of Edinburgh, Session 1873-74. 
229 
Monday, 22 d December 1873. 
Sir W. THOMSON, President, in the Chair. 
Professor Andrews, Hon. F.R.S.E., Vice-President of 
Queen's College, Belfast, gave an Address on Ozone. 
Monday, 5th January 1874. 
Professor Sir WILLIAM THOMSON, President, 
in the Chair. 
The following Communications were read ■ 
1. A new Method of Determining the Material and Thermal 
Diffusivities of Fluids. By Sir William Thomson. 
2. Continuants — A New Special Class of Determinants. 
By Thomas Muir, M.A., Assistant to the Professor of 
Mathematics in the University of Glasgow. 
1. A determinant which has the elements lying outside the 
principal diagonal and the two bordering minor diagonals each 
equal to zero, and which has the elements of one of these minor 
diagonals each equal to negative unity, may be called a Continuant. 
Thus 
a l b l 0 0 
- 1 a 2 b. 2 0 
0-1 a s b a 
0 0-1 a. 
is a continuant of the fourth order. 
2. A continuant is evidently a function of the elements of the 
principal diagonal and the variable minor diagonal, and of these 
alone. Let this function be denoted by K. The above continuant, 
for example, may then be written 
