734 
Proceedings of the Boycd Society 
the freedom it possesses till comes into that line BB, and then let 
us make that conjuncture binding for the future. 
Now all will be clamped or locked completely during our main- 
tenance of the temporarily employed condition of AA being kept at 
an unchanging distance from C. 
Next release that condition and shift A A to any new distance 
from C, and it will follow that BB will be fixed in a new situation ; 
and, for AA moving, BB will be bound to an exact movement 
accordingly. 
But now introduce one mote of the templets^ templet A^CB^ , 
with its point A^ brought into the line AA and kept botmd to 
remain in that line, and v/ith its line CB^ brought into the plane of 
C and BB. This being done, the point B5 will generally not find 
itself in the line BB; but we can shift AA towards or from C, 
moving consequently the plane CBB and the line BB in that plane 
till the line BB gets Eg entered into ik 
Thus all is completely clamped ; and the two straight lines of 
motion of the points A and B relative to the desired frame in which 
C is at rest, are found relative to each one of the configurations 
ABC at the successive instauts of the measurements. But those 
past configurations of the points A, B, and C, are already lost to 
us ; and so we must proceed to find the lines AA and BB relative 
to one or more future configurations of those three points which are 
the only things that are to be available to us to make measurements 
from. It is here to be distinctly noticed that the lines of motions 
AA and BB, being fixtures in the desired frame, may perfectly well 
be accepted as constituting that frame ; or even one of them along 
with the point C (which is also a fixture in the desired frame) might 
equally well be accepted as constituting the desired frame. 
Now we have to observe that, from the nature of the data, and of 
the operations performed in the kinematical model or mechanism, 
and result arrived at in it, it must be the case that the lengths 
AjA 2, A2A3, AgA^ &c., and BjB2, B2Bg, BgB^, &c., found in the 
model as reprrsentatives of simultaneous travels of the real points 
A and B relative to the desired frame, must be mutually propor- 
tional. Hence, by continuing forward for the future a like propor- 
tional division along BB for any arbitrarily marked graduation 
along AA, we can by measurements from the model foretell future 
