Aug. 3, 1883.] 



♦ KNOWLEDGE 



69 



occasion was neat and decisive enough ; and bf/ore the 

 experiment I have not a doubt the loser thought the trial 

 could have but one result. It may serve as one among 

 the " pretty proofs " now to be dealt with, while the de- 

 lusive experiment which the loser wished to substitute 

 after the matter was settled may also be considered with 

 advantage. 



On the Bedford level, where there is a water surface 

 without bend for more than twenty miles, are two bridges 

 as at A and C in Figs. 2 and 3, six miles apart, the 

 water surface between them extending straight from A 

 to C. Supposing the earth's surface plane the straight 

 line ABC (Fig. 2) will correctly represent this water sur- 

 face. On the other hand if the earth's surface is globular, 

 ABC will be an arc of a large circle as in Fig. 3, the 

 straight line A C falling as A h C. 



Now at A a telescope was set up as at i, At being a 

 given length, say 10 ft. (it really matters not what the 

 length so that the same lengths were used at all the 

 stations). At B midway between A and C a pole of the 



It is clear then that the test is a very simple and ob\dous 

 one. For supposing we have a disc 1 ft. in diameter at b, 

 and a disc 2 ft. in diameter at c, so that seen from t both 

 look equally large, it is obvious that the centre of the 

 disc c will be seen 6 ft. below the centre of the disc b, or 

 the appearance presented will be as at Fig. 4, the distance 

 ey' being five times </ e or^'^ the diameter of either disc, 

 while b k is six times d e or/g. And though in the tele- 

 scope the scale on which what is shown in Fig. 4 would be 

 seen may be very small, for a distance of G ft. is but small 

 at three miles from the eye, yet the discs would show the 

 displacement distinctly enough. As a matter of fact 

 atmospheric refraction would diminish the distance e /'by 

 about one-fourth ; but this would not atlect the aspect of 

 the discs. Manifestly the difference between a single disc 

 such as would be seen if the water surface were plane as in 

 Fig. 2, and the two discs separated by three or four times 

 the apparent diameter of either, would be obvious, even to 

 the eye of the most unpractised telescopist 



This then was a most suitable test, considering that 





Fig. 3. 



same length was set up bearing a round disc as at b, 'Bb 

 therefore being 10 ft. On the bridge at C a disc c was set 

 up at the same height of 10 ft. above the water surface. 

 Thus A/ = B('.=Cc = (say) 10 ft. 



Now it is obvious that if, as in Fig. 2, A B C is a 

 straight line, t b cis also a straight line ; so that the telescope 

 at t directed to the disc c bears also on the disc b. Thus if 

 the earth flatteners were right b and c would lie in pre- 

 cisely the same direction from /, or the disc b if of the same 

 size as c would centrally hide c from view. 



On the other hand, if A B C is the arc of a circle, so is 

 I b c the arc of a circle, of appreciably the same radius ; so 

 that the telescope at t directed to the disc c, does not bear 

 on b but on a point k below b, where the straight line t c 

 cuts b B. 



Let us see what b k is, in order that we may see whether 

 we have here a delicate or an obvious and very simple test. 

 We have t k c a, chord to a circle 7,920 miles in diameter, 

 and b k B ]i produced is a diameter of this circle, bisecting 

 i c in k. Hence we have by a well known property — 

 tk- = bk (earth's diameter — 6A-) 

 or (3 miles)'- = 6A (7,920 miles) 

 (for the bk within the brackets can obviously be neglected). 

 9 



Hence 



bk = — '- — ths of a mile. 

 7920 



9x3x1 760 



7920 

 3xl760j 

 880 



ft. 



6 feet. 



( 

 Fig. 4. 



neither of the bettors was an astronomer, and that the 

 umpires were altogether without skill in telescopic work. 



But when the observation had been made, and the disc 

 at b had been seen well above the disc at c, the loser's 

 umpire, and naturally the loser himself, began to doubt 

 whether the test was right after all. Could it be right, to 

 begin with, when it seemed to prove that the loser was 

 wrong and that his money ought therefore to be handed 

 over (as in point of fact it was handed over) by the stake- 

 holder to the winner? No one who knows anything of 

 paradoxical human nature can doubt what answer was 

 given, by the loser, to this question. 



The loser's umpire and the loser himself therefore 

 suggested that the test ought to have been different. By 

 some strange perversity they persuaded themselve.s that 

 even though ABC were straight as in Fig. 2, / c should 

 pass below b. Bttt, said they, if the earth's surface is 

 really curved, and therefore A B C an arc as in Fig. o, the 

 telescope at ( must lie depressed below the true horizon 

 to point towards c, which is true enougli ; and therefore, if 

 the telescope at t is made perfectly horizontal, by means 

 of a level, then it would bear on a point above c ; and 

 if there is a point marking tlie centre of the tele- 

 scopic field, c ought to be seen below that point. But 

 having, as they assert, correctly and perfectly le\elled 

 their telescope, c was not found to be below the 

 central point of the field marked by the intersection of 

 two cross lines. The loser's umpire looked and saw c on 

 the cross hair. The loser found it so too. They therefore 

 not only denied the validity of the other test, but claimed 



