730 Proceedings of Royal Society of Edinburgh. [sess. 
The General Secretary read the following special account of the 
reasons for the award : — 
In awarding the Keith Medal and Prize for a second time to Dr 
Thomas Muir, the Royal Society desires to express its sense of the 
importance of the continuation of Dr Muir’s Researches in the 
Theory of Determinants and its Applications. Since 1883 he has 
enriched the Proceedings and Transactions of the Society with a 
continuous stream of papers, many of them containing new results 
of permanent importance, others co-ordinating, extending, and 
tracing to their sources theorems already known, and all of these 
marked by the peculiar analytical sagacity which is familiar to the 
reader of Dr Muir’s mathematical writings. 
Prominent among these memoirs is a series of papers on the 
Theory of Determinants in the Historical Order of its Development. 
The series contains the most complete bibliography of the subject 
in existence, accompanied by a critical analysis and comparison of 
the various memoirs from the dawn of the theory to its latest 
modern development. This monograph will form a monument of 
the learning and mathematical acumen of its author more enduring 
than the Keith Medal ; for it cannot fail to remain a permanent 
chapter in the history of mathematics, which will no doubt be 
added to by future investigators, but which will never be wholly 
superseded. 
The Makdougall-Brisbane Prize for the period 1896-98 having 
been awarded by the Council to Dr William Peddie, for his 
papers on the Torsional Rigidity of Wires, the prize was presented, 
the General Secretary reading the following statement as to the 
reasons for its award : — 
The Makdougall-Brisbane prize for 1896-98 is awarded to Dr 
William Peddie in recognition chiefly of his experimental researches 
in physical science. In his investigations on the torsional rigidity 
of wiles, he has studied the effect of large oscillations on the 
elasticity of the wire, thus supplementing in a very important 
direction Lord Kelvin’s well-known results for small oscillations. 
In the second paper, communicated to the Society in 1896 ( Trans- 
actions , vol. xxxviii.) the formula which had been found to repre- 
sent with great accuracy the relation between range of oscillations 
