742 
Proceedings of the Boyal Society 
Postscript. 
The ideas noted in what follows had not completely occurred to 
me till after the evening of the meeting of the Society when the 
paper was read, and a suggestion towards their development came 
from Professor Tait’s paper of the same evening On Reference 
Frames.” Thus it seems suitable to annex them here as a postscript. 
It may be noticed that in the case referred to in the last sentence 
of the paper just before this postscript — the case of three original 
movingpoints retaining their distances apart unchanging — the method 
of procedure employed throughout the paper would collapse because 
the points A and B would be at rest relatively to the vice-original 
frame, and so the straight lines of motion AA and BB previously 
used would become only two points. Yet a solution is in this case 
even more readily available than in the previously considered cases. 
It thus becomes desirable to find some way of harmonising the two 
modes of thought or of procedure so as to bring them into connec- 
tion ; rather than to be content to suppose that, in passing from one 
to the other, we should have quite to abandon the one mode of 
thought, and take up another and quite unallied mode instead. 
A satisfactory connection between the two presents itself, if, 
instead of taking frorn the kinematic model only the lines of motion 
AA and BB, as the basis for our desired frame, we take from that 
model also the points A^ and B^ on those lines, getting them known 
by measurement of their distances from any future points A„ and 
B;i , so that when, among the three original points A, B, and C, 
the particular configuration A,iCB,j found in anticipation from the 
model shall come to exist, the old triangular frame A^CB^ shall 
become known to us relatively to the then existing frame A„CB„ . 
In this way of procedure, the solution, for the case of A and B 
being, as well as C, at rest in the vice-original frame, will come out 
simply by the distances and B,^Bj being each zero in length, 
and by the concomitant of this, that the old frame A^CB^ is to be 
found as being coincident with the new momentarily existing and 
known frame A??CB^ , 
