MOVING FORCE. 
17S 
nerallynclopted and improved upon by himself and by 
engineers in this country, that although undershot water wheels ilor''iiut‘< 
were, about fifty years ago, the most prevalent, they are now '=* * <^'***0 forcc- 
rarely to be met with ; and wherever the economy of power 
is an object, no new ones a: e made. So that all the poinis in 
question, as far as they relate to undershot water-wheels, al- 
though highly important at the time when Mr. Smeaton wrote 
his first paper, are now become matters of mere .‘■peculative 
curiosity, and, in this country at least, they can no longer be 
of any practical use. The question, however, respecting that 
yart of the power w'hich is expended in producing a change of 
figure, is highly interesting in other points of view, and we 
shall have occasion to consider it more fully when -we come 
loexamirre the 0 ’lh, 7 ih, 8 th. 9 th, Tith, and 13th cases. 
Dr, Milner, in allusion to Mr. Smeaton’s remarks on the 
theory, observes that, “ It is acknowledged, that the experi- 
ments which have been made to determine tlw effects of w iiid 
land water mills, do not agree with the computations of mathe- 
maticians ; but this is no objection to the principles here maiiv- 
tained. Writers generally projxjse such examples with a view 
rather of illustrating the n.ethoOs of calculation by algebra 
and fluxions, than of making any useful improvements in prac- 
itice. They suppose the particles of the water to move in 
straight lines, and to strike the machine w-ith a certain velocity, 
aand after that to have no more effect As such suppositions 
^re evidently inconsistent with the known properties of a 
rfluid, we are not at a loss to account for a difference between 
experiment and theory ; and therefore it slrould seem unreason- 
able to assert, that certain .authors of reputation have neglected 
the collateral circumstances ot time, space, or velocity in the 
resolution of these problems, unle.ss we are able to point out 
such omissions*." But if the theory be applicable to specula- 
tive objects only, why are its conclasions laid dow n as rules 
:to be adopted in practice ? Mr. Smeaton objected to the prac- 
tical application of the theory by the distinguished authors 
* I'hil. Trans. 1778, p-S7I 
which 
