660 Theory of Compound Sounds. 
limited in time; because it evidently begins 
and ends with the cycle of the vibrations of the 
sounding bodies. 
Prorosttion 1V. The coalescence of two 
sounds is impossible on mechanical principles. 
For, suppose the thing possible ; then the coa- 
lescence of two sounds requires, that a particle 
of air should possess a motion, compounded of 
the motions which the two sounding bodies 
would impart to it separately ; and that this com- 
pound motion should act ina given right line, for, 
an assignable part of time, otherwise it could not 
excite a similar motion in the elastic particles 
occupying that given right line. Let A be 
such a particle, and let the construction used 
in the last proposition, be retained; conse- 
quently (Principia, Prop. 23, Lib. 2.) VA and 
AW are in the ratio of the forces that act 
at any moment in the right lines TA and SA. 
Make AK as AW, and draw KL parallel to 
AW, and make it as AV; also join AL; then 
will the particle A be urged in the direction 
LA at that instant. But the ratio of AK to 
KL varies perpetually, by Prop. III. ; there- 
fore the species of the triangle AKL is equally 
inconstant; consequently the compound force 
does not act ina given direction for an assignable 
part of time. Now the production and propa. 
gation of motion in a given right line requires 
