8 
to contain the most philosophical foundation for statics. 
Lagrange, whose writings are a mine of historical informa- 
tion, says (‘ Mec. Anal/ i, 13) that the ancients knew the 
composition of motions, as we see by some passages of 
Aristotle, in his Mechanical Questions; and that the geo- 
meters especially have employed it for the description of 
curves, as, Archimedes for the spiral, Nicomedes for the 
conchoid, &c. 
7. Secondly, we may seek to arrive at the composition of 
pressures, independently of the second law of motion, by 
processes which are valid whether that law be a law of nature 
or not, and which would be valid even if we had not any 
conception of motion, and which indeed do not render it 
necessary to consider whether pressure does or does not 
tend to produce motion. Lagrange (‘Mec. An.’ i, 19) thinks 
that the principle of the composition of forces, in being 
separated from that of the composition of motions, loses its 
principal advantages ; and he, just before saying this, throws 
out a doubt as to whether a principle used by Daniel Ber- 
noulli in his demonstration was altogether independent of 
the conception of motion. The whole subject of composition 
is discussed by De Morgan in his paper “ On the General 
Principles of which the Composition or Aggregation of Forces 
is a consequence.” (Carab. Trans. Yol X. Part II, 1859). 
8. Lagrange (‘Mec. An.’ i, p. 14 No. 11) observes that, 
although the principles of the lever and of composition lead 
always to the same results, it is remarkable that the simplest 
case for the one becomes the most complicated for the other. 
He adds (ib. No. 12) that we can establish an immediate 
connection between these two principles by a theorem of 
Varignon. Newton’s view is noticed by Lagrange (ib. No. 10). 
9 Thomson and Tait have a special object (“Treatise” &c. 
vol. i, Preface p. v; p. 141 par. (f); p. 341 § 453), in refer- 
ence to which Newton’s proof may be the more appropriate 
or elegant. I here use the word “elegant” in the sense which 
