128 On the Measure of 
Mr. Atwood, however, has shewn that Mr. 
Emerson himself has been led into error, by 
neglecting this very principle which he pro- 
poses to weed out. In reference to a particu- 
lar problem, he says, “ In Emerson’s Fluxions, 
p- 177,* there is this problem: 'The radii of a 
wheel and axle are given in the proportion of 
b:a; aweight 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 y, when y x into its velocity gene- 
rated 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 generated; and ac- 
cording to the usual doctrine of momentum, 
assumes 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 matter 
into the velocity. From this reasoning 
he deduces the weight sought, Ya 2-1 x2 
b+ hsb 
when its true value is y=wxX ery gee Ts 
(page 249.) agreeing with the former only in 
the extreme case when b=a, that is, when the 
yadius of the wheel is equal to that of the 
axle.” + 
* 2d Edit. + On Rectilineal Motion, Preface, p. x. 
