112 Mit. W. M. Buchanan's Theory of the Reaction Water- Wheel 



engine of Hero, full eighteen centuries prior (120 B.C.) ; and when the 

 history of this branch of mechanics shall be fully investigated, it will 

 be necessary to award to the sage of Alexandria the merit of the first 

 discovery, and to point to his engine as the archtypeof all those mechanisms 

 by which the motive force developed in the reflex action of fluids is 

 rendered available. Between the rotatory steam-engine of Hero, and the 

 Water-Mill of Dr. Barker, there is, in the present comparatively 

 advanced state of hydrodynamical science, no other essential difference 

 than belongs to the two conditions of fluidity of the agencies employed : 

 their dynamical efficiency may be measured and expressed by formulse, of 

 which the terms are strictly homologous; and .the conditions of their 

 action are reducible to laws common to elastic and non-elastic fluids. 

 But, at the time when Dr. Barker added his machine to the scanty list 

 of hydraulic motors then in use, the laws of hydrodynamics were too 

 partially developed to justify us in assuming that he was guided by 

 analogy, much less, by a rigorous induction of elementary principles. 

 Hydraulics had no foundation in experiment, and those abstract methods 

 of investigation which had led to results of surprising accuracy in the 

 mechanics of solid bodies, in their applications to the motions of fluids, 

 conducted to conclusions which were much too general to constitute a 

 practical theory. 



But, although we are thus conducted to the inference that the dis- 

 covery of the Reaction Water-Mill was empirical, and independent of 

 all scientific deduction, and although in its original form, it is admitted 

 to be nearly worthless — far inferior to the common bucket wheel, as a 

 means of economising hydraulic power — still the merit of the discovery 

 remains unimpaired. A new principle in hydraulics was thereby esta- 

 blished, and bequeathed to science ; and although its value in the arts 

 has been slowly recognised, the explanation is readily found in the 

 absence of that experimental knowledge which is necessary to appreciate 

 correctly those collateral influences which enter as elements of the tech- 

 nical problem. This is fully manifested by the fact, that the machine, 

 when constructed with due attention to those conditions for which an 

 extended knowledge of the principles concerned in the motions of fluids, 

 and an advanced state of the mechanical arts, have enabled us to pro- 

 vide, is found capable of transmitting fully 80 per cent, of the power 

 of the water expended : whereas, in the older examples, and in some 

 also of modern date (e. g. the American tub- wheels), constructed less in 

 accordance with those hydraulic precepts with which experiment has 

 made us acquainted, the result has seldom been found to exceed half 

 the mechanical value of the water expended; and even half that moiety 

 would, in general, be a full measure of the efficiency of the machine 

 if applied in its primitive form. This form it has, nevertheless, steadily 

 retained in scientific treatises which touch on the practical applications of 

 hydrodynamics, and even in the model rooms of our scientific institutions, 

 and periodically on the lecture-table, where it is adduced in illustration 



