Sept. 19, 1878] 



NATURE 



557 



visible just on the horizon. Hence it followed from a calculation 

 similar to the above that Rhodes lay about 7J° farther north 

 than Alexandria, and taking the distance of the two places 

 to be 5,000 stadia, he reckoned the earth's circumference at 

 240,000 stadia. Here also we find the assumption that the 

 two places lay on the same meridian, nearly 1 4° t- wrong. 

 But the chief source of error in this observation lay in ignoring 

 the refraction of the atmosphere, which is subject to very great 

 differences near the horizon, and makes the stars not only appear 

 at greater altitudes than they actually have, but disturbs the 

 places of the lower stars much more considerably than those of 

 the upper. But we are not now in a position to be able to discover 

 satisfactorily the extent of these sources of error in the results of 

 Eratosthenes and Posidonius, since the stadium was of uncertain 

 length, and we do not know in what relation it stood to our 

 modern measures. 



These are the only "results worthy of notice that have 

 reached us from these times, for then commenced the de- 

 cay of science in the east, and it was only at a much later 

 period that it flourished for a short time among the Arabs. 

 The Kalif Al Maimon had obtained from the Greeks the writings 

 of their philosophers, and turning his attention chiefly to 

 mathematics and astronomy, he was incited to undertake an 

 investigation into the mathematical figure of the earth. He 

 formed the resolution of undertaking the measurement of a 

 new degree, and collected for this purpose a great number of 

 mathematicians. These selected an extensive and level tract of 

 land, the Sinjar Desert, and made their measurements from 

 one point, some going north, others south. The result was 

 that the one party found a degree of the meridian to measure 

 56 Arabic miles, and the other 56^. Al Maimon had the opera- 

 tion repeated in order to obtain a better result, but the figures 

 obtained were the same. We have more certainty as to the 

 unit of this measurement, the Arabic mile, than in the case of 

 the stadium, but yet not sufficient for perfect accuracy, as appears 

 from the following definition : — According to Alfraganus the 

 Arabic mile contained 4,000 ells of twenty-four inches, the inch 

 being the space covered by six barleycorns laid side by side. 

 P. Snellius compared this measure of length with one of his 

 own units of measure, and after numerous observations found that 

 on an average eighty-nine barley-corns are equal to a Rhenish 

 foot. By this proportion it is found that an Arabic mile is equal 

 to 6472 Rhenish feet. It is usual to reckon the Rhenish foot 

 as '16 103 of a toise, and thus the mean length of the measured 

 degree would be 58710 toises, which is too great by 1700 toises 

 according to recent measurements. The toise is equivalent to 

 6 "3946 feet, or 1-949040 metre. 



We have mentioned already that from the decline of science 

 we had no other than this Arabic measurement to produce, and 

 we may further add that the most boundless ignorance, par- 

 ticularly with reference to natural science, reigned supreme, 

 especially among the European nations. But it was not enough 

 that this inaccurate determination of the size of the earth should 

 stand as the only one for centuries ; very soon it, and with it the 

 knowledge of the spherical form of the earth was forgotten. It 

 was not imtil the sixteenth century that a French physician, Fer- 

 nel, again undertook the measurement of a degree. He made use 

 for this purpose of a peculiar apparatus, which would certainly 

 not lead us to hope for an accurate result, but, nevertheless, 

 through fortunate circumstances, he came very near to the 

 truth. He had a waggon constructed which, by means of 

 a piece of mechanism, registered the number of turns made by its 

 wheel. With this he set out from Paris in the direction of 

 Amiens until he had gone a degree of latitude northwards, cal- 

 culated from the number of turns of the wheel the linear measure, 

 and obtained for this distance, which, according to his observa- 

 tion, was equal to a degree, 57070 toises. This result, as we shall 

 see further on, agrees very closely with later observations, which 

 is all the more wonderful from his finding the geographical latitude 

 of Paris too little by 12'. But since this resulted from a 

 constant error of his instruaaent, he must also have observed 

 the latitude of the^other end of the arc as too little by the same 

 amount, and thus since in the calculation only the difference of 

 the two observations is used, these errors are without any influ- 

 ence in the result. The other sources of error, which arose 

 from the unevenness of the measured distance, and evidently 

 must have given too great a result, be eliminated by subtracting 

 a certain quantity from his calculation, and he did this so success- 

 fully that, as we have said, his result very cbsely agrees with 

 modern measurements. 



Another investigation at this period into the circumference of 

 the earth, without the help of the stars, but simply by terrestrial 

 measurements, deserves mention. Starting from a point as high 

 as practicable (a mountain top or high tower, whose height was 

 known), the observer went as nearly as possible in a straight 

 line until he reached a distance at which the top of the mountain 

 or tower disappeared in the horizon. The distance of this 

 point from the mountain or tower was then measured, and 

 from simple trigonometrical considerations it will be seen 

 that the square of this distance divided by the height of the 

 mountain or tower would be equal to the earth's diameter. But 

 in this method the irregular action of terrestrial refraction is so 

 disturbing, that the point at which the mountain-top would seem 

 to vanish must be very uncertain, and the result as to the 

 diameter of the earth consequently veiy erroneous. 



All the methods hitherto referred to as in use in ancient times 

 and in the middle ages, for obtaining a knowledge of the size 

 and figure of the earth, are deficient in trustworthiness, partly from 

 their defective theory, but still more from the impossibility of 

 then carrying out those practical geodetic operations which are 



Fig. r. 



necessary for the solution of the problem with anything like 

 accuracy. We shall see in the sequel with what wonderful 

 accuracy it became possible to solve this important question. 



The method of measuring degrees underwent, in the beginning 

 of the seventeenth century, a fundamental reformation. Hither- 

 to, in all such measurements, only the simplest points iH the 

 geometry of the circle had been applied, but Snellius of Leyden, 

 making use of the properties of triangles, founded a new 

 method for the measurement of a meridian arc, and applied it 

 first in the year 1615 — viz, the method of triangulation. His 

 method, which has been followed ever since, possessed the in- 

 valuable practical advantage over the earlier methods, that it 

 considerably reduced the most difficult operation in the measure- 

 ment of degrees, namely, the measurement of a base line on 

 the earth's surface. How it is possible, even in regions of very 

 uneven surface to measure a large extent of a meridian arc with 

 great accuracy, will be seen from the following short explanation. 

 Suppose two places, A and B, one or more degrees of latitude 

 distant from each other, but in the same meridian; if the 

 uneveimess of the intervening surface, from mountains and 

 valleys, allowed of no direct measurement, one would proceed 



