on which it fell with the utmost fury, and in a moment effected its complete destruction. The house was of wood, 2 stories high, and both the chimneys of stone. Near the house were a shop and small shed; and the barn stood on the opposite side of the road, about 10 rods distant. As soon as they perceived the storm coming near the house some men within endeavoured to shut the south door; but before they could effect it they were surprized by the falling of stones around them, from the top of that chimney which was in the middle of the house. All the people in the house were in that instant thrown into such a consternation, that they can give no account of what passed during this scene of confusion, which was indeed very short. Where the house stood nothing remained but the sills, and the greater part of the lower floor, with part of the two stacks of chimneys, one about 10 feet, and the other not quite so high; the stones which had composed the upper part lying all around them. Except these sills, there were only 3 pieces of timber, and those very large, left entire; one of which, about 16 feet long, and 10 inches by 8, was found on the opposite side of the road, nearly south, about 20 rods distant from the house. The rest of the timbers, from the greatest to the least, lay broken and twisted to pieces between N.N.E. and E. for 70 or 80 rods from the house; some on the ground, others sticking into it a foot and two feet deep in all directions. Part of one of the main posts, about 10 feet long, with part of one of the plats of nearly the same length, and a brace which holds them together, were left sticking in the ground, nearly perpendicular, to a great depth, in a field southerly from the house about 8 rods distant. The boards and shingles of the house, with 3 or 4000 new boards which lay by it, were so entirely shattered, that scarcely a piece could be found above 4 or 5 inches wide, and vast numbers were not more than 2 fingers wide; some within the course of the wind and some without, at great distances on both sides of it. What has been said of the boards and shingles was likewise true of the wooden furniture of the house: the tables, chairs, desks, &c. shared the same fate; not a whole stick was to be found of any of them. Some of the beds that were found were hanging on high trees at a distance. Of the heavy utensils, pewter, kettles, and iron pots, scarcely any was found. Some nails that were in a cask in the east chamber were driven in great numbers into the trees on the eastern side of the house. The shop and shed before mentioned were torn in pieces, nothing of the shop remaining but the sills and floor; and a horse standing under the shed was killed. Only one person was killed. From the whole, it seems highly probable that the house was suddenly plucked off from the sills (to which the upright posts are not fastened), and taken up into the air, not only above the heads of the persons who were on the lower floor, but to the height of those parts of the chimneys which were left standing, where, by the violent circular motion of the air, it was immediately hurled into ten thousand pieces, and scattered to great distances on all quarters, except that from which the wind proceeded. And it further appears, that the violence of the wind in that place was over as soon as the house was taken up; otherwise no person could have been left on the floor. IV. A Theorem on the Aberration of the Rays of Light Refracted through a Lens, on Account of the Imperfection of the Spherical Figure. By the Rev. Nevil Maskelyne, F. R. S. Dated from Prince Henry, St. Helen's Road, Jan. 16, 1761. p. 17. About 2 years since, becoming acquainted with Mr. Dollond's curious discovery in optics, of correcting the aberration of the rays of light arising from the different refrangibility of the different sorts of rays, by a combination of 2 different kinds of glass; and learning from him in conversation that he had invented a theorem, showing the quantity of the aberration of the rays refracted through a lens, on account of the imperfection of the spherical figure; by the application of which, he was able to make the aberrations of the combined concave and convex object lenses perfectly equal to, and consequently to correct each other; Mr. M. was desirous of being more minutely acquainted with this further great improvement in optics; and Mr. Dollond accordingly readily offered to gratify his curiosity. But in the mean while that Mr. D. was looking over his papers, in order to lay them before Mr. M., Mr. M. having leisure, set about the investigation of a similar theorem himself; which having completed, he interchanged with Mr. Dollond for his theorem. The theorems, though similar, were not exactly the same; but by reduction to the same form Mr. M. inferred Mr. D.'s theorem from his, which gave him a further confidence of the exactness of both. Let the form of the lens assumed, in the investigation of the theorem, be a meniscus, the radius of whose convex surface is greater than that of its concave surface; and the centre of the two surfaces lie on the same side of the lens as the radiant point, from which the rays diverge that fall on it. The ray falling on the extreme part of the lens will, after refraction, diverge from a point before the lens, nearer to it than the geometrical focus of rays diverging from the same radiant point, and passing indefinitely near the vertex. Let a express the distance of the radiant point, before the lens, from its vertex; R, the radius of concavity of the surface on which the rays first fall; and r, the radius of convexity of the second surface; F, the principal focus, or the focus of parallel rays, which will be on the same side of the lens as the incident rays; because R, the radius of the concave surface, is supposed less than r, the radius of the convex surface. Let the ratio of m to n be the same with that of the sine of incidence to the sine of refraction of rays passing out of air into glass, and let y express the semidiameter of the aperture of the lens; the angular aberration of the ray falling on the extremity of the lens, or the angle made between this ray, after being refracted through the extremity of the lens, and another ray or line, supposed to be drawn from the same extremity of the lens, to the geometrical focus of rays diverging from the same radiant point, and passing indefinitely near the vertex of the lens, expressed in measures of the arc of a circle to (mn + 4n2 — 2m2) × Y3 the radius unity, will be (m3 - 2m3n + 2n3) × y3 + (m -n) × 2m × F2r 3m2) x y3 (2m + 2n) x r3 (3m+2n) x Y' + 2m x QF2 2m x Q2r (m + 2n) × Y' (4n2 + 3mn (m — n)2 × 2m x F3 -- + m X QFr Where R, the radius of the first surface, is exterminated; and r, the radius of Or, exterminating r, the radius of the second surface, and retaining R, the radius of the first surface, the angular aberration is also expressed by (2m + n) x y3 (m + 2n) x Y' (3m + n) × Y3 n.)2 x 2F3 (m n) x 2г'R + 2m X FR2 + (m + (m (2m + 2n) × Y3 MX QFR (3m + 2n) x y3 2m X Q2F As in these theorems, the principal focus is supposed to lie before the glass, as well as the radiant point, to adapt the theorem to other cases, if the lens be of such a form as that its principal focus lies behind the glass, F must be taken negative: likewise, if the rays fall converging on the lens, or the point to which they converge lie behind the glass, a must be taken negative: lastly, if the first surface be convex, R must be taken negative; and if the second surface be concave, r must be taken negative; and if, after all these circumstances are allowed for, the value of the theorem comes out positive, the aberration is of such a nature, as to make the focus of the extreme rays fall nearer the lens before it than the geometrical focus, or farther from the lens behind it: but if the value of the theorem comes out negative, the aberration is of such a kind as to make the focus of the extreme rays fall farther from the lens before it than the geometrical focus. With respect to the application of this theorem to Mr. Dollond's combined object glasses, it is evident that if the aberrations of the convex and concave lenses added together (paying due regard to the signs of the theorem) are made equal to nothing, the two lenses will perfectly correct one another: but as there are two unknown quantities unlimited in the equation, namely, the radius of one surface of each glass (for F and are given, as well as m and n) there is room for an arbitrary assumption of one of them, at the discretion of the theorist or artist; which being done, there will remain a quadratic equation, whence there will result two values of the radius, which remains unknown, either of which will produce an aberration equal to that of the other lens. V. Extract of a Letter from the Abbé De la Caille, of Paris, and F. R. S. to William Watson, M. D., F. R. S., recommending to the Rev. Nevil Maskelyne, F. R. S., to make at St. Helena a Series of Observations for discovering the Parallax of the Moon. p. 21. The Abbé takes notice, "That though the parallax of the moon seems sufficiently well determined, by the observations made in 1751, in Europe and at the Cape of Good Hope; yet an element of this importance cannot be too well ascertained. He is of opinion that Mr. Maskelyne's continuance in St. Helena may be advantageously employed in making new observations; since the base on which these parallaxes should be calculated, ought to exceed the earth's radius. That if the R.S. approve of his proposition, and recommend to Mr. Maskelyne the execution of the scheme of correspondence which he has drawn up, he promises to comply with it punctually on his part. The Abbé has accordingly sent Dr. Watson a series of observations, which he recommends to Mr. Maskelyne to make, from the 13th of June 1761, a few days after the transit of Venus, till the 9th of May 1762. This paper Mr. Maskelyne has transcribed, and proposes to make these observations in concert with the Abbé de la Caille. And if a copy of this paper, which Dr. Watson proposes to lay before the Society at their next meeting was put into the hands of Dr. Bradley, that gentleman might likewise make correspondent observations. The Abbé likewise adds, that he has supposed that the sector, which Mr. Maskelyne takes with him to St. Helena, would take in 5 degrees on each sidethe zenith; and that his clock would be regulated by sydereal time.' This sector extends much beyond the Abbe's expectation, as it takes in 84 degrees on each side of the zenith. |