FLY
- ' - .'- are of the third clafs, and as far as has appeared
t 4-xxr
hitherto, cannot be reduced to the former. See Maclaurin, Flux. B. II. Ch. 3. Art. 798, &c.
F L Y
It is to be obferved, as to the fluent of
- , or of
•/* x V 1 i. xx
s ,2 that it does not appear poflible to reprefent them
by any hyperbolic arc and algebraic quantities. But by af- firming an elliptic arc likewife, they may be comlructed. See Mackur'm, Lib. cit. Art. 802.
So likewife to reprefent the fluent of
•/% x^i^' z — z z -, we mull have recourfe to
or of ' -' , , —
y'a* *»+ %a ep* — /«
both the hyperbolic and elliptic arcs. Maclaurin, L. c, Art.
805.
rn z — 1 %
The fluent of 4 is afllgnable by the arcs of co-
/* + /■"
nic fections, when r is an integer number ; that is, by right lines, when r is equal to 4 or to any multiple of 4 ; by circu- lar and parabolic arcs (reducible to logarithms) with right lines, when r is any other even number ; by arcs of an equilate- ral hyperbola with right lines, when r is any number of the feries 3, 7, II, 15, &c. and by arcs of the fame hyperbola and right lines, with arcs of an ellipfis, that has its excentri- city equal to the fecond axis, when r is any of the numbers
- > 5> 9. '3> &c. See Maclaurin, ibid. Art. 809.
We prefume, upon the whole, that few will be fo Scrupulous as to deny the Newtonian doctrine of Fluxions to be intelligi- ble, and accurately demonftrated. But on the other hand it mull be confeffed, that the introduction of the notions of motion and velocity, which are mechanical, feems not to have thrown any light on this part of geometry. The confede- ration of the limiting ratios of variable quantities, and that of the limiting polygons of curves, as it requires no other knowledge but what depends on the common properties of number and magnitude, fo it feems, in all refpects, the molt clear and un- exceptionable manner of confidering the fubjefls treated of in the higher geometry. An eminent mathematician feems to declare himfelf of this opinion, when he fays, that quadra- tures by limiting polygons is one of that kind which requires no other knowledge but what depends on the common pro- perties of number and magnitude ; and fo may ferve as an in- stance to fhew, that no other is requilite for the eftablifh- ment of principles for arithmetic and geometry. A truth, which, though certain in itfelf, may perhaps feem doubtful from the nature and tendency of the prefent inquiries in ma- thematics. For among the moderns fome have thought it ne- ceffary, for the inveftigation of the relations of quantities, to have recourfe to very hard hypothefes ; fuch as that of num- ber infinite, and indeterminate j and that of magnitudes mjla- lu fieri, exifting in a potential manner, which are aftually of no bignefe. And others, whofe names are truly to be re- verenced on account of their great and lingular inventions, have thought it requifite to have recourfe even to principles foreign to mathematics, and have introduced the confideration of efficient caufes and phyfical powers, for the production of mathematical quantities ; and have fpoken of them, and ufed them, as if they were a fpecies of quantities by themfdves. Vide Machin, in Phil. Tranf. N°. 447. FLY. The account of the feveral fpecies, genera and claffes of fiies, is no fmall part of the natural hiftory of infecls. The number of the fpecies of fiies exceeds perhaps even that of the butterfly ; but the fiies are in general fmall, tho' there are fome, as the libells, whofe bodies are longer and larger, than thofe of the largeft butterflies. The cicada; alfo belong to the fiy clafs, and there are fome of thofe, whofe fize exceeds that of the largeft butterflies in the thicknefs of their bodies. The generality of fiies however are much fmaller than the butter- fly clafs, and many of them are indeed fo very fmall, as not eafily to be diftinguifhed.
Many of the fiies are in their prior ftate hid from us, or de- tained among very difpleafing matters; it is in their winged flate, that they become an agreeable objeft of our refearches and it may be moft proper therefore, to begin their hiftory in that ftate, occafionally defending to the others. Reaumur's Hift. Inf. Vol. 4. p. 124.
It is a common error to imagine, that the fmall fiies one fees in the fpring, will become larger in fummer. This is wholly without foundation, iince all the fiies, like other in- fects which undergo a metamorphofis, become of their full bignefs, as foon as they arrive at the fly ftate, and never grow afterwards.
The general and obvious charaaer of fiies, by which they are diftinguifhed from other winged infias. is their having tranf- Supj-i.. Voi. I. "
parent wings, made as it were of gawze, and never having or. them any of that powder which dulls the fingers in touching the wings of butterflies, and having no cafes or covers ibr them. They are by this plain charter of their tranfparent and naked wings, diftinguifhed from the butterfly, the beetle, the grafshopper; and other claffes of winged infects. The parts of fires are the head, the corcelet, and the bodv. The corcelet many authors have called the breaft, becaufe it is placed as the breaft in us ; but as that name might natural- ly lead us to believe, that the lungs and trachea: had their place there, it is very neceffary to change the term, when fpeaking of animals whofe tracheae are diftributed all over their bodies.
To the corcelet the wings are affixed, and in the body are contained the ftomach, inteftines, the parts of generation, and a great many of the trachea;. The head inTfe'cj is ufually joined to the corcelet by a very fhort neck, and can often turn on it as on a pivot. Some fiies there are which have as it were two corcelets, one feparated from the other ; the firft in this cafe is ufually very fmall, and the wings are affixed to the fecond. The corcelet is the moft prominent and rounded part of the infect, it is always the ftrongeft parr, and is fre- quently the thickeft. The formica leo and fome water in- fects, are transformed into fiies which have double corcelets, or corcelets divided into two.
The mod obvious diftinctions for the arrangement of fiies into claffes, is the number of their wings ; fome having only two, others four. And this is fo plain and obvious a divilion, that it is wonderful, that the writers of natural hiftory have not long fince fallen into it, nay, many of them have often omitted to tell us the number of wingsof the fpecies they defcribe; The firft general divifion of fiies is therefore into that of the two Winged, and four winged kinds. A very flight obfervation is generally fufficient to determine to which of thefe divifions, a fiy belongs; but if we afterwards examine a fiy with more at- tention, and take into confideration-, the organs by which it takes its nourifhment ; one may obferve, that fome of them are able to thruft out that organ to a confiderable diftance from their head; and that this organ, which while in a ftate of reft is folded up or fhortened, or turned about, or laid clofely down, when the creature wants to ufe it, is unfolded, lengthened, extended or railed. This organ, is what naturalills call the trunk of an infect, but there are many other flies which have no trunk ; thefe have no other than an opening, fc-rving for a mouth, furrounded with lips and with fome other parts. This fort of opening from its fituation and figure, may very proper- ly be called a mouth.
Some of thefe mouths have nothing analogous to teeth about them ; but there are others which have teeth, faws, or grind- ers, placed on the outfide of the mouth, and moveable as in the caterpillars, with which the fiies tear and deftroy leaves fruits and flefh ; finally there are alfb fome fiies to which na- ture has allotted both a trunk, and thefe organs. Thefe charaaers give us very naturally the diftinflions of four Subordinate claffes under the two former general ones. The firft contains thofe fiies which have a trunk and no teeth or faws. The fecond contains thofe which have a mouth without any fenfible teeth. The third, thole which have a mouth furnifhed with teeth ; and the fourth, thofe which have both trunks and teeth. Among the fiies which have mouths furnifhed with teeth, fome have them not only without, but within their mouths alfo.
All the two winged fiies belong to the firft or fecond of thefe dalles; the great blue flefh fiy, the fmall fiies that are fo troublefome about our houfes, and the gnats are all of the firft clafs, and have trunks and no teeth. The fpring ft. fo common in gardens, and a fort of fiy refembling the gnat kind, but much larger, are of the fecond clafs, and have mouths but no fenfible teeth.
The four wingedjfe furnifh us with great numbers to fill up the other two claffes, left vacant by the former. All rhe bee kind have a trunk and two teeth ; all the wafp kind have a mouth furnifhed with two teeth; and there are befide thefe feveral of the four wingedyfrw which belong to the fecond clafs ; all the papilionaceous fiies produced of water tteniae, are of this' fort, as having a mouth without teeth. Several fmall four winged fiies are alfo of the firft clafs ; as the flying pucerons, and falfe pucerons, which have all trunks and no teeth : neither are the fmaller fpecies only of this clafs, iince the cicada; alfo belong to it.
A fifth clafs may however be alfc eftablifhed, tho' the fpecies of it are only few, there being only two kinds of fiies of it, this is of thofe which have their head fcrving the office, or made in the form of a trunk. The fiies of this" kind have ve- ry long heads, which like thofe of birds terminate in a fort of beak : this however in the fiy kind is never opened except at the end, or in other words, thefe fiies have heads, which are lengthnrd out into the refemblahce of a bill, or figure of a trunk, but which is ftiff and cannot change its figure, nor alter its pofition otherwife than by the altering that of the whole head. At the end of this fort of trunk are placed the 11 O ,«, lh
