The Contrast of Practice and Theory. 29 



the steam engine and iron structures began to be used exten- 

 sively. 



X, Y, and Z had been well tethered to the laboratory experi- 

 ments ; indeed, some branches of pure mathematics may be 

 almost described as invented for that very purpose. Electricity 

 had been extensively used in the telegraph, though the power 

 (measured in steam engine horse power) was minute, and many 

 of the smaller practical questions connected with the construc- 

 tion and use of commercial, as distinguished from scientific, 

 instruments, had been worked out in consequence. 



It is not difficult to imagine that where the theory, meaning 

 thereby the process of evolving conclusions from an assumed 

 set of facts, was such as to have even led to the invention of 

 special mathematical methods of dealing with the facts, the 

 conclusions, though really involved in the data, would not be 

 at all obvious to any one who had no idea of how to reason 

 about them. It had been found, besides, that the false and 

 imperfect assumptions always made before trying to estimate 

 from theory the results to be expected in practice, usually led 

 to errors of no great importance. Even in the early days of 

 dynamos, a return of over 80 per cent, of the work expended 

 was obtainable in the form of electrical energy ; and, in respect 

 of the loss, much of it could be accounted for by the appli- 

 cation of the same rules as those by which the useful work was 

 calculated. The same rule which calculates the useful work 

 expended in overcoming the resistance of a set of glow lamps, 

 serves to calculate much of the loss incurred by resistance of the 

 conducting wires, armature, and so forth. Nothing like this 

 occurs in the steam engine ; for the rule for expenditure of heat 

 necessary (at the least) to turn out a certain horse power gives 

 no assistance in calculating the loss by radiation from the 

 boiler, friction in the pipes, initial condensation, &c. 



The typical practical man who never knows anything, in the 

 least out of the way, about why or how consequences follow 

 when drawn by unaccustomed methods, was at a loss in dealing 

 with electrical machinery ; and his most valuable qualities, his 



