m 
Dr. Young's Lecture on 
PROPOSITION VIII. 
When two Undulations , from different Origins , coincide either 
perfectly or very nearly in Direction , their joint effect is a Com- 
bination of the Motions belonging to each. 
Since every particle of the medium is affected by each undu- 
lation, wherever the directions coincide, the undulations can 
proceed no otherwise than by uniting their motions, so that 
the joint motion may be the sum or difference of the separate 
motions, accordingly as similar or dissimilar parts of the undu- 
lations are coincident. 
I have, on a former occasion, insisted at large on the appli- 
cation of this principle to harmonics; (Phil. Trans, for 1800. 
p. 130.) and it will appear to be of still more extensive utility in 
explaining the phenomena of colours. The undulations which 
are now to be compared are those of equal frequency. When 
the two series coincide exactly in point of time, it is obvious 
that the united velocity of the particular motions must be 
greatest, and, in effect at least, double the separate velocities; 
and also, that it must be smallest, and if the undulations are of 
equal strength, totally destroyed, when the time of the greatest 
direct motion belonging to one undulation coincides with that 
of the greatest retrograde motion of the other. In intermediate 
states, the joint undulation will be of intermediate strength ; 
but by what laws this intermediate strength must vary, cannot 
be determined without further data. It is well known that a 
similar cause produces in sound, that effect which is called a 
beat ; two series of undulations of nearly equal magnitude co- 
operating and destroying each other alternately, as they coincide 
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