1893.] on Economies in the Utilisation of Energy. 83 



other of these transformations. About them are three fundamental 

 facts which I will ask you to note. 



1. Every transformation of energy is accompanied by some waste 

 of energy. 



2. Every transformation occurs in absolute accordance with certain 

 phenomena which reproduce themselves so exactly that they have come 

 to be called physical laics. 



3. All the quantities which can appear in every transformation 

 are as exactly measurable and have been as exactly measured as could 

 be the temperature of this room, or the breadth of Albemarle Street. 



As to the first point, I use the expression " waste " rather than 

 " loss " because the energy cannot well be said to be lost. The amount 

 of energy wasted in a transformation is measured by noting what is 

 called the efficiency of the transformation, which is usually expressed 

 as a percentage. A transformation with only one per cent, loss, for 

 example, would be said to have an efficiency of 99 per cent., and so 

 on. Perpetual motions are simply transformations of 100 per cent, 

 efficiency. 



In spite of the great and admitted imperfection of our knowledge 

 of the physical universe, I think it is not impossible to arrive at some 

 understanding as to how far the knowledge which we have can be held 

 to be final, and how far or in what directions it is provisional. I 

 mean, of course, so far as affects our particular object of saying what 

 is, and what is not, possible in one special direction. 



It seems perhaps contradictory, but I think it is true, that our 

 superstructure in physical knowledge is much more solid than our 

 foundation. Our knowledge of the ultimate constitution of matter, 

 and particularly of the ultimate constitution of " not-matter," cannot 

 be said to be accurate as yet. But higher up in the scale matters are 

 different, and it is as well that we should remember that there are 

 physico-chemical facts and numbers that are just as fully established, 

 although they refer to phenomena which we cannot entirely follow, as 

 are the figures of the Nautical Almanac. 



Let me take the combustion of coal as an example with the 

 external phenomena of which we are all familiar. Chemists have 

 analysed the coal and know of what it consists ; so much carbon, so 

 much hydrogen, so much oxygen ; they have measured for us that its 

 elements in the combustion enter into various combinations, so that they 

 can tell us exactly the maximum amount of heat energy which can be 

 given out by the burning of a given weight of coal. Yet I have often 

 enough met people who were quite convinced that they possessed the 

 secret by which an amount of heat equal to double this quantity could 

 somehow be obtained. The finality of our knowledge in this respect 

 is quite independent of our ignorance of the ultimate nature of the 

 coal or of the combustion. 



I have taken the phenomena of combustion as among those with 

 which every one is fairly familiar. Let us deal with it for a few 



g 2 



