732 
Proceedings of the Royal Society 
AA, movable in tliat plane j and, by motions of the lines CA^ , 
CA2 , CA3 , together with the motion of the line AA itself if neces- 
sary, bring the templet points A^ , A2, Ag, into the line AA, 
Keep, until further notice, the line AA at a constant distance from 
C. This last bondage temporarily applied (that of keeping AA at 
a constant distance from C) is introduced merely as an aid in the 
reckoning of freedoms, and of their successive abolitions. It is not 
essential, and for some possible varied modes of thought it may well 
be omitted. 
The figure here illustrates the arrangement so effected. It is to 
be understood that we are to suppose ourselves free from any doubt 
as to whether, at the instant of any measurement, the moving point 
A or B, as the case may be, is diminishing or increasing its distance 
from C ; for instance, we are to suppose that we are fully aware 
at which side of M in the line AA we are to place the point A^ ; the 
the line CM being the line of shortest distance from C to AA. 
Kext take another straight line to be denominated as BB, and 
place it passing through Bj and Bg wherever these templet points 
may happen to be. Then rotate templet AgCBg round its side 
CAg till its side GBg , regarded as an interminate straight line, comes 
to meet the line BB which itself is movable, and may, if necessary 
or desirable, be shifted while retaining the points B^ and B2 in it. 
This operation may be stated in other words as being the operation 
of bringing the templet line CBg into the plane of Bj and B2 and C, 
or, what is the same, into the plane of the point C and the line BB 
