Mr. W. M. Buchanan's Theory of the Reaction Water- Wheel 113 



of the principle of fluid reaction, it may bo recognised under the same 

 uncouth form. 



The value of the machine as a hydraulic mover, depending thus 

 entirely upon its construction, it would perhaps have been more in con- 

 formity with the order in which the conditions of the problem present 

 themselves, to have devoted the present opportunity to an investigation 

 of those principles which determine the condition of maximum effici- 

 ency. That part of the inquiry possesses, besides, a popular interest 

 which does not belong to an examination, necessarily compressed and 

 incomplete, of the dynamical relations involved in the working of the 

 machine. But the order adopted has, in some degree, been forced 

 upon me by the continually iterated and erroneous interpretations of the 

 terms of tho problem to be found even in late works of much preten- 

 sion; and as tho problem of construction has not hitherto undergone 

 any professedly scientific investigation, and is consequently not encum- 

 bered with any false hypotheses,* its discussion is less urgent, and may 

 bo deferred until another opportunity shall offer to bring the subject 

 under the notice of the Society. 



But although it does not come within my present purpose to exa- 

 mine the technical conditions prescribed by the modus operandi of the 

 machine, it will still be necessary to indicate the general features of 

 tho mechanism. Without this it would be difficult to induce a clear 

 conception of its mode of action, and especially of those conditions of 

 dynamical equilibrium to which a mathematical investigation of its prin- 

 ciples must have essential reference. I might indeed refer to the primi- 

 tive form of the machine which is familiarly known to all in any degree 

 conversant with the elements of hydrodynamics: but an apparatus so 

 manifestly ill adapted to fulfil the condition most eagerly desired in the 

 construction of all prime movers — the greatest possible effect from a 

 given expenditure of power — can convey only a very imperfect idea of 

 the adaptations of the machine in its recent and more complete forms. 

 The same is true, although in a less degree, of all those various modifi- 

 cations of the parent machine which have from time to time been 

 attempted on the Continent, where horizontal water-wheels — on account 

 of their economy as regards first cost and readiness of application — 

 have been far more extensively studied and employed than in this 

 country. Several of these have, indeed, yielded results, at least, suffi- 

 ciently high to throw doubt upon the crude hypothesis, that " the mechani- 

 cal effect, derivable from a given head of water, is essentially greater in 

 amount when it acts by pressure, than by impulse or reaction." But the 

 success has in no instance been complete ; and it is not difficult to por- 



* If we except the rules given by Waring, (Trans. American Phil. Soc., Vol. III., p. 

 193,) which are repeated by Dr. Gregory in his Treatise on Mechanics, (Vol. II., p. Ill,) 

 and by Sir David Brewster in his Edition of Ferguson's Lectures on Select Subjects, 

 (Vol. II., p. 208,) but which are too evidently erroneous to have any injurious influence. 



