In the following exposition of the Calculus of Finite Differences, particular attention has been paid to the connexion of its methods with those of the Differential Calculus–a connexion which in some instances involves far more than a merely formal analogy.

Indeed the work is in some measure designed as a sequel to my Treatise on Differential Equations. And it has been composed on the same plan.

Mr Stirling, of Trinity College, Cambridge, has rendered me much valuable assistance in the revision of the proofsheets. In offering him my best thanks for his kind aid, I am led to express a hope that the work will be found to be free from important errors.