4D+5 E+ &c.: and substituting these in the given equation it becomes as below; namely, li 1A+2/Bt+3/C + 4 / Di3 +5/Et+ &c. —pti— p A t -2pBt-spCt-4pDt- &c. Whence, equating the homologous terms, to find the quantities A, B, C, &c. they become E= 414 35 k p2 q3 — 52 g k p2ql+8k2q3+12g1 kla p2+12 p*q—24/p*q &c. 5 15 &c. Therefore the fluent required is v= pq 212 g l p*q=2g !p2+kq" ¿? + P*q—2!p*q+2kpq" — 2xk/pq • + 313 414 35kp2q2-52g kp3ql+8k*q3+12g2kl2p2+12p*q—24lp*q 515 1+ &c. And hence the space x is readily found = "+ r p q — 2 g l p13 p2 q — 2 g lp2+k q2+ p3q—2lp3g+2kpq® 6P + 19 2014 — 2 g k l p q μs + &c.; where, making ta in both expres sions, the values of v and x as required by the proposition will be determined. SCHOLIUM. SCHOLIUM. In this solution, the resistance of the air to the rocket's Scholium, motion is supposed to vary directly as the square of the velocity; an hypothesis which experiments disprove when applied to military projectiles with cannon balls; but it is to be apprehended, that in the motion of rockets the deviation from this law is scarcely to be regarded, since, what takes place in the flight of shot and shells to violate it, is in a great measure obviated in the rockets, by the extreme heat of the flame that rushes from them; this rarifying the ambient air promotes the motion of the particles striking the head of the rocket towards its hinder parts; and since it is only the immediate motions of such particles backwards that can cause the law to obtain (for it would obtain correctly, if, after the impact of the particles they had no power to impel others lying before them, but either glided off from the surface struck, or had their force annihilated by it at the moment of striking) it is to be expected that the conclusions here brought out which are grounded on this law of resistance, will be found to agree pretty correctly with the results determined from experiment. But if they should not, let then the law of resistance be as the nth power of the velocity; and the method of solu tion will remain precisely the same as before. For it is only the fourth equation in the preceding process, namely, kv" &c. that will vary or become affected by any deviation from the law we have assumed; and therefore when this shall have been settled by experiment (the only way in which it ever can be settled), and the absolute resistance determined in any one case of velocity, and the real strength of the rocket composition ascertained; then, and not till then, shall we be able to offer any unerring rules to the military practitioner. II. The beautiful Tint of Flowers acquired by the same Means that paint the Rainbow. In a Letter from Mrs. AGNES IBRETSON. Dissection of towers. SIR, As To Mr. NICHOLSON. S I mean to dedicate the present year to the considerthe corolla of ation of the interior of plants in general, I cannot better begin it, than by giving to the public the dissection of the corolla of flowers, a subject in itself so very curious, that I scarcely know any in botany (where utility is not concerned) that more merits the attention of the inquisitive. By taking the petal of each different sort of flower, and splitting it, drawing off the upper and under skins, and leaving only the pabulum or middle part to be examined singly, and then magnifying each skin alternately, the most exact result is gained; which I shall now lay before you. Petals of flow the aqueous The petals of flowers owe none of their beauty to the coes derive their lour that paints them, which is, when drawn off, dull and beauty from dead: nor do they owe their brilliant tints to the skin that particles in covers them but the greatest part of their loveliness is detheir pabulum, rived from the bubbles of water, that compose their pabulum. Receiving the sun's rays they are enlivened and brightened by the reflection and refraction, from those drops of water, and from that spot of light seen in every bubble of water, and striking to the focus underneath them; by which means the whole flower would at times be a blaze of light, had not nature, to soften it, covered the petal with an upper and under skin, which curtails their diamondlike rays, and leaves them only a lightness and beauty unequalled. Uncovered they would resemble the rainbow formed by the same means (though coloured by the division of light): but, shaded as they are with a gauselike matter, they acquire a more chastened tint, and are equally delightful, without being oppressive to the sight. It must be rewembered, that I treat only of flowers which have regular petals, petals, and touch not on the cryptogamiæ, or any that pos sess not those direct parts. corolla. Taking the corolla of flowers in this strict sense, they Five kinds of may be divided into five different sorts: the thin petal, such as the rosa; the moist petal as found in the hyacinthus; the velvet denoted by the viola tricolor, and sweet scabious; the thick petal by the magnolia and lilium; and lastly, the everlasting, by the xeranthemum. their colour The petals of most flowers differ from leaves in many re- Petals differ spects, but particularly in one essential point; in leaves the from leaves in coloured part is within, and the upper skin (even of the being external. darkest leaves) is white; but in flowers, the coloured part is without, and the white is within; for almost every flower (the orange excepted) have their pabulum or interior white. The rose. Most thin petals (which I shall first describe), have, like Thin petals. the rose, when its upper surface is peeled off and examined, an extremely thin skin, in which are tiny bladders of pink liquid, woven in a sort of gauselike texture. But when this is taken off, it displays a pabulum of white or rather water bubbles, to which nature, (to lessen the brightness,) has added two circular white lines, which give a tenderness to the pink impossible to describe. The common violet is The common formed in the same manner; but the darker colour and violet. thicker skin lesssen the sparkling of the water. To prove that bubbles of water are the cause of the Experiment to beauty that flowers generally transmit, either in vivid flashes, show how or tender tints, to the retina; take the dullest colour that much colours are brightened was ever painted, and, filling a small glass bubble with wa by the sun's ter, let the rays of the sun fall through it on the colour, rays transmit ted through and it will become the brightest and most beautiful ima- water. ginable; and exactly resemble the tint of flowers. It was this discovery, that made me more than five years ago dedicate a whole summer to dissecting the petals of flowers, which I suspected to be beautified and enlivened by water. I then proved ny ideas. were just, that their tints were formed by colours transmitted through water, and like clouds and the rainbow owed their perfection to this cause; but I shall recur to this subject at the conclusion of my letter. -་ The Moist petal. Velvet petal. The second or moist petal is so filled with water, that it only excites our astonishment how such a thin gauselike matter can contain such a quantity of liquor; and yet the flower reposes on the hand without wetting it. No person can examine it, and not see that it owes its sparkling appearance to the water it coutains; for when we look at it in the sun, it almost dazzles the eyes. When I said that flowers owed the beauty of their tints to the bubbles, I did not mean all their charms: there are other arts by which they shine, and well deserve that encomium our blessed Lord bestowed: "not Solomon in all his glory was arrayed like one of these." The velvet petal I was long discovering the formation of. I saw it differed from every other, yet could not understand how, as it was evidently in the upper surface; for when this was taken off, its pabulum resembled that of the rose: but putting it a little sideways in the solar microscope, I soon Its structure. found out the secret. A vessel extremely diminutive is carried up and down in a scallop, as at a a, Pl. V, fig. 10, and each of the upper points divided. Why this produces such extreme softness, it would be very curious to inquire. The fact however is certain; it is by this means we make velvet, chenille, &c.; it is this that causes such extreme softness in feathers in general; in miniature painting it is this makes a stroke so much softer than a dot; and is it not the down on the cheek of beauty, which gives so exquisite a softness, that paint must directly destroy? Is is that the ray of light, instead of being repelled or absorbed, is reflected down the scallop, and therefore declines by degrees? It is curious that our method of making velvet should be precisely the same by which these flowers are formed, so that the studying of nature would have taught us that art. But how many secrets may she not teach, if she was pursued with avidity! To proceed, this scallop is found in every flower, which has this velvetty appearance, though in some it is deeper, in others less deep, and therefore not so soft: still it is always a scallop. Thick petal. The next petal I am to explain is the thick. It is composed of a thick but double surface skin; the pabulum having fourteen or sixteen layers of extremely diminutive round |