arising from the age of the canella, the part of the tree from which it is gathered, and from the manner of cultivating and curing it. In the Philosoph. Transact. N° 278, in Mr. Strachan's account of Ceylon, he says, that there are 2 sorts of cinnamon-trees, of which the tree which is esteemed the best has a leaf much larger and thicker than the other; but otherwise no difference is to be perceived. And in an account given some years ago to. the Royal Society, 3 or 4 sorts were mentioned; and it was said the best sort was cut every 3 or 4 years. This superiority Mr. W. then guessed to arise from the cutting the tree down. every 3 or 4 years, which occasioned it to produce strong and vigorous shoots, thicker and larger leaves, as well as a greater quantity of bark, and of a superior quality. A large shoot or sucker of this plant was produced in the year 1750, or 51, by Dr. Watson, together with an account of the cinnamon-tree; which is published in the Philosop. Transact. vol. xlvii. p. 301. This shoot was a plain proof that the cinnamon was frequently cut down, and that this shoot arose from the root of a plant so cut; for it was of the size of a walking-cane; and no shrub could have produced such a shoot, unless a strong plant cut down. The specimens which Mr. W. now produced, of the canella or bark of the cinnamon of Sumatra, he procured in the year 1755, from Mr. Tho. Combes, a gentleman then in the service of the East India Company in Sumatra, by means of a friend and an abstract of Mr. Combes's letter on the occasion, is as follows: I am of opinion, says Mr. C. that the true cinnamon grows no where but on the island of Ceylon, unless cassia be allowed to be the same tree, which I am inclined to think. N° 9 contains seeds of the cassia or wild cinnamon tree. As for the eeds of the true cinnamon-tree, I believe they are very difficult to be got; for as the Dutch are the sole masters of this spice, and get a good deal of money by it, they have very well guarded against the transplantation of it. I hope however that these seeds will not be unacceptable to you, as cassia itself is of some value; and as I am very doubtful whether this tree is not the same with the true cinnamon, being of opinion that the difference observed in them arises from the different method of curing their barks, or from the taking the bark from different parts of the tree, or at different seasons, or of different ages, or perhaps all these. I have made inquiry concerning this from some very intelligent persons, and found them to be of opinion that the cassia and cinnamon tree were of the same genus. I have inquired further concerning the method of curing it at Ceylon; but as this is done by the natives, the Dutch are not very well acquainted with it; nor could I obtain any good account of it, different people giving me different relations. Some said it was the inner bark, some the middle, and some the outer; though of the young branches, they seemed in general to agree, that it was gathered at a certain season of the year, and that one part of the cure was burying it in sand for some time. This may be tried with cassia, and may perhaps take away that viscosity or glutinous quality observed by chewing it, and which is the principal mark for distinguishing it from cinnamon. their chemical oils, I have heard many people say, that they are not distinguishable, otherwise than that from cinnamon is generally better, or, as it may be called, stronger than that from cassia; and accordingly bears a better price. But the Dutch company's chemist at Batavia, if I may give him this title, informed me that they are essentially different, and plainly distinguishable. But I must confess myself very doubtful of the knowledge or veracity of this chemist, and strongly suspect that they are no otherwise different than in goodness, as many other oils drawn from the same subject are. In Persia, I think they make not so great a difference between them as elsewhere; and I myself, for want of cinnamon here for some months past, made use of the fine quilled cassia; and the difference I observe between them I imagine to arise rather from the greenness and want of dryness in the cassia, than any thing else, or perhaps from the method of curing it: for if there happens to be a little too much cassia put into my chocolate (and other things I use in it,) a little bitterish taste arises, something like what we meet with in most barks; though I do not remember to have observed this of cinnamon but as to its boiling to a jelly, as Quincy mentions, I find no such thing, and think it bears boiling as well as cinnamon. Nor do I think its distilled water more subject to an empyreuma than that of cinnamon. I have inquired of the country people here who bring it us, and they tell me the finest sort is the inner bark of the small branches: and indeed that it is the inner bark, I think, is evident in cinnamon as well as cassia; no outer bark of the youngest branches of any tree having, in my opinion, that smooth surface observable in both these barks. END OF THE, FIFTIETH VOLUME OF THE ORIGINAL. Art. I. On the Greatest Effect of Engines with Uniformly Accelerated Motions. By Francis Blake, Esq., F. R. S. p. 1. Vol. LI. Anno 1759. The writers on the maximum of engines, or the greatest effect possible in any given time, have supposed the working parts of the machine to retain their direction, and be uniformly moved by the force of a current. They have therefore considered only the case of a uniform rotation, as in the action of grinding; where the impediments and impulses being brought to a balance, the impulses are only sufficient to prevent a decay in the generated motion. And, on that view of the problem, the load of an engine, when the effect is a maximum, and the force a current, is determined by computation to be * of the weight which would cause the engine to rest. This then being suited only to a uniform velocity both in the lever and obstacle, Mr. B. considers the case of a uniformly accelerated one in repeated vibrations. The maximum which corresponds to it is adapted to the steam-engine, and of no less importance to be determined than the other. A general expression for the time of a stroke in such vibratory engines, will easily lead us to a computation of their effects. Let AD be a lever, whose brachia are a and b, and supposed without weight. Let m be a power, and n a weight. Then ab::n: ba, the balance for n at a, a bn ma- nb and mbis the effective force at A, which multiplied by the lever a gives ma — nb for the efficaciousness of that force in the angular velocity of the power and weight. Now by the principles of mechanics, the inertia of any bodies revolving about a centre, is as the quantities of matter into the squares of the brachia; in the present case therefore, the whole inertia of m and n is as ma2 + nb2. . Hence then, and because the velocity generated in a given particle of time is as the force directly and inertia inversely, we have as the accelerating force or the measure of the angular velocity of the power and weight at the end of the said given particle of time. But again, the times of descent by means of uniform forces, through a given space, are inversely as the square roots of the accelerating forces, or measures of the velocities generated in a given particle of time; therefore ✔ is a general expression for the time of a stroke. This being had, the solution is easy; for, supposing n only to be variable, say n: 1, a constant or given time: n the effect in time 1, ex hypoth. the greatest effect which can possibly given time. Taking then, as usual, the fluxion equal 0, we per reduction, 2a3 m2 —3a2mnb + amnba—2n2b3 = 0, and n as ✔ ma2+nb2 ma2+nb ma nb ma- -nb ma2 +nb2 be produced in the said have, after a pro = amx (3a-b). Therefore, in these sorts of engines, when 462 a given, the weight: power :: ;-√ +(ab). ax (3a-b) b 46 462 : brachia are equal, i. e. if a = b, the weight: power :: ✔―÷: 1, viz. 0.618: The theory however is erroneous which brings out as may be seen fully explained in vol. 3, p. 144, &c. losophical Society; or in my Dictionary, v. 2, art. mill. - of the weight; it should be instead of of the Transactions of the American PhiC. H. 1 nearly when the effect is a maximum. And so, in like manner, when b, m and n are given, and a is made variable, it is easy to see that, instead of the load, the best distance of the power from the fulcrum of the lever will be the result of the process; viz. a : b : : n + √ n2+mn: m. But, this by the way. In the proportion here determined, the power m is a weight, and therefore ma-nb, which is the generating force, being partly employed to overcome the inertia of the quantity of matter m, it is not wholly taken up in giving motion to the weight n; and the relative velocity is continually decreasing. But on the other hand, if m be the force of a spring, as is that of our atmosphere, or if n can be uniformly accelerated any how, in repeated vibrations, that there may be no sensible diminution of the relative velocity, the whole will be exerted on the weight to be raised; i. e. the tension of the rope or chain, by which the power is confined to act on the weight, will always be the same as though the beam were at rest; and then, by expunging ma2 out of the expression for the greatest effect, n√ ma2+nb2 becomes evidently enlarged to n The consequences are these. 1st, The greatest effect of this engine when m is a spring, will al ways exceed the contemporary effect where m is a weight. 2dly, The proportion of the power and weight will then be n: m :: a: 26, as appears by taking the fluxion of n√ = 0, and reducing the equation in the manner above. Whence the load to be raised for the greatest effect of a steam-engine, if the inertia of the materials composing its working parts be put out of the question, will be just half of what is sufficient to balance the atmosphere, whether the brachia of the lever be equal or not. ub2 ma-nb ma-nb ma-nb ma`+nb2 Mr. B. here adds 2 or 3 remarks on what he formerly laid down concerning the proportion of the cylinders. And, 1st, in all values of the brachia, with regard to their lengths, and all values of n, the expression ✔ for the time of a stroke, when m is a weight, is the general expression to be used for the time. 2dly, m being considered as a spring, the time of a stroke is as mab; and then if, according to what he there directed, a be taken variable, and m the reciprocal of a, the advantages to be gained by the breadth of the cylinder can only arise from a diminution of friction, and from the matter in the beam; for, the expression ✔ becomes constant, and thence the strokes are isochronal. I might, furthermore, says Mr. B. proceed to examine into these advantages, more explicitly than is there done, on the principles laid dawn, when m is a weight, But many particulars (such as the form of the brachia and various appendages, with their quantities of matter and centres of gyration) being wanting to perfect the theory of the construction, I shall drop the nb2 ma-nb It is this: the shortness of inquiry when I have made only one remark more. the brachia diminishes the resistance of the engine to motion: and therefore the inequality which I proposed in them, was in part to avail myself of that obvious advantage, without incurring the inconvenience of enlarging the pump-bores. I say it is an obvious advantage; for, the matter in the brachia, that the equilibrium may be preserved, being inversely as their lengths, and the resistance to motion in the direct ratio of the squares of those lengths, the resistance of the longer arm is to that of the shorter as the lengths of them directly. II. Observations on the Growth of Trees. By Robert Marsham, of Stratton in Norfolk, Esq. p. 7. Measures of Trees, taken in April 1743, before they began to shoot; and again in Autumu 1758, after the Year's Growth was completed. The Measure taken at 5 Feet from the Earth. Now as the 12 trees above, contained 213 cubic feet 300 inches of timber in spring 1743, and have increased to 322 cubic feet 333 inches in autumn 1758; that is, 109 cubic feet 33 inches in 16 years growth; if all the trees were of the same kind, 109 feet pays 3 per cent. for standing: and the 6 oaks pay near the same interest, though one of them, N° 2, appeared past thriving in 1743; for the increase of the 6 oaks is from 112 feet 1 quarter 171 inches of timber, to 167 feet 138 inches, i. e. 54 feet 2 quarters 399 inches; which is above 3 per cent. But if we take only the 5 thriving oaks, then their content is, from 57 feet 3 quarters 267 inches, to 103 feet 2 quarters 58 inches; i. e. 45 feet 2 quarters 223 inches of timber; or near 5 per cent. And the increase of the most thriving oak, N° 8, appears, by the above table, to pay above 12+ per cent. and the Scotch fir, N° 9, being under 2 feet of timber in spring 1743, |