190 
Proceedings of the Royal Society 
Solution of Indeterminate Problems,” has been shown to me. In this 
excellent work the properties of the muarif angles of the tetragonal 
system are given ; and as there is no hint concerning the higher 
systems of these angles, my impression is confirmed that this part 
of the subject is entirely new. 
4, On Superposition, No. II. By Professor Kelland. 
5. On Centrobaric Bodies. By Professor W. Thomson. 
(Abstract by Professor Taiti) 
This is an abstract of an investigation which will be published 
in full in “ Thomson and Tait’s Natural Philosophy.” It contains 
the application of Gfreen’s wonderful results regarding the potential 
to the determination of the centre of gravity of a system when 
there is such a point. Some of the more remarkable propositions, 
which are thus established are as follows : — 
If the action of terrestrial or other gravity on a rigid body is 
reducible to a single force in a line passing always through one 
point fixed relatively to the body, whatever be its position relatively 
to the earth or other attracting mass, that point is called its centre 
of gravity^ and the body is called a centrobaric body. 
If a body is centrobaric relatively to any one attracting mass, 
it is centrobaric relatively to every other ; and it attracts all matter 
external to itself as if its own mass were collected in its centre of 
gravity. 
The centre of gravity of a centrobaric body necessarily lies in its 
interior ; or, in other words, can only be reached from external space 
by a path cutting through some of its mass. 
No centrobaric body can consist of parts isolated from one an- 
other, each in space external to all ; in other words, the outer 
boundary of every centrobaric body is a single closed surface. 
A given quantity of matter may be distributed in one way, but 
in only one way, over any given closed surface, so as to constitute a 
centrobaric body with its centre of gravity at any given point 
within it. 
Matter maybe distributed in an infinite number of ways through- 
