This celebrated philosopher maintained that mathematics ought to be applied to psychology, in a separate tract, published also in 1822: the one above seems, therefore, to be his challenge on the subject. It is on _attention_, and I think it will hardly support Herbart's thesis. As a specimen of his formula, let _t_ be the time elapsed since the consideration began, [beta] the whole perceptive intensity of the individual, [phi] the whole of his mental force, and _z_ the force given to a notion by attention during the time _t_. Then, z = [phi] (1 - [epsilon]^{-[beta]t}) Now for a test. There is a _jactura_, _v_, the meaning of which I do not comprehend. If there be anything in it, my mathematical readers ought to interpret it from the formula _v_ = [pi][phi][beta]/(1 - [beta])[epsilon]^{-[beta]t} + C[epsilon]^{-t} and to this task I leave them, wishing them better luck than mine. The time may come when other manifestations of mind, besides _belief_, shall be submitted to calculation: at that time, should it arrive, a final decision may be passed upon Herbart. ON THE WHIZGIG. The theory of the Whizgig considered; in as much as it mechanically exemplifies the three working properties of nature; which are now set forth under the guise of this toy, for children of all ages. London, 1822, 12mo (pp. 24, B. McMillan, Bow Street, Covent Garden). The toy called the _whizgig_ will be remembered by many. The writer is a follower of Jacob Behmen,[579] William Law,[580] {255} Richard Clarke,[581] and Eugenius Philalethes.[582] Jacob Behmen first announced the three working properties of nature, which Newton stole, as described in the _Gentleman's Magazine_, July, 1782, p. 329. These laws are illustrated in the whizgig. There is the harsh astringent, attractive compression; the bitter compunction, repulsive expansion; and the stinging anguish, duplex motion. The author hints that he has written other works, to which he gives no clue. I have heard that Behmen was pillaged by Newton, and Swedenborg[583] by Laplace,[584] and Pythagoras by Copernicus,[585] and Epicurus by Dalton,[586] &c. I do not think this mention will revive Behmen; but it may the whizgig, a very pretty toy, and philosophical withal, for few of those who used it could explain it. {256} SOME MYTHOLOGICAL PARADOXES. A Grammar of infinite forms; or the mathematical elements of ancient philosophy and mythology. By Wm. Howison.[587] Edinburgh, 1823, 8vo. A curius combination of geometry and mythology. Perseus, for instance, is treated under the head, "the evolution of diminishing hyperbolic branches." The Mythological Astronomy of the Ancients; part the second: or the key of Urania, the words of which will unlock all the mysteries of antiquity. Norwich, 1823, 12mo. A Companion to the Mythological Astronomy, &c., containing remarks on recent publications.... Norwich, 1824, 12mo.