2 6 Mr. Davies Gilbert on the expediency of assigning 
the velocity squared (w x v*) ; till, in the early part of the 
last century it was fortunately observed, that the different 
properties indicated by these two functions were not, in any 
respect, at variance with each other ; and the terms momentum 
and impetus reconciled all opinions, by removing every ground 
for dispute. 
For a full and detailed explanation of this subject, I would 
refer to the admirable treatise on “ The Rectilinear Motion 
and Rotation of Bodies,” by the late George Atwood, Fellow 
of Trinity College, Cambridge, F. R. S. printed in 1784 ; and 
to the Bakerian Lecture in the Philosophical Transactions for 
1806, by an existing member of this Society, who has never 
touched any point of science that he has not elucidated and 
adorned. 
In this Lecture it is observed, that neither impetus nor 
momentum have usually much to do with the action of ordi- 
nary machines ; which is undoubtedly true; since neither of 
these functions measures directly their efficient power. The 
criterion of their efficiency is force multiplied by the space 
through which it acts (/ x s); and the effect which they pro- 
duce, measured in the same way, has been denominated duty , 
a term first introduced by Mr. Watt, in ascertaining the 
comparative merit of steam engines, when he assumed one 
pound raised one foot high, for what has since been called, in 
other countries, the dynamic unit.* And by this criterion, 
one bushel of coal, weighing 84lbs. has been found to perform 
a duty of thirty, forty, and even fifty millions ; augmenting 
* The dynamic unit used in France is a cubic metre (3,2809 feet) of water 
raised through a metre in height zz 7220 pounds of water one foot high, being to 
a million as 1 : 138,5 as 72 : xoooo nearly ; the log. 2,14139 66. 
