of the Equinoxes. 63 
dent from article 3. In the following articles, linear velocity, 
is meant when no adjective is annexed to the word velocity. 
9. Let AB, DC (Fig. 6.) be the two axes about which 
separately the body would revolve, as stated in article 5, and 
let TS be the axis about which it revolves, in consequence of 
a combination of these two revolutions. Let TE be at right 
angles to AB, and meet it in H, and let TF be at right angles 
to DC and meet it in K ; and let GV, GW be the angular 
velocities about AB, DC, as in the preceding articles. Then 
it follows, from the last article, that the velocity of the point 
T, by the revolution about the axis AB only, is equal to 
GV xHT. And as this velocity is in the direction of a tangent 
at T to the circle of which TE is a diameter, and as this circle 
is perpendicular to the plane ADBC, the direction of this 
velocity is evidently perpendicular to the plane ADBC. The 
direction of this velocity of the point T is also upwards from 
the plane of the figure, agreeable to the statement in article 5. 
Again, by the revolution about the axis DC only, the velocity 
of T is equal to GW x KT, and, for the foregoing reasons, 
the direction of this velocity of the point T is perpendicularly 
downwards below the plane, according to article 5. Now as 
TS is the axis about which the body revolves, in consequence 
of the combined revolutions about AB, DC, every point in 
TS is rendered quiescent by the compound motions. It is 
therefore evident that GVxHT=GWxKT. 
10. The revolutions about DC, AB may be supposed to be 
caused by instantaneous impulses at A and D, made at the 
same time, or at different times ; or they may be supposed to 
be occasioned by the agency of constant forces, like that of 
