162 Scientific Proceedings, Royal Dublin Society. 



engine we must work rapidly if we are to get a good efficiency, 

 for the efficiency vanishes at the slow limiting velocity. In the 

 case of statical engines, the efficiency is a maximum when they 

 are working at their slow-limiting velocity, and vanishes when 

 working at their quick-limiting velocity. In the case of a perfect 

 turbine, the efficiency is a maximum when going at its quick- 

 limiting velocity. In the case of water engines there is evidently 

 a limiting velocity also depending on the rate of propagation of 

 energy by the water, i. e. its rate of propagating sound. Gas 

 engines have similarly a limiting rate of working, depending on 

 the rate of explosion, i. e. of propagation of energy by the working 

 substance. 



Capillary engines and muscles have probably limits of rates of 

 working analogous to those depending on the rates of diffusion 

 of the molecules of the working substances at the working sur- 

 faces. We know that muscles like kinetic engines have a zero 

 efficiency when working at their zero limit of velocity, and there 

 is almost certainly a maximum limit to their rate of working. 

 Capillary engines, like M. Lippmann's, are evidently limited by the 

 rate of diffusion of the molecules at the capillary surfaces, i. e. of 

 the superficial energy. 



Electric engines have got analogous properties. There are the 

 two classes — electro-static engines, such as a reversed Holtz 

 machine, and electro-kinetic engines, such as ordinary magnetos 

 and dynamos. The former can be worked as slowly as we please, 

 without waste of energy ; but the latter require to be worked at 

 near their limiting velocity to have a good efficiency. A limiting 

 velocity in the case of dynamos is well known, and is attained 

 when the inverse electro-motive force of the dynamo is equal to 

 the driving electro-motive force; but with a given electro-motive 

 force it does not seem at first sight as if there were any limit 

 to the rate of working of a Holtz machine or any electro-static 

 engine. 



If we, however, consider the electro-magnetic action of moving 

 electricity, it becomes evident that the forces between the different 

 parts of an electro-static engine must diminish as its velocity of 

 motion increases, until its parts have a relative motion equal to the 

 velocity of light, when there will be no more forces between them. 

 If it move faster than this it will become an electro-magnetic 



