De Attentionis mensura causisque primariis. By J. F. Herbart.[578] Koenigsberg, 1822, 4to.
{254}
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.
