36 
Proceedings of the Royal Society 
Further it may easily be seen that we can gradually change the 
directions (or clinures) of the two sets of parallel projectors until we 
get the point to coincide with. , and maintaining that coinci- 
dence we can go on changing the directions of both sets of parallel 
projectors till we get also to coincide with Bg. This being done 
we can, by observing whether or not coincides with Bg ascertain 
whether or not it be the case that : B^B 2 : : A^Ag ; B^Bg. 
The general principle thus indicated can be applied to the case 
immediately before us in a simplified combination by choosing 
to make the transversal pass through the points Ag and Bj 
as in fig. 2, where TT represents the transversah The figure 
is to be understood as being a pictorial representation on 
the paper, of lines and points not themselves situated in the 
plane of the paper, and not all existing in any one plane. Then 
take a pair of straight lines kept parallel by mechanism (as for 
instance is the case in some commonly used kinds of parallel rulers) 
and place one of these lines so as to pass through Aj and Bj and 
make the other pass through A 2 . This secolid line being parallel 
to AjBj (see fig. 2) must be in a plane with it and with the line A A 
and consequently with the transversal. So it meets the transversal. 
