" 1 We prefer giving them here in Swainson's version, because he seems to have set them forth more clearly and concisely than Macleay ever did, and, moreover, Swainson's application of them to ornithology - a branch of science that lay outside of Macleay's proper studies - appears to be more suitable to the present occasion.
This is expressed by saying that the sequence converges to (x+h)" as its limit; it may be stated concisely in any of the three ways, (x+h) n =lim(x"+n(1)xn-lh+....+ n(T)xn-rhr+ï¿½ï¿½.),(x+h)n =lim Sr, Sr. (x+h)n.
Illingworth has said very concisely: " The physical speculations of the Ionians and Atomists rendered a God superfluous, and the metaphysical and logical reasoning of the Eleatics declared Him to be unknowable."
The arrangement down to this point is far from strict, and beyond it is almost impossible to describe concisely, though there is still a rough grouping of characters according to resemblance of form, nature or meaning.
The course of reform may now be concisely summarized.