310 Miscellaneous. [Junk, 



Extracts for Hutto7i , s Mathematical Recreations, vol. ii. p. 201. 

 "A more philosophical principle advanced by Dr. Barrow is, that the eye per- 

 ceives the image of the object in that point where the rays forming the small diver- 

 gent bundle, which enters the pupil of the eye, meet together. It is indeed natural 

 to think that the divergency as it is greater when the object is near, and less when 

 it is distant, ought to enable the eye to judge of the distance." 



" By this principle, also, we are enabled to assign a pretty plausible reason for 

 the diminution of objects in convex, and their enlargement in concave mirrors ; 

 for the convexity of the former renders the rays which compose each bundle that 

 enters the eye more divergent than if they fell on a plane mirror, consequently 

 the point where they meet in the central ray produced is much nearer. It may 

 even be demonstrated that in convex mirrors it is much nearer, and in concave, much 

 farther, distant than the point H., considered by the ancients, and the greater part 

 of the moderns, as the place of the image. In short, it is concluded that in con- 

 vex mirrors, this image will be still more contracted, and in concave ones, more ex- 

 tended than the ancients supposed ; which will account for the apparent enlarge- 

 ment of objects in the latter, and their diminution in the former." 



" We must allow that even this principle is attended with difficulties, which 

 Dr. Barrow, the author of it, does not conceal, and to which he confesses he 

 never saw a satisfactory answer." 



2. — Replies to Lieut. Burt's Questions, by Lieut. W. S. Jacob, Engineers. 

 Sir, 



Having just seen in your No. for December last, several questions proposed 

 by Lieut. Burt, Engs. I take the liberty of sending you the following answers 

 to them, for insertion in your Journal, should none more satisfactory have been 

 received in the mean time. 



Reply to Q. 1st. The longest known period of any comet that has appeared 

 twice is about 575 years, but it was calculated that of 1811 would return in not 

 less than 3000 years ; then by Kepler's rule, the major axis of its orbit — 2d X 

 (3000)§=2d x 208 nearly, (d being the mean distance of © and Q :) now it is 

 very certain, that no star has an annual parallax of 2" (nor probably 1''), conse- 

 quently the nearest star will be distant more than 2d x 100,000, or nearly 500 

 times as far as the furthest known comet. There may, however, be others more 

 distant, which have never appeared to us ; but as the period of one, which should 

 extend from our system to another star, would be at least 11,000,000 years, it is 

 not easy to see, what connection this could form between the two systems. 



Q. 2nd. Supposing the moon to have an atmosphere like our own, this 

 would be insufficient to render visible the whole of her dark disc, for we find that, 

 on the earth, the sun's light is extended by refraction to barely 18° beyond the 

 limit of direct vision, instead of 90°, as it appears to be in the moon. The pheno- 

 menon alluded to is much more simply accounted for by the light reflected from 

 the earth, which will be nearly 14 times greater than what we receive from the 

 moon. The limit of light and darkness on the moon's disc is more clearly defined 

 than it could be, if she were surrounded by an atmosphere like ours. 



With regard to the law of attraction of fluids, I conclude it to be the same with 

 that of all other bodies, viz. that they are attracted in proportion to their mass, or 

 in equal bulks, directly as their specific gravities ; as far as I know there is nei- 

 ther fact nor analogy to support the idea that the attraction is either directly or 

 inversely as the cube root of the specific gravity. 



