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Proceedings of the Royal Society 
heart and respiration, this agent is, in a very high degree, safer 
than chloroform. 
9. These results confirm and amplify those stated in a previous 
report, to the effect that ethidene does not compromise the heart 
as does chloroform. By the method of experimentation then 
employed, the effect on the blood-pressure could not be deter- 
mined, and altogether the results here obtained are more exact and 
unequivocal. 
3. Experiments with Botating Discs. By Mr John Aitken. 
Communicated by Professor M‘Kendrick. 
4. General Theorems on Determinants. 
By Thomas Muir, M.A. 
5. Preliminary Note on Alternants. By Thomas Muir, M.A. 
(Abstract.) 
When the elements of the first row of a determinant are all 
positive integral powers of one quantity, the elements of the second 
the like positive integral powers of another quantity, and so on, the 
determinant is called an Alternant ; for example, 
a m a n a? 
b m b n 
c m c n c p . 
Every alternant of the n th degree is evidently a function of n 
variables, viz., the n quantities whose powers are the elements. To 
interchange two of these variables would be the same as to inter- 
change two of the rows of the determinant, and therefore would 
have the effect of merely changing the sign of the function. A 
function having this property, and therefore closely resembling a 
symmetric function, Cauchy called a symmetric function also, dis- 
tinguishing the two kinds as alternating and permanent. The 
narrower meaning of symmetric having, however, been adhered to, 
the other kind of function, viz., that above exemplified, has been 
known as simply an alternating function, and hence Sylvester’s word 
alternant. 
