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• The cochineal, in the ftate in which it is hroughtto us, is in fmall bodies of an irregular figure, ufually convex, and ridged and furrowed on one fide, and concave on the other. The colour of the belt is a purptifh grey, powdered over with a fort of white dull. All that the world knew of it for a long time, was, that it was gathered from certain plants in Mexico, and therefore it was naturally fuppofed to be a feed. Reaumur's Hilt, of Infers, Tom. 4. p. 88.

In the year 1692, Father Plumier gave Pomet, the French author of a hiftory of drugs, an account of its being an ani- mal : this, however, was difregarded ; but Melli's. Hartfoeker, De La Hire, and Geoffroy, afterwards evidently proved it to be one ; and after this there were printed the depofrtions in form of a number of perfons upon the fpot, who all declare it to be a viviparous animal, and that it panes a great part of its life fixed to the vegetable body on which it feeds ; and that it was a creature fubject to no change, nor ever appearing in any other ftate. Thefe and many other qualities found in the cochineal, all analogous to thofe of the clafs ' of progall infects, give great room to believe that it is truly and properly an in- fect' of this clafs.

There are two kinds of cochineal, the finer called mejliquc, the other termed the wild cochineal. The firft is gathered from fuch plants of the opuntia as .are prepared and managed pro- perly on purpofe for the production of the animal, the other is found wild on the wild plant, and is much inferior to the mejlique in value. The mejt'cue has- its name from the name of the place, where it is propagated in the greateft quantity, Mcflique, in the Province of Honduras. As to the other, it is not yet determined whether it be another fpecies of the ani- mal, or whether the fame fpecies in a lefs thriving condition.

tl-j e"

ibid. p. 01.

7 he Indians plant about their habitations the opuntias, on which they propagate and raife the cochineal; they gather fe- veral quantities of it in the year, and what they are moft afraid of in regard to it, is, a cold or a wet feafon. In fuch cafes they cut off the leaves of the plant ftored with the in- fects, and take them into their habitations. Thefe are of fuch a nature as not to dry and wither immediately, like the lefs fucculent plants, but often keep their juices lon» enough to furnifh the creatures a fufficient nourifliment, till the dan- gerous feafon is over. -The infects are at this time in a ftate to produce their young ; and the Indians place them in a fort of little nefts, twelve or fourteen together, on difFerent parts of the opuntias of their plantation, "ibid. p. 93.. The animal is feldom more than three or four days in this condition, before it produces its young ones; each produces many thoufands, each fcarce fo large as the fmalleft mite ; the young brood foon quit their neft, and like the other gall and pr-gatl-infeRs, wander about the plant for a little time, and then fix themfelves upon it in feveral places. They do not eat the plant, but only introduce their trunks and fuck the juice, and wherever they fix themfelves, which is ufually in the more fucculent parts of the plant, there they remain till they have acquired their full growth, and are in a condition themfelves to produce young ones. Ibid. p. 94. The figure of this infeft is oval, and its utmoft fize is that of a fmall pea. It has fix legs armed with claws, two eyes, and a trunk by which it fucks its nourifliment. Ibid. p. 95. The ants, and many other little animals, are very fond of eating the cochineals ; and it is with great difficulty that the Indians defend the young brood from thofe devourers. Ibid. The firft of the gatherings of the cochineal, is at the time the Indians carry the parent animals to the plants ; when thefe have produced their young they die in the nefts, and the In- dians take down the nefts and take them out. The fecond gathering is three or four months after this, a little fooner or later, according to the feafon. The young ones produced from the former crop, have now acquired their full growth, and are ready to produce their young. In this fecond ga- thering they take care not to take off the whole generation, but leave enough on the plant to multiply and give them a new crop afterwards. About three or four months after this, they have another gathering from thefe. Soon after this the rainy feafon comes on, and the young ones produced from what are left on the plants from this gathering, are what the Indians houfe, for the parents of the next year's crops. The laft of thefe crops is the leaft valuable, being Generally foul and full of fmall infects of the new brood, among the right and full grown ones. Ibid. p. 96.

After the Indians have gathered the cochineal they kill it, other- wife they would loofe"a great part of their harveft ; for the parent race would live fome days after their being taken from the plant, and would produce their young, which would be nimble enough to run away in great numbers. Some to kill the creatures plunge them in hot water, and afterwards dry them in the fun ; others kili them by a proper degree of heat. Ibid. p. 97.

The living cochineals are covered, like all other infects of this kind, with a kind of white powder; but in the water ufed to kill them they loofc much of this powder, and are there- fore of a different colour from thofe ki led by heat. Ibid.p.98. The accounts from the place where the cochineal is produced, give us -all thefe particulars ; but to decide the long difputed

point, whether they are of the animal or vegetable kingdom, we have the means in our own hands* even in this part of the world. We need only moiften and foak in water, or in vi- negar, a number of cochineals till they arefwelled and diftend- ed, to know that every one is the more or lefs perfect bodv of an infect ; the moft imperfect and mutilated fpecimens al- ways fhew the rings of the body, and from obferving others it will be eafy to find the number and difpofition of the leo-s ■ parts, or even whole ones being left on feveral, and often compleat pairs. Ibid. p. 100.

People of warm imaginations no fooner knew it to be an in- fect, but before they were perfecily acquainted with its form,

■ they were for alluting it its proper dais. Some would have it to be a worm, others a fpider, and others a beetle. Petiver is of the number of the laft, and has been fanguine enough to figure it in all the ftates he fuppofed it to have pafted, the hexapodc worm, the nymph, and die perfect beetle ; tho' we now find by pofitive accounts from the place, that it un- dergoes no change at all, and from its whole figure and hif- tory, that it is properly of a clafs of animals then not known. Many have alfo been of opinion, that it was only a part of an animal, but a clofer and repeated obfervation would have fhewn them that it conies to us often more perfect than is imagined, and frequently wants only its horns and a leg or two, of being a perfect animal.

It is eafy to fee in fome of thefe the head 1, and fometimes a tubercle on c ach fide of it, which may very naturally be fup- pofed the eyes, or elfe the roots of the antenna; or horns. The firft pair of legs are thus found to be very near the head of the animal, and placed exafily as in all the gall-infect and progall-infecl clafs; a little above thefe one may diftinguifti alfo the remainder of the trunk fituated exaftly as in the gall in- faSts awl ptogsll-mfeeis ; the anus is alfo eafily diftin^uiihed. Ibid. p. 1 01.

As the manner of the fecundation of the gall-infefls was fo long unknown in Europe, it is no wonder that that oi the cochineal fhould not be very early difcovered in Mexico : but we have an account among Mr, Ruyfche's pieces from whence al- moft all the true hiftory of this animal is had, that at the feafon of the cochineals becoming big, there is feen continually among them a fmall butterfly, which is bred upon the fame plants, and by means of which the cochineals conceive This is fo ftriflly analogous to the manner of the gall-infefl clafs that there is no room to doubt the fafl; and it is a farther great proof, how little truth was before in the gueffes con- cerning the clafs of animals this belonged to. Ibid, p, 10?. It would be an eafy miftake for any one not profeffediy a ni- turahfl to miftake the male gall-infea for a butterfly, as it has white opake wings ; and affuredly the male cochineal' is an animal of the fame fpecies, a true two winded fly. If a full grown cochineal be foaked a confiderable time in wa- ter or vinegar, and afterwards gently preffed, there will fre- quently be protruded from its hinder part a number of fmooth oblong bodies, which might be eafily miftaken for eggs; but a good microfcope will fhew in thefe the traces of rhe leg's and other lineaments fufficient to prove it to be a true embryo fcetus. Ibid p. J04.

The wild cochineal differs from the mcflique in being lefs pure and confifting of animals of all ages and fizes, as bein<* <r a I thered wuh lefs care, and without the intent of propagating future crops ; the larger fpecimens in this fometimes exceed the finer cochineal in fize, and when moiftened and fqueczed fend forth vaft numbers of the fame oblong bodies ibid o' 105. *

Duhamel, while he refided at St. Domingo, found in that ifland the fame ammal which Father Plumier had before ob- ferved there, and accounted the fame creature with the cochi- neal infect ; he gathered fome of thefe animals from off the opuntias there, and fent them over to Paris ; they were found to have all the exterior marks of co.hincal; but it is much to be feared they are really no more than that to the cochineal, which the common peach and vine gall-infeSts are to the kermes of the ilex. Poffibly, however, a proper care and at- tention, and the bringing over the very creatures from Mexico toother parts of the world, might, with many tryals to de- termine what fpecies of the opuntia it is that they moft thrive on, be a means of propagating them to vaft advantage Ibid p. 108. °

JofTelin, in his account of the produfls of New England men-

■ tions a particular kind of fun-flower, called b v fome a fpe- cies of golden-rod; the ftalks of which are covered about the knots in the fummer months with infeds of the fize of large fleas. Thefe prefcrved in a proper manner, yield a very ele- gant fcarlet colour, and the author thinks might be made to tupply the ufe of cochineal.

PROGRESSION (Cyct )-A, a right line, or figure, may in- create continually, and never amount to a given line or area - fo there are progreffwm of fractions which may he continued' at pleafurc, and yet the fum of the terms be always lefs than a given number. If the difference between their fum and this number decreafe in fuch a manner, that by continuing the progreffiort it may become lefs than any fraction how fmall foever, that can be affigncd ; this number is the limit of the fum of the progrejfion, and is what is underftood by the value

of