334 A. B. Quinby on Water-Wheeis: 
lower extremity of the first quadrant: and that a Bréast- 
Wheel is one that receives the water exactly at the lower ex- 
tremity of the first quadrant.* It is demonstrated in my pa- 
per on the Overshot-Water-Wheel, that the effect of water in 
descending upon the circumference of a wheel, is always in 
proportion to the vertical space passed through. 
This fact being regarded, it is easy to apply the theory of 
the Overshot-Water-Wheel to the Pitch-back and Breast- 
Wheel 
S. 
If we assume the condition that the water is delivered upon 
the wheel with a velocity equal to that of the circumference 
of the wheel, (in practice the water should be delivered upon 
the wheel with a velocity a little exceeding that of the cir- 
cumference of the wheel,) then there is no difference in prin- 
ciple between the Overshot-Water-Wheel, and the Pitch-back 
and the Breast-Wheel ; the effect of any quantity of water 
descending upon either wheel, being always in proportion to 
the vertical space passed through—and being always meas- 
ured by the quantity of water expended, multiplied into the 
vertical space through which it descends upon the wheel.t 
Having now given my theory on the subject of the Over- 
shot Water-Wheel, the Pitch-back and the Breast-Wheel, I 
will add one remark on the subject of constructing these 
wheels. 
Construct either wheel so that the water may descend upon 
it through as great a vertical space as possible—giving to the 
wheel, at the same time, the proper velocity. 
I have forborne offering any remarks on the theory of the 
Undershot-W ater-Wheel, as I have understood from my friend 
Prof. Robert Adrain, that he has a paper prepared for pub- 
lication on that subject. 
A. B. QuinBy. 
August 7, 1826. 
*I am aware that these definitions differ from those given by some authors ; 
but I think the meaning o word Pitch-back reqnirdl the definition Ihave 
iven of that wheel; and this definition beiug adopted, the definition | have 
given of the Breast-wheel, follows. The definitions, however. are matters of 
but little importance. : : 2 
+ Friction is here not regarded, 
