259] HOMOGRAPHIC SCREW SYSTEMS. 273
are so related, that when nine are given, the tenth is immediately deter-
mined ; for this two data are required, that being the number required to
specify a screw already known to belong to a given three-system.
We may, as before, denote by 12 the condition that the screws 3, 4, 5
shall be co-cylindroidal. This, indeed, requires no less than four distinct
conditions, yet, as pointed out (§76), functions can be found whose evanes-
cence will supply all that is necessary. Nor need this cause any surprise,
when it is remembered that the evanescence of the sine of an angle between
two lines contains the two conditions necessary that the direction cosines are
identical. The function
12.34
13.24
can then be shown to be an invariant which retains its value unaltered when
we pass from one set of five screws in a three-system to the corresponding
set in the other system.
B.
18