268 THE THEORY OF SCREWS. [252-
Similarly, by omitting the first screw, we can have seven impulsive wrenches
which equilibrate, where
^ = ^5 = ^= =#18-
12 13 14 "■ 18’
hence we have
12.38^.^
13.28 FVi.Fw
Let the instantaneous twist velocity corresponding to F13 be denoted by
K13, then, as when seven wrenches equilibrate, the seven corresponding twist
velocities must also equilibrate, we must have in the corresponding system,
g.38
13.28 KK'
But we must have the twist velocity proportional to the impulsive intensity;
hence, from the second pair of screws we have
Fw : Kæ :: Fn : K12,
and from the third pair,
- ^3S : KiS ” • 1^13 >
hence we deduce
K12.K38_ #12.^
Vri.K F13.Fæ’
and, consequently, the function of the eight impulsive screws
12.38
13.28’
must be identical with the same function of the instantaneous screws.
It should, however, be remarked, that the impulsive and instantaneous
screws do not exhibit the most general type of two homographic systems. A
more special type of homography, and one of very great interest, characterizes
the two sets of screws referred to.
253. Special type of Homography.
If the general linear transformation, which changes each screw a into its
correspondent 0, be specialized by the restriction that the co-ordinates of 6
are given by the equations
~ _ 1 dll
1 - pi da! ’
.LdU
* p2da.2’
1 IE
ps dae ’