of Edinhurcjh, Session 1883-84. 
5 Ho 
/ O 
in itself the whole difficulty of our inability to form a distinct 
notion of identical points or places in unmarked space at successive 
times, or of our inability to conceive any means whatever of recog- 
nising afterwards in any one point of space, rather than in any 
' other, the point of space which, at a particular moment of past time, 
was occupied by a specified point of a known body. 
To aid in the apprehension of the underlying truth referred to, 
and also as an aid to the understanding of the enunciation about to 
be given in the present paper as The Laio .of Inertia and^ Princijple 
of Chronometry, some purely kinematic principles will now be 
. adduced for consideration. Thus the question is to be opened up 
as to what may be the nature of relative mpfions of various bodies, 
W’hich can in any sense truly be regarded as uniform rectilinear 
mutual motions. Explanations are to be given on such motions of 
•points in unmarked space, as can have a reference frame and 
reference dial-traveller relatively to ivhich jointly those motions are 
rectilineanar and are uniform in the sense of being changeless in 
quasi-velocity. In other words, quite to the same effect — Explana- 
tions are to be given on such motions of points in unmarked sp>ace as 
can have a reference frame relatively to loIiicJi those motions are 
rectilinear and are changeless in mutual rate; or what is the same, 
are mutucdly proportional in their simultaneous progress. 
Let us imagine a reference frame, rigid in its configuration, and 
for simplicity let it be taken as including three rectangular reference 
planes firmly connected. Let several points or small bodies be 
kept moving by geared mechanism, such as that o| toothed wheels 
on variously inclined axles, and toothed straight sliding racks with 
pinions, all carried or guided in bearings firmly a,ttached to the 
reference frame, the arrangements being such that those moving 
points shall be made simultaneously to travel over mutually pro- 
portional lengths along straight lines fixed in relation to the 
reference frame. The motion may be given by a w;inch handle like 
that of a barrel organ, fixed on one of the axles ; and, for help in 
consideration of the subject, we may imagine a uniformly graduated 
dial surrounding the winch handle axle, and an ipdex attached to 
the axle so as to project .radially outwards like a hand of a clock, 
and to travel round the dial keeping pace in angular motion with 
the winch handle. Thus fhe simultaneous travels of the various 
