MOVING FORCK. 87 
many cases, and is so obscure in itself, it ought to be weeded Cases of diffi- 
out. and not to pass for a principle in mechanics* * * § .’* ciilty in the 
. Mr. Atwood, however, has shewn, that Mr. Emerson him- moving force. 
lelf has been led into error by neglecting this very principle 
which, he proposes to weed out. In reference to a particular 
problem, he says, " In Emerson’s Eluxions, p. l/zf, there is 
this problem : The radii of a wheel and axle are given in the 
proportion of : a j a weight w acting by means of a line on 
the circumference of the wheel, elevates a weight y suspended 
from a line which goes round the axle ; it is required to assign 
the quantity when iy x into its velocity generated in a given 
time, is the greatest possible.” 
. “ In the solution, the author supposes the momentum of 
bodies to be as the quantity of matter into the velocity gene- 
rated j and, according to the usual doctrine of momentum, 
lassumes it as an universal truth, that if a force acts on any 
different quantities of matter for a given time, it will always 
{generate the same moment, estimated by the quantity of mat- 
ter into the velocity. From this reasoning he deduces the weight 
bw * ~ /b* ifi i-> 
y— ^ 2-7 1 X — ' when its true value is ^ = u’ x vC r~" 
n «• aJ a’ 
I (page 249.) agreeing with the former only in the extreme case, 
when Z'=a, that is, when the radius of the wheel is equal to 
I that of the axlej.” 
Mr. Smeaton, at the commencement of the description of 
■his experiments on water-wheels, says, “ The word power, 
as used in practical mechanics, I apprehend to signify the 
t exertion of strength, gravitation, impulse, or pressure, .so as to 
: produce motion§.” And near the end of his Experimental Exa- 
■minalion, we have the following conclusion : 
“ It therefore directly follows, conformably to what has been 
'deduced from the experiments, that the mechanic power that 
• Emerson’s Principles of Mechanics, p. -20. 
t Second Edition. 
J On Kectilincal Motion, Preface, p.x. , 
§ Phil. Trails. 1795, p. 105. 
most. 
