exviii Proceedings of the Asiatic Society of Bengal. [N.S., XV, 
mathematics to physics is based on the postulate that physical 
problems can be expressed by differential equations. But it is 
now recognized that our knowledge as to the possibility of 
solving differential equations is of the most meagre description. 
An inquiry into the subject, which has been largely undertaken 
in recent years, is of immediate physical interest though it is 
generally classed under pure mathematics. 
same way, a new investigation has been under- 
he 
question of the stability of the solar system, has immediate 
and pressing interest to the physical enquirer. 
Talking of the foundations of the dynamical theory, I 
cannot omit to refer to the change of Method due to G. W. Hill 
and others, whereby planetary and lunar theories have under- 
from a xed orbit, and this has introduced a remarkable sim- 
ones | into the treatment of celestial mechanics. 
A 
group is a set of operations, which is closed, in the same 
sense that the performance of any two of these operations in 
succession is equivalent to another operation of the set. We 
know, for instance that the result of a successive translation 
and rotation of a rigid body is equivalent to a single movement. 
And it is clear even to the uninitiated like most of us that the 
subject is likely to be fruitful on both the physical and mathe- 
matical side. as to the theory of numbers it is only 
_ Recessary to mention that men of highest mathematical genius, 
such as Gauss and Dirichlet, who are also among the founders 
