422 Professor Hamitton on Conjugate Functions, &c. 
reasoning, the usual principles respecting Imaginary Quantities, and was content to 
prove the symbolical necessity without showing the interpretation, or inner meaning, 
of his formule, the present Theory of Couples is published to make manifest that 
hidden meaning: and to show, by this remarkable instance, that expressions which 
seem according to common views to be merely symbolical, and quite incapable of 
being interpreted, may pass into the world of thoughts, and acquire reality and signi- 
ficance, if Algebra be viewed as not a mere Art or Language, but as the Science of 
Pure Time. The author hopes to publish hereafter many other applications of this 
view ; especially to Equations and Integrals, and to a Theory of Triplets and Sets of 
Moments, Steps, and Numbers, which includes this Theory of Couples. 
THE END. 
