Imatges de pàgina
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determine

tiously, the

59. Suppose B DE the curve, B C the ab- A rule to cifax, CD the ordinate = y, A B the tan- expedigent linet, and the nature of the curve be fuch, that the greatest power of y ordinate be curve lines. on one fide of the equation; then y 3x3

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ayy: but if the greatest power of y be wanting, the terms must be puto.

E

tangents of

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Then make a fraction and numerator; the numerator, by taking all the terms, wherein the known quantity is, with all their figns; and if the known quantity be of one dimension, to prefix unity, and of two, 2, if of three, 3, and you will have 3a32aay-2aax +

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ayy:

The fraction, by affuming the terms wherein the abfciffa x occurs, and retaining the figns, and if the quantity x be of one dimension, to prefix unity, as above, etc, etc; and then it will be ~3×3 - 2 x xy + xyy - a ax + 2 axx:

then

vations

Jubræ,

then diminish each of these by x, and the denominator will be 3xx - 2 x y +yy—aa+

2 ax.

This fraction is equal to A B, and therefore t is — — 3 a3 + 2 aa y − zaa *+ax x— ayy

-

of

3x-2xy +ÿy—aa+za x In this eafy way may the tangents of all geometri cal curves be exhibited; and I add, by the fame method, if you are skilful, may the tangents infinite mechanical curves be determined. Many other fine things, in the mathematical way, I looked over in the journal of these gentlemen. I likewife faw them perform several extraordinary experiments.

Microfco- 60. They make all the mathematical inftrupical obfer. ments they use, and have brought the micromade at U. fcope in particular, to greater perfection than I have elsewhere seen it. They have them of all kinds, of one and more hemifpherules, and from the invented spherule of Cardinal de Medicis, not exceeding the smallest pearl placed in a tube, to the largest that can be used. They had improved the double reflecting microscope, much farther than Marshal's is by Culpepper and Scarlet, and made feveral good alterations in the fo lar or camera obfcura microfcope; and in the catoptric microscope, which is made on the model of the Newtonian telescope.

the micro

61. In one of their beft double reflecting Colours in optical inftruments, I had a better view of fcope. the variety and true mixture of colours than ever I faw before. The origins and mixtures were finely vifible. In a common green ribbon, the yellow, the light red and a blue, appeared diftinct and very plain: the lively green was a yellow and blue: in a fea green, more blue than yellow: the yellow was a light red and a pellucid white: All the phœnomena of colours were here to be found

out.

microscope.

62. In this inftrument, the fineft point of a works of needle appeared more blunt and unequal, and art in the more like a broken nail, than I had before feen it the fineft edge of a razor was like the back of a dog, with the hair up: the finest paper, was great hairs, cavities, and inequalities and the fmootheit plate of glafs, was very rough, full of cracks, fiffures and inequalities. Very different, indeed, are the things finished by human art, from the things finished by the hand of nature. The points, the edges, the polish, the angles, every thing that nature produces, appear in the inftrument in a perfection that aftonishes

the beholder.

dom in a

63. In the views I here took of the vege- The vege table world, with my eye thus armed, I faw table kingmany extraordinary things I had never ob-microfcope, ferved before. I took notice, in particular,

that a fage leaf is covered with a kind of cobweb, in which fwarms of little active creatures, with terrible horns and piercing eyes, are butily employed: a mulberry leaf was an amazing flexus or net-work: we can fee but 9 ribs on the figillum Solomonis; whereas my armed eye perceived here 74: in a nettle I obferved its whole furface coof a nettle vered over with needles of the most perfect ble reflect- polish, every one of which had three points, ing micro- (points very different from our finest points,

An account

in the dou

[cope.

A forrel leaf, and buds of

not flat, but to perfection fharp); and that these needles refted on a bafe, which was a bag of a flexible fubftance, in form of a wild cucumber, and filled with a sharp, poisonous liquor this is discharged at the extremity of every point of the needles that cover the furface of the nettle: from a hole visible in every point the poifon is thrown out, and excites a sense of pain; and a heat arises as the blood flows more copiously to the wounded part: By preffing with my finger the extremity of the prickles, the bag of poifon fell; and on taking off the finger, it fwelled again. What a piece of workmanship is here in a nettle! Wonderful are thy works, O Lord God Almighty!

A leaf of forrel in this microscope exhibited to my eye oblong, rough and straight and almond atoms, fharp as needles, and from thence the in a micro tongue is twinged. In a bud cut away

french bean

fcope.

with

a fine

2

a fine needle from a steeped feed of a french bean, I faw the intire plant; and in an almond fo cut away, the perfect tree. Many other wonderful things I obferved of the vegetable kingdom, in the microscopes of thefe gentlemen.

flea in a mi

A defcrip

64. As to the animal kingdom, my ob- A loufe and fervations on it, in the optical inftruments at croscope. Ulubra, were fo many, that I could fill a volume with the things I faw: but, as I have little room or time to fpare, I fhall only mention two or three.In the double reflecting telescope, a loufe and a flea were put; which are creatures that hate each other as much as fpiders do, and fight to death when they meet. The flea appeared first in the box, and as he was magnified very great- tion of a ly, he looked like a locuft without wings; fiea. with a roundish body, that is obtuse at the end, and the breaft covered with an armature of a triangular figure; the head fmall in proportion to its body, but the eyes large, red, and very fierce; his fix legs were long, robuft, and made for leaping; the antennæ short, but firm and fharp; its tail was fcaly, and full of stings, and its mouth pointed into active pincers: his colour was a deep purple.

The louse in white was next brought on, The louse, and had a well-shaped, oblong indented body: his fix legs were fhort, made for walk

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