748 Proceedings of Royal Society of Edinburgh. [sess. 
and when minute or therapeutic doses are given, the muscle action 
does not assert itself so conspicuously as the nerve action ; hut when 
the doses are large, the action on the muscle of the heart over-rides 
the less powerful action upon the intra-cardiac nervous structure. 
Whether this latter structure can further be defined by experi- 
ment or not, the most important consideration is that the action 
upon it contributes greatly to enhance the value, for therapeutic pur- 
poses, of the action of Strophanthus upon the muscle of the heart ; 
as the two actions in combination render the contractions of the 
heart stronger and more ample than they could he rendered by 
either action alone. , 
In thus presenting to the Society a synopsis or sketch of the 
observations made, during a series of years, on the Natural History, 
Chemistry, and Pharmacology of Strophanthus, I have endeavoured 
to select what appear to be the more important of the results that 
have been arrived at. In the pharmacological part of the observa- 
tions these are probably the results that relate to the action upon 
the circulation. The nature of this action, determined by pharma- 
cological experiments , rendered it obvious that Strophanthus would 
produce beneficial effects in many forms of disease of the heart. 
It was, therefore, employed for that purpose, and the most sanguine 
anticipations of its value have now been amply confirmed. 
The Theory of Determinants in the Historical Order 
of its Development. By Thomas Muir, M.A., LL.D. 
Part I. Determinants in General (1841-44). 
(Continued from p. 448 of Vol. XYI.) 
It is next pointed out that the transformation of the primitive 
permutation into any other may be accomplished by interchanges 
only, because by this means any given letter may be made to 
occupy the first place, then any other given letter to occupy the 
second place, and so on. From this also it follows that any system 
of circular substitutions may be replaced by a system of inter- 
changes. Should the transformation of one permutation into 
another be effected by interchanges, the number of these will be 
