114 Mr. W. M. Buchanan's Theory of the Reaction Water- Wh. 



ceive by tbo light of a more exact knowledge of the conditions and data 

 of the problem, that the degree of approximation corresponds in all 

 recorded examples with tho degree of obedience to the laws of fluid move- 

 ment, manifested in tho construction of the machine, and in those subor- 

 dinate arrangements, by which its practical efficiency is hardly less 

 influenced. 



The form in which the machine has principally occupied my attention, 

 is that made by Messrs. Randolph, Elliot, & Co., of this city, under the 

 patent of Messrs. Whitelaw & Stirrat. In this the precepts of legitimate 

 theory are united with the highest quality of workmanship, and with a 

 fertility of technical appliance and adaptation unknown in the Reaction 

 Water- Wheels of the Continent. It is not, however, to be supposed that 

 it started into the high state of efliciency which it has ultimately attained, 

 with the first effort. The first trials were sufficiently successful to en- 

 courage a reasonable expectation of the final result ; but much active 

 experience was required to arrive at the root of the quantative of all those 

 influences which necessarily enter as elements of the practical question. 

 A correct theory required to be constructed, and, in order to arrive at 

 the requisite data, it was found necessary to institute an experimental 

 examination of those laws of hydraulic action concerned in the problem, 

 perhaps more searching and comprehensive, more intense and persevering, 

 than had previously been directed to any question involving the economy 

 of water-power. Mathematical deductions required a more precise inter- 

 pretation than they commonly received in practice, loose analogies were 

 to be rectified, defective formulas to be rendered complete by new induc- 

 tions, modified in their coefficients by the facts of experiment, and 

 reduced from the condition of abstract generalizations to maxims of prac- 

 tice of ready and certain application. 



This protracted and laborious inquiry was necessary to the develop- 

 ment of the actual theory of the machine, and collaterally to establish 

 its position in relation to prime movers of the same class. Comparative 

 efficiency among hydraulic motors is the criterion of absolute value, and 

 although the standard is unstable — altogether deficient in numerical 

 exactness, and especially at the higher points of oscillation, ill defined — 

 still there is an acknowledged measure which must be reached, and 

 reached through the strict ordeal of experiment, before a claim to the 

 first rank of excellence can, with propriety, be instituted. This is the 

 more requisite, that in general the impelling agency is sparingly dealt out, 

 and neither admits of augmentation nor of unlimited accumulation. If 

 this constant dependence on the immediate supply which Nature affords 

 in her fertilising operations, has the effect of rendering water-power com- 

 mercially less valuable, especially in those localities where the bowels of 

 the earth are replete with the means of cheaply feeding the energies of 

 the all-mighty steam-engine ; it has also the effect of inducing economy 

 in the means of application. Where the power is abundant and admits 

 of ready increase, we can afford to look less narrowly into the expenditure; 



