Infinite Divisibility of Matter. 99 
loss whatever of the acting power;” therefore the steam- 
engine cannot be improved. 
THE WRITER OF THE ARTICLE ON IMPROVEMENTS IN MACHINERY, ? 
NORTH AMERICAN REVIEW, VOL. V- NEW SERIES. 5 
July 30th. 
Ss 
Ast.XII.—Remarks on Art. 24, of No. 2, Vol. 1X. of the 
Amer. Journal of Science and Arts. 
So many cavils and objections have been made, in past 
times against the doctrines of the infinite divisibility of mat- 
ter, or rather of extension, and the arguments opposing it 
have been so completely refuted by Mathematicians, that 
one could hardly expect a revival of them after a slumber of 
more than a century. The men of genius of the present day 
would do well not to depend entirely on that exalted faculty, 
A knowledge of what has been done by others, on any sub- 
ject, ought ever to precede any attempts towards its exten- 
sion, or improvement. Had the writer of the 24th Art. of 
the last number of the Journal, read, and fully comprehend- 
ed the irrefragable arguments of Keil, in his introduction to 
Natural Philosophy, it is presumed he would not have con- 
sidered the infinite divisibility of extension as an impossi- 
bility, because he had conceived a case of motion apparently 
inconsisient with it, and made that the basis of an argument, 
neglecting the most essential attribute, and measure of mo- 
tion, viz. Time. 
It is a well known principle in mechanics, that the space 
passed over by a body in uniform motion, is to be estimated 
by the time and velocity conjointly, or s=tv, and that what- 
ever the kind of motion may be, we shall always have 
s=tv. Now assuming these principles, which are the funda- 
mentals of all mechanics, we shall have t= *, and ¢= fh and 
v v 
if we take the case proposed by the author, suppose 
a body in motion te have commenced its motion 
at A and to proceed in a right line towards B, 
A__________*._# SB. and that this motion’ be 
considered as made by intervals, first by the passage over 3 
the line, or from A to a, and then over ! of what remains, or 
a to C, and again over 3 the remainder, and so on continually ; 
