The reviewer expresses doubt, rather than decision, on our placing military and naval architecture in the department of pure mathematics. Military architecture embraces fortification and fieldworks, which, with their bastions, curtains, hornworks, redoubts, &c., are based on a technical combination of lines and angles. These are adapted to offence and defence, with and against the effects of bombs, balls, escalades, &c. But lines and angles make the sum of elementary geometry, a branch of pure mathematics; and the direction of the bombs, balls, and other projectiles, the necessary appendages of military works, although no part of their architecture, belong to the conic sections, a branch of transcendental geometry. Diderot and D'Alembert, therefore, in their _Arbor scientiæ_, have placed military architecture in the department of elementary geometry. Naval architecture teaches the best form and construction of vessels; for which best form it has recourse to the question of the solid of least resistance; a problem of transcendental geometry. And its appurtenant projectiles belong to the same branch, as in the preceding case. It is true, that so far as respects the action of the water on the rudder and oars, and of the wind on the sails, it may be placed in the department of mechanics, as Diderot and D'Alembert have done; but belonging quite as much to geometry, and allied in its military character to military architecture, it simplified our plan to place both under the same head. These views are so obvious, that I am sure they would have required but a second thought, to reconcile the reviewer to their _location_ under the head of pure mathematics. For this word _location_, see Bailey, Johnson, Sheridan, Walker, &c. But if dictionaries are to be the arbiters of language, in which of them shall we find _neologism_. No matter. It is a good word, well sounding, obvious, and expresses an idea, which would otherwise require circumlocution. The reviewer was justifiable, therefore, in using it; although he noted at the same time, as unauthoritative, _centrality_, _grade_, _sparse_; all which have been long used in common speech and writing. I am a friend to _neology_. It is the only way to give to a language copiousness and euphony. Without it we should still be held to the vocabulary of Alfred or of Ulphilas; and held to their state of science also: for I am sure they had no words which could have conveyed the ideas of oxygen, cotyledons, zoophytes, magnetism, electricity, hyaline, and thousands of others expressing ideas not then existing, nor of possible communication in the state of their language. What a language has the French become since the date of their revolution, by the free introduction of new words! The most copious and eloquent in the living world; and equal to the Greek, had not that been regularly modifiable almost _ad infinitum_. Their rule was, that whenever their