Aug. 17, 1883.] 



♦ KNOWLEDGE ♦ 



101 



It is easy, however, to see how the dilhculty arose, and 

 to devise a way by which a vertical mirror may be made to 

 prove instead of disproving the rotundity of the earth. 



Let us see what is the actual depression of the sea 

 horizon, viewed from a goodly height, such as 200 feet. 



made uppermost either by changing the supports or by 

 shifting the mirror in the pivot holes E and F. 



After setting the mirror exactly vertical, K uppermost, 

 let the observer retire from it to such a distance — say two 

 yards — that he can see with perfect distinctness not only 



Fig. 8. 



Let a (Fig. 8) be the place of the observer's eye, A a 

 being 200 ft. ; A B the sea surface; a B the direction of the 

 line of sight from a to the curved sea surface ; lib' h ver- 

 tical at B, and a b the direction of the real horizon. Draw 

 A b' parallel to a J to meet B i in U. Then obviously 

 B6' = Aa = 6i' (since B 6 is appreciably parallel to A a. 

 Therefore B i = 2 A a=400 ft. Hence the dip of the 

 horizon, or the angle B a ^ is that subtended by 400 ft. at 

 the distance n B or A m B (appreciably the same). Kow 

 (Euclid, Bk. IIL) the square on a B is equal to the 

 rectangle under A a and the earth's diameter. Hence with 

 feet for our unit of length 



a B^ v/7920 x"l760 x 3 x 200 



= 911:.')0ft. approximately ( = 17^ miles). 



Now 400 ft. at a distance of 914.50 ft. subtend the 

 same angle as 1 ft. at a distance of about 228 ft., or about 

 one-fourth of a degree. This is very different as anyone 

 can see by looking at a circular protractor and noticing 

 how small are the half degrees usually marked in, from 

 the enormous depression usually indicated in pictures 

 supposed to illustrate the globular shape of the earth. 

 The real angular dip of the horizon is only three-fourths 

 even of this, atmospheric refraction diminishing the true 

 or geometrical dip by one-fourth. The real angle of dip is 

 that subtended by 1 (foot or inch or tenth of an inch) at a 

 distance of about 300 (feet or inches or tenths of an inch). 



In Parallax's experiment, supposing the eye one foot 

 from the mirror or two feet virtually from the imaged eye, 

 the imaged horizon (if the station were 200 feet above the 

 iea level, would be tjo''^ ^^ ^ ^°o* o*" about 4-liun- 

 Jredths of an inch above the imaged eye-level. This 

 ■would not be discernible by ordinary eyesight, the line of 

 the imaged sea horizon being intercepted by the imaged 

 heid. But I shall now show how this difficulty can be 

 renoved, and a pretty illustration of the earth's rotundity 

 be ibtained by the mirror method. 



let A B i) (Fig. 9) be a rectangular mirror, broad 

 enoigh to include the imaged face (the breadth of which is 

 alwtys exactly half the breadth of the real face), and to 

 sho\i an inch or two clear on either side, as shown. Let a 

 line I b be drawn with a line diamond exactly parallel to the 

 sidesAB DC. I^ot the mirror be supported at E and F by 

 rods I G, and F £1, which can be fixed into the ground pretty 

 firmlj Let the observer so fix them into a turf sward 

 some 200 feet (say) above the sea level, on a spot com- 

 mandng a fine sea horizon, putting the face of the mirror 

 seawaids. Suppose that at K there is a line thread K /.; 

 bsarin; a blumb-bob P, by means of which the face of the 

 nrirrormay be made perfectly vertical by suitably turning 

 it on tie pivots E F. But as the glass of the uiin-or may 

 no'} be of pcrfixtly equal thickness throughout, let the 

 plunblne admit of being fastened at L, the side D C being 



the pupils of his eyes in the glass, but the diamond line. 

 Let him bring the pupils of his eyes centrally on the line 

 a b. He will then see that the water surface cd \b about a 

 quarter of an inch below a b. On the other hand if by 

 slightly lowering his head he brings the water surface to 

 exact coincidence with the diamond line, he wiU see that 

 the pupils of his eyes are about a quarter of an inch above 



/-^^ 



that line. Inverting the mirror and letting the plumb-line 

 hang from L, he will get the same result precisely if the 

 mirror is a good one, and very nearly the same result if the 

 mirror is a bad one. 



By using a brightly polished plane of steel, which" need 

 not be more than four or five inches square, a better result 

 still will be obtained. 



But a polished plane of steel four or five inches long 

 and only an inch broad or even less, may be very efiectively 

 used without a plumb-line, as follows :- 



^fe=s 



Fig. 10. 



Let A B D (Fig. 10) be tlie polished steel plane, set on 

 Se etlgo of a saucer E F, containing a little mercury (or ink). 

 uppose the cup set on a little platform, admitting of 



