On the Calculus of Operations. 331 
The entire structure of the Calculus of Operations is based, 
upon the principle of wniformity of action. Under this principle, © 
_ when the order of the primitive operator is higher than unity, 
the final result will be a corresponding power of*the general 
number x; but when the operator is of the first order only, we 
get powers of unity. 
It is conceived that a uniform action is susceptible of accurate 
measurement in its immediate result, which must necessarily in- 
_ The principle of uniformity of action, it is believed, will be 
found to hold a place in algebraical logic, similar to that held by 
comprises the categories of existence complete ; that these cate- 
gories are not merely subjective, like those of the system of Kant, 
but have full objective validity; and that they are not liable to 
the charge either of deficiency or redundancy, as are the famed 
_Itis to be recollected that this is the first publication of the 
discoverer of this method (if peradventure it shall be admitted to 
. 
f tation, it may be remarked, that in ordinary multiplication, 
& linear unit (unit of operation) is constant, and successive, mu id 
Plication merely increases the dimensions of x, as 1, 2, 4°, 2°, 
etc. But when it is shown how the unit of operation may in- 
