1 84 



SCIENTIFIC NE\VS. 



[Oct. 1st, 18S7. 



bit at arm's length, a plate at two or three yards, and a 

 cartwheel at perhaps forty to fifty yards, but this is not so, 



A circle o'22-inch in diameter, fairly represented by \J, 



at two feet distance, would just hide the moon, supposing 

 the pupil of the eye were a point. The coin would have to be 

 seventy inches away, and a ring of light would be seen 

 round a four-foot wheel were it more than 530 feet distant. 

 Sir John Herschel informs us that many persons spoke of 

 the tail of the great comet of 1858 as being several yards 

 long, without at all seeming aware of the absurdity of such 

 an expression. 



Among the ancient Greek philosophers, Anaxagoras was 

 laughed at for saying that the sun might be as large as all 

 Greece, while another sage put himself beyond criticism by 

 maintaining that it was " precisely as large as it looks to 

 be." The latter idea may be more than a mere truism, 

 and might have meant that, in the absence of any informa- 

 tion as to the distance, the only measurement was one of 

 apparent, or angular magnitude. The measurements of 

 astronomers are always given in the first instance as angles. 

 The oldest method of expressing an angle was to state how 

 many times it was contained in a right angle. Archimedes 

 attempted to measure the apparent diameter of the sun by 

 means of a cylinder standing upright on a level beam. He 

 observed it at sunrise, when it could be looked at without 

 injuring his eyes, and he noted how far the cylinder was 

 from his eye when it just hid the sun. He made another 

 experiment to find the correction for the size of the pupil 

 of his eye, which, having an appreciable size, could, as it 

 were, see round the sides of the cylinder. He then mea- 

 sured the length of the bar, and the diameter of the 

 cylinder, and expressed the angle in the number of times it 

 was contained in a right angle. It is hardly credible that 

 he had not sufficient knowledge of trigonometry to calcu- 

 late the angle of the triangle of which he knew the base 

 and the length of two equal sides. 



We measure angles in degrees, of which there are 360 in 

 a complete circle, and 90 in a right angle. Each degree is 

 divided into 60 minutes, and each minute into 60 seconds. 

 The signs ", ', and ", are used for degrees, minutes, and 

 seconds respectively. 



The apparent size of the moon varies for two reasons. In 

 the first place, it does not revolve round the earth in a 

 circle, but in an ellipse, the earth being at one focus. The 

 length of the ellipse is to its width as i is to "05485. 

 When the moon is nearest to the earth it is said to be in 

 perigee, and when it is at the farthest it is in apogee. Its 

 apparent diameter under these circumstances varies from 

 33' 3°" to ~9' 20", the observer being supposed to be at 

 the centre of the earth. The surface of the earth im- 

 mediately under the moon is evidently nearer, by half the 

 diameter of the globe. The distance of the moon from the 

 centre of the earth is about thirty diameters of the latter, 

 and therefore the moon will appear about one-sixtieth larger 

 when it is over head than when it is on the horizon. 



It is, however, well known that the sun or moon near 

 the horizon appear to be considerably larger than when 

 high in the sky, and much ingenuity and not a little bad 

 science has been brought to bear upon the question. Gas- 

 sendius, who ought to have known better, thought that as 

 the moon was less bright when near the horizon, the pupil 

 of the eye would be more dilated than when the brilliancy 

 was greater, and therefore it appeared larger ; this opinion 

 was supported by a French Abbe, who supposed that the 

 opening of the iris made the crystalline lens flatter. This is 

 on a par with the idea that as the eyes of horses magnify 

 more than those of most other animals, their stepping so 



high is thus accounted for, since each stone must appear to 

 be a serious obstacle ; this is also given as a reason for 

 their timidity. It is hardly necessary to explain that in both 

 cases, all the surrounding objects would also be magnified, 

 and the relative sizes, by which we judge absolute sizes, 

 would remain the same. 



Another explanation is, that the effect is produced by re- 

 fraction ; in fact, at a well-known school, Cowper's " Winter 

 Evening " was being discussed, and at the line describing 

 the rising moon, 



" Resplendent less, but of an ampler round," 



the question went round the class, " Why should it appear 

 larger when near the horizon ? " when the present writer, 

 who, it may be inferred, was not at the head of the form, 

 feeling that it was more politic to give the answer which in 

 all probability was in the master's mind, than to attempt to 

 expound the theory which he believed to be the more 

 correct, replied, " the refraction of the damp air," which 

 sent him unjustly joyful to the top. 



Descartes was the first to give a reasonable explanation, 

 and if it is not generally considered to be correct, it sug- 

 gests a still simpler solution. He said that we are accus- 

 tomed to judge of the size of objects by mentally comparing 

 their apparent magnitude with their apparent distance, and 

 that when the sun or moon is low we are reminded, by 

 comparing it with surrounding objects, that it is very far 

 off; but when it is high in the sky we have nothing in its 

 neighbourhood with which to compare it, and it therefore 

 appears nearer, and consequently smaller. But does the 

 moon appear more distant when it is high ? Does it not 

 rather, when rising, appear as though it were at the hori- 

 zon ; and when it is high does it not appear to be among 

 the stars, at a distance which the mind makes no attempt 

 to grasp ? 



The true solution appears to be that when it is near the 

 horizon we can readily compare the moon with trees and 

 houses, which look small beside it. A tree fifty-five feet high, 

 five miles off, would appear to be about equal to one quarter 

 of the vertical diameter of the moon when it had just risen. 

 But when it is high we can only compare it with the 

 upper boughs of trees, or with chimney-pots, one of which 

 would completely hide it ; then it is dwarfed by its sur- 

 roundings, instead of the reverse. It is easy to prove that 

 it is the effect of its surroundings which alters the apparent 

 size by simply looking at it through a roll of paper, or 

 even through a loosely-closed fist. 



The refraction of the air not only does not magnify, but 

 has the opposite effect. The sun setting at sea, or behind 

 a very distant horizon, loses its circular outline, and becomes 

 irregularly elliptical. The vertical diameter is shortened, 

 while the horizontal remains the same. It was probably 

 not until the effect of refraction had been carefully 

 studied and reduced to a definite rule that it was known 

 that at the moment we see the lower edge of the sun 

 touch the horizon the sun has really already set, and that 

 it is merely on account of refraction that we still see 

 it. The eflect of refraction of the air is to make the sun, 

 moon, or stars higher in the sky than they really are. The 

 effect is much greater near the horizon than at higher 

 angles. Assuming the sun to have an apparent diameter 

 of 32' when the lower edge, or limb, as it is called by as- 

 tronomers, appears to touch the horizon, the refraction at 

 that limb is ^^', the upper limb is 32' above the horizon, 

 and at this point the refraction is only 28' 6'; there is there- 

 fore a difference of 4' 54'', which is the difference between 

 the vertical and horizontal diameters. 



There is a very prevalent idea that mist or fog has a 

 magnifying power. Not only has the presence of moisture 



