518 Mr. milner on the 
ment of their feveral methods; but I am deterred 
from entering into fuch a difcuffion by the length of 
time which it would require; efpecially as I think thofe 
who have read the authors mentioned will eafily con- 
ceive the fubllance of what I fhould have to obferve, and 
to thofe who have not read them I fhould hardly be able 
to fay any thing intelligible. 
§ 12. The above folution, if it had no other advan- 
tages, is, I apprehend, much more concife than any that 
has hitherto been given. Abft rafted from what is faid 
by way of illuftration, articles 4th to 9th contain all the 
calculation requifite, and as I have ftudioufly avoided the 
ambiguous ufe of the terms force , vis , efficacia , mo- 
mentum, &c. as well as every doubtful reprefentation of 
times, fpaces, and velocities, which are often fubftituted 
by authors in equations, I believe the whole procefs will 
appear eafy, and the evidence upon which the conclulion 
refts be exaftly afcertained. 
§ 13. The principles defcribed in articles 2. and 4. 
depend upon the third law of motion, and the property 
of the lever, and are demonftrated in the following man- 
ner. Every thing remaining the fame as in art. 2. (fig* 
6.) let av and br, perpendicular to the right line or axis 
ae, reprefent the forces and dir eft ions with which thofe 
bodies are refpeftively urged, when at liberty to move 
1 freely 
