be determined in various ways : here is the 

 simplest and most obvious, although not a very accurate 

 method of determination, which was devised by the French 

 scientist Hirn. It consists roughly in the following : a heavy 

 iron hammer is made to fall from a certain height upon an anvil 

 on which a piece of lead is laid. This piece of lead becomes 

 hot from the blow of the hammer. We take a kilogramme- 

 metre for the unit of work, as explained before, and for the 

 unit of heat the rise in temperature of one kilogramme of water 

 by one degree Centigrade. Knowing the weight of the hammer 

 as well as the height from which it falls, knowing also the weight 

 of lead and the amount of heat it has acquired, possessing 

 moreover some other data, which we wiU not mention here, 

 we can find out how many units of work have been expended 

 as well as into how many units of heat they have been trans- 

 formed. Exact determinations give the value of 426 for the 

 mechanical equivalent of heat. This number indicates the 

 constant ratio by which heat transforms itself into mechanical 

 work or vice versa. This means that a unit of heat on trans- 

 formation into work gives 426 units of mechanical work, i.e. 

 can do work equal to raising 426 kilogrammes to the height of 

 one metre, or of one kilogramme to the height of 426 metres. 

 On the other hand, by expending 426 units of mechanical work 

 to heat water, we can raise the temperature of one kilogramme 

 of it by one degree. 



We have mentioned many examples of the transformation of 

 mechanical energy into heat ; examples of the opposite are also 

 often met with. The steam engine may be taken as a striking 

 illustration ; heat developed by burning fuel becomes transformed 

 through the medium of steam into mechanical work. The heat 

 of the sun evaporates water from the surface of the earth, 

 causes it to rise to a certain height whence it falls down again 

 upon the earth, runs from the mountains into the valleys and 

 thence into the ocean, producing all the way mechanical work, 



