
1904.| Anmversary Address by Sir William Huggins. 23 
Bakerian Lecture on the same subject. It perhaps still remains a task for the 
future to verify or revise the details of these remarkable transformations of 
material substances, resulting apparently in the appearance of chemical 
elements not before present; but, however that may issue, by the detection 
and description of radio-active emanations and their transformations, 
Prof, Rutherford has added an unexpected domain of transcendent theoretical 
interest to physical science. 
RoyaL MEDAL. 
A Royal Medal is awarded to Prof. W. Burnside, F.R.S., on the ground of 
the number, originality, and importance of his contributions to Mathematical 
Science. The section of our “Catalogue of Scientific Papers” for the period 
1883-1900, enumerates fifty-three papers by Prof. Burnside, the first dated 
1885, and the “International Catalogue of Scientific Literature” thirteen 
more. His mathematical work has consisted laregly of papers on the Theory 
of Groups, to which he has made most valuable additions. In 1897 he 
published a volume “On the Theory of Groups of Finite Order,” which is a 
standard authority on that subject. Two recent papers on the same theory, 
published in 1903, may be specially mentioned. In one of these he succeeded 
in establishing by direct methods, distinguished by great conciseness of 
treatment, the important subsidiary theory of group-characteristics, which had 
been originally arrived at by very indirect and lengthy processes. In the 
other he proved quite shortly the important result that all groups of which 
the order is the product of powers of two primes are soluble. 
Besides the treatise and papers relating to group theory, Prof. Burnside 
has published work on various branches of pure and applied mathematics. 
His work on automorphic functions dealt with an important and difficult 
special case which was not included in the theory of these functions as 
previously worked out. The paper on Green’s function for a system of non- 
intersecting spheres was perhaps the first work by any writer in which the 
notions of automorphic functions and of the theory of groups were applied to 
a physical problem. He has also made important contributions to the Theory 
of Functions, Non-Euclidean Geometry, and the Theory of Waves on Liquids. 
His work is distinguished by great acuteness and power, as well as by unusual 
elegance and most admirable brevity. 
RoyvaL MEDAL. 
The other Royal Medal is awarded to Col. David Bruce, F.R.S., who, since 
1884, has been engaged in prosecuting to a successful issue researches into 
