But Mr. Dollond was not satisfied with bare reasoning on the subject. It occurred to him that it would be worth while to repeat the experiment of Sir Isaac Newton, upon which the presently received theory was founded. He took two thin glass plates, cemented them together at one of the edges, fitted brass plates to the ends, and filled this vessel with water, so as to make a water prism. Into this vessel he put a glass prism, with its reflecting angle uppermost. Thus he had two prisms, one of glass, and another of water, acting opposite ways; and by altering the angle of the water prism till an object seen through both prisms occupied its natural place, he made both to refract equally, so that they mutually destroyed each other's refractions. In this case, if Newton's principle were accurate, the object ought to be seen without colour; but, on the contrary, it was as much coloured as if seen through the glass prism alone. Hence it followed that Newton's principle was inaccurate; and that therefore refraction might be effected without inducing colour. To prove this, he put a glass prism, with a very small refracting angle, into his water prism ; and altered the angle of the water prism, till objects seen through both were free from colour. In this case there was a considerable refraction. Having determined this important principle, his next object was to find whether there were different sorts of glass that possessed this difference in their dispersive power to a remarkable degree; and after trying various kinds, he found a remarkable difference between crown glass and flint glass in this respect. He found that two wedges of flint and crown glass, ground to such angles that the refraction of the flint was to that of the crown as two to three, when placed together, showed objects free from colour. Therefore a concave flint glass, and a convex crown glass lens, placed together, would act in this manner, supposing the focal distances of each inversely as. the ratio of the refraction of the wedges. Upon trial, he was able, after overcoming various difficulties, to construct refracting telescopes in this manner greatly superior to any former ones.* To these new telescopes, Dr. Bevis gave the name of Achromaţie achromatic. They have been of great service to astronomy, by being applied to fixed instruments; and to navigation, by being applied to Hadley's sextant. For this important discovery, Mr. Dollond was presented with the annual gold medal by the Royal Society; though not yet a Member of that learned body. He was elected into the Royal Society in 1761, and appointed Optician to the King. But he did not long enjoy these honours; for on the 30th of November, of the same year, a fit of apoplexy terminated his life in a few hours, in the 55th year of his age.† While upon this subject, we ought to mention a very excellent paper by Mr. Murdoch, in which he shows that Mr. Dollond's discovery is not inconsistent * Phil. Trans. 1758. Vol. L. p. 733. + Phil. Magazine. Vol. XVIII. p. 47. glasses. Objections to the opinion body answer ed. with the doctrine of Sir Isaac Newton; but that a meaning had been affixed to his expressions which he never intended to convey.* Sufficient attention has not been paid by optical writers to this paper. 15. The next paper deserving notice, is a posthumous one, of Mr. Short, which he delivered sealed up to the Society, on the 30th of April, 1752. After his death it was opened by the council, and ordered to be printed. It is a minute description of the method which he employed for grinding the object glasses of refracting telescopes truly spherical; and must be of considerable importance to practical opticians.† 16. The next paper is one by Dr. Horsley, to obviate certain objections that light is a started by Dr. Franklin, against the common opinion, that light is a body emitted from luminous substances. Dr. Franklin supposes, that if light were a body, its velocity is so great that it would have a momentum greater than that of a 24-pounder fired from a cannon; and that the sun, by the emission of such a vast quantity of matter, would shrink in its dimensions, and cease to act upon the revolving planets with the same energy. Dr. Horsley demonstrates that, on the supposition that the particles of light are sphericles, having a diameter equal to one millionth of one millionth of an inch, and a density three times as great as that of iron, the momentum of each will not be greater than that of a sphere of iron 4th of an inch in diameter, and moving at the rate of less than an inch in 12,000 millions of millions of Egyptian years: that is, it will be absolutely insensible. He demonstrates likewise that, on the most unfavourable supposition possible, the sun could only loseds of his matter in the space of 383,130,000 Egyptian years; and that at the end of that period the diminution of his bulk, and the alteration in the planetary motions, would be absolutely insensible. Hence Dr. Franklin's opinions are obviously of no weight. But, even if the Newtonian doctrine of light be admitted, it is very conceivable that a great proportion of the light thus emitted is returned again into the sun. Newton himself was of opinion, that the light thus emitted gradually collected together, and formed masses of matter, which revolved round the sun. He conceived the comets to be masses of this kind, and that, after circulating for a given period, they at last fell into the sun's body, and thus restored all the loss of matter which that luminary had sustained. He even conceived that the very bright comet, which appeared in his time, and which is supposed to make a revolution in rather more than 500 years, would, from the extreme nearness of its approach to the sun, fall into it in the course of five or six revolutions ; and the consequence, he supposed, would be such an increase of heat, as would destroy all the living beings on this earth. + *Phil. Trans. 1763. Vol. LIII. + Phil. Trans. 1769. Vol. LIX. p. 507. There is a tendency among the British philosophers of the present day, to adopt the hypothesis of Huygens, or rather indeed of Dr. Hooke. This is chiefly owing to a paper by Dr. Wollaston, in which he shows, that the double refraction of Iceland crystal can be accounted for in a satisfactory manner on Huygens's principles, and on no other. This very ingenious paper is printed in a volume of the Transactions, which does not come under our review. Some curious discoveries of Malus, and some observations by La Place, in the two volumes of the Memoires d'Arcueil, lately published, have added still farther to the probability of this opinion. We must confess, however, that we think it impossible to get over the objections pointed out by Newton himself, in his answer to Dr. Hooke. pable of distin lours. 17. The next paper is a curious account of three brothers, who were born at Persons incaMaryport, in Cumberland, who could distinguish the figure of objects per-guishing cofectly well, and saw to as great a distance as other people, but could not distinguish colour. They knew the difference between light colours and dark colours, and never confounded white and black; but if two colours had the same degree of liveliness, they could not distinguish between them: thus green, red, and orange, they considered as the same. This defect of sight is by no means uncommon. Mr. Dalton, of Manchester, who is himself affected with it, has given us a curious account of it in one of the volumes of the Memoirs of the Manchester Society. He mentions two other persons that he knew, who were affected with the same disorder. He conceives it to arise from the lens of the eye, or some of the humours, being tinged of a particular colour. * telescopes. 18. The next paper is a very valuable one, by Mr. Mudge, giving directions Mirrors of for making the best composition for the metals of reflecting telescopes; with a description of the process for grinding, polishing, and giving the great speculum the true parabolic curve. For this paper, Mr. Mudge was honoured with the annual gold medal of the Royal Society. The composition consists of two pounds of good copper, and 14 ounces of grain tin, melted together; and to prevent the speculum from being porous, it is always necessary to melt it twice over, giving it the second time just heat enough to melt it. Mr. Mudge's rules for grinding and polishing the speculum are excellent. But we must refer for an account of them to the paper itself. termining the 19. The next paper we shall notice is a very curious one, by Mr. Wilson, Method of dein which he proposes an experiment for determining, by the aberration of velocity of the the fixed stars, whether the rays of light, in pervading different media, change rays of light, their velocity according to the law which results from Sir Isaac Newton's ideas concerning the cause of refraction; and for ascertaining their velocity in every * Phil. Trans. 1777. Vol. LXVII. p. 260. + Phil. Trans. 1777. Vol. LXVII. p. 296. · 5 medium whose refractive density is known.* This method is to employ a telescope, filled with water, and to observe with it the aberration of the stars in the same way as Dr. Bradley did with his sector. Mr. Wilson demonstrates, that if the light be accelerated in its passage through the water, its direction will not be altered; and this sameness in the direction constitutes the expected proof of the acceleration of light during its passage through the water, and consequently of the truth of the Newtonian theory of refraction. Boscovich had proposed a similar method of determining the point; but he had fallen into an error respecting the alteration of the direction, which he conceived would be produced by the water. + 20. The last papers we shall notice are two very curious ones, by Mr. Brougham, on the flection and reflection of light;† and one on the same subject by Prevost, of Geneva, opposing some of Mr. Brougham's conclusions, and defending the Newtonian doctrine. We regret that we cannot enter upon the examination of these excellent papers. But to do them justice, or even to render them intelligible to our readers, would require a length of discussion totally inconsistent with the limits of this work. Here then we close our observations on optics. We acknowledge that various other papers would have been entitled to notice; but we have still so much ground to travel over, and have already exhausted so great a proportion of the limits allowed us, that any further details would be made at the expence of the sciences which we have yet to notice. CHAP. III. OF DYNAMICS. THE term Dynamics is applied by natural philosophers to that preliminary branch of their science which treats of the theory of moving bodies. Statics, or the theory of equilibrium, is usually considered as a part of it, because it depends upon similar principles. It is a very important branch of knowledge; but it is so well understood, and treated so fully in all systems of natural philosophy, that we do not think it necessary to enter into details. We may mention, however, in a few sentences, the principal topics which enter into the * Phil. Trans. 1782. Vol. LXXII. p. 58. + Phil. Trans. 1796. Vol. LXXXVI. p. 227; and 1797. Vol. LXXXVII. p. 352. science called Dynamics. We shall then notice the few papers on the subject to be found in the Philosophical Transactions. S = บ dynamics. Motion is estimated by the space passed over in a given time, and the rate of Outline of motion is called velocity. Let s denote the space, t the time, and the velocity. Then, in uniform motions, we have 1.stv. 2. v = 3. t These three simple theorems comprehend the whole doctrine of uniform motions. But motions are seldom uniform; they usually either increase or diminish. In such cases, philosophers have conceived the motion to be uniform during a very small time, and to receive a certain addition or diminution at the end of it. These additions or diminutions are called increments, or rather fluctions. And we have as before vt, v = andi. A body continues for ever either in a state of rest, or of uniform rectilineal motion, unless affected by some external cause. This cause is called a force, by writers on mechanics. Now forces are measured by the quantity of motion which they produce in a given time. When a body is acted on at once by two forces, if these forces be represented by lines meeting in an angle according to their direction, if we complete the parallelogram, of which the two lines constitute two sides, then the body will move in the diagonal of that parallelogram. Now these three lines constitute a triangle. Hence it follows, that if a body be acted on at once by three forces represented by the three sides of a triangle, it will remain in equilibrio. The next branch of dynamics considers the collision of bodies: 1st, of such as are not elastic; 2d, of elastic bodies. In the first case, if a strike against в, whatever motion it communicates to в it loses itself, so that the quantity of motion continues unaltered. Suppose both bodies going the same way with different velocities, and let the velocity of a be a, and that of в, b; and let the common velocity after collision be r, then x = If the bodies move in opposite directions, then r = mulas become a = v a + b AⱭ Bb A + B A Aа + вb A+ B Supposing the bodies equal the for and. Or, in the first case half the sum, and in the second half the difference of the original motions. A + B If the bodies be elastic, they rebound after collision with a velocity equal to the stroke. In that case the velocity lost is double, and is represented by 2B (a - b) When the forces are equal, the bodies rebound back with interchanged velocities. In elastic bodies, the difference of velocities is the same after as before collision; and in them, as well as in non-elastic bodies, the sum of the motions is the same after as before collision. Hence the following proposition may be demonstrated: the square of the velocities, multiplied into the |