730 
Proceedings of the Royal Society 
Explanation of Plate. 
Figs. 1~3. Amphium bellis, Lyman, var. tritonis, nov. 
1. Under surface of disk. 
2. Side view of arm, 
3. Transverse section of arm. 
Figs. 4-7. Opliioglyplia signata, Verrill. 
4. Upper surface, natural size, 
5. Upper surface of disk. 
6. Under surface of disk. 
7. Side view of arm. 
8. Transverse section of arm, 
4, On the Principles of Economics, By Mr Geddes. 
Part Y, Psychological, 
Monday, 1th Jidy 1884, 
EOBEET GEAY, Esq,, Vice-President, in the Chair. 
The following Communications were read : — 
1. A Problem on Point-Motions for which a Eeference-Erame 
can so exist as to have tlie Motions of the Points, 
relative to it, Eectilinear and Mutually Proportional. 
By Prof, James Thomson, 
111 a paper read in this Society on the 3rd of March last, “ On the 
Law of Inertia,” &c,, I had occasion to adduce for consideration a 
problem to the following effect j — 
Eelatively to a reference-frame which may itself have any motion 
whatever (but which is to be regarded as unknown or as disallowed 
for any use in observation or measurement), a set of points are known 
to have motions which are rectilinear and mutually proportional in 
simultaneous progress. From observations or measurements on suc- 
cessive simultaneous configurations of the set of points merely, to 
find a reference-frame relatively to which their motions will have 
that same character. 
On the suggestion of this problem for solution being made to 
Prof. Tait, on the evening of the meeting already referred to, he 
