of Edinburgh, Session 1883-84, 
737 
These two parallel lines are represented in the figure as and 
A2 ^2 • now we have, in the figure, 
AjA2 : Bj^2 ' ’ • ^ 1^3 * 
Take two other straight lines kept parallel by mechanism, and 
place one of them across from to B2 and make the other pass 
through A3 , and then it will necessarily meet the line BB, So 
these two parallel lines will be represented in the figure as ^2^2 
A3&3 ; and we shall have : — 
AjA2 3 BjB2 3 3 AjAg 3 Bj?;g ^ 
ITow in general it will result that so found wdll not coincide with 
B3 j but let us now keep the line BB moving in the freedom it 
possesses, and keep the two pairs of parallel lines maintaining the 
conditions to which they have been set, arid continue the motion 
until the points 63 and B3 come to coincide, and bind these two 
points to remain together ; or, in othet words, bind the line Ag&g , 
when brought to pass through the point B^ hitherto movable along 
the line BB, to continue holding the templet point Bg , Thus all will 
be clamped as long as the temporarily imposed condition of change- 
less distance from the templet point C to AA is maintained. 
But if now we change that distance, and fix on a new changeless 
distance instead, while maintaining all the conditions already 
attained to, the whole system will take up a new configuration and 
will become clamped therein. 
Or we might express this by saying : — Fix AA at an altered dis- 
tance from C, and by going through the same process as before we 
get one fixed configuration for the whole system. So if we relax 
the condition of changeless distance of AA from C, the whole 
system has one and only one freedom. 
For the next step we do not require another complete templet. 
We may use merely the lengths CA4 and CB^ got by measurement. 
That is let us have a portable triangle with two sides CA^ and CB^ 
given, but the angle between them left unknown, and that, for our 
present operations, is the same as to say 3-— left variable. Put the 
vertex C, or joint C, of that portable triangle at the point C of our 
model. Bring CA^. into the plane CAA, and swing it round till A^ 
comes into the line AA, Also put the rod or bar CB^ into the 
VOL. XII, ' 3 b 
