( 144 ) 
N°. XVII. 
Obfervations on the Theory of Water Mills, &c. by 
W. Warinc. 
Read June EIN G lately requefted to make fome calcu- 
BS, 419% lations relative to mills; particularly Doct. 
Barker’s conftruGtion, as improved by James Rumfey, 1 
found more difficulty in the attempt than [ at firft expect- 
ed. It appeared neceffary to inveftigate new theorems for 
the purpofe, as there are circumftances peculiar to ‘this 
conftru@ion, which are not noticed, I believe, by any 
author; and the theory of mills, as hitherto publifhed, 
is very imperfe@t, which I take tobe the reafon it has 
been of fo little ufe to pratical mechanics. 
The firft itep, then, toward calculating the ‘power of 
any water-mill (or wind-mill) or proportioning their 
parts and velocities to the greateft advantage, feems‘to be, 
The correction of an effential miftake adopted by writers 
on the Theory of Mills. 
This is attempted with all the deference due to eminent 
authors, whofe ingenious labours have juftly raifed their 
‘reputation and advanced the fciences; but when any 
wrong principles are fucceflively publifhed by a feries of 
fuch pens, they are the more implicitly received, and 
‘more particularly claim a public rectification; which muft 
be pleafing, even to thefe candid writers themfelves. 
George Atwood, M. A. ¥. R. S. inchis mafterly trea- 
‘tife onthe reCtilinear motion and rotation of bodies, pub- 
lithed fo lately as 1784, continues this overfight, with its 
pernicious confequences, through his propofitions and co- 
rollaries (page 275 to .284,) although he knew the theo- 
ry was rag for: he obferves (page 382) Mr. Smea- 
ton 
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