May 26, 18S1] 



NATURE 



midday in the summer equinox, and thus found 7° 12". 

 It is added that at Syene the bottom of the wells was 

 fully lighted by the sun on that day, so that Eratosthenes 

 concluded zero for the zenith distance of that body. I 

 believe rather that the Greek astronomer caused an 

 observation to be made at Syend with a gnomon, an instru- 

 ment then very common in Egypt, and that that distance 

 resulted from an effective observation, as well as in the case 

 of Alexandria. We shall see that this conjecture is perfectly 

 justified. We know that the observations made on the 

 dark shadow of a gnomon bear a constant error equal to 

 the semi-diameter of the sun, or, to speak more accu- 

 rately, that they give the zenith distance of the upper 

 edge of that body. The ancients do not seem to have 

 remarked this ; and in fact, as they deduced from their 

 observations only the obliquity of the ecliptic or the epoch 

 of the solstice, it did not concern them, for by combining 

 the observations of the summer with that of the winter 

 solstice, the error in question disappeared from the difler- 

 ence. But it is exactly the same here, since we have not 

 to do with absolute latitude, but with the difference of 

 latitude of two places at which the centre of the sun is 

 found at midday on the same side of the vertical. Thus 

 the amplitude 7° 12' concluded by Eratosthenes is cor- 

 rect ; it has moreover the advantage of not being sensiby 

 affected by refraction. 



Here is a first verification. On opening the Connais- 

 sance des Temps we find — 



For the latitude of Alexandria 

 ,, ,, Syene ... 



Difference 



31 12 



24 S 



7 7 



instead of 7° 1 2'. The difference, whatever may be the 

 cause, is very small. 



Here is a second and more delicate verification. The 

 latitude of the point m Alexandria, where Erdtosth<^"»- 

 observed, could not differ much fron' that which we have 

 given. By adopting that and 7- 12' for the zenith distance 

 of the upper edge of the sun at the winter solstice we find 

 31° 12' - (7° 12'+ 16') = 23° 44' for the obliquity of the 

 ecliptic. Syen^ gives 24" 5' - 16' = 23° 49'. Is it possible 

 that in the year 250 B.C. the obliquity of the ecliptic was 

 from 23° 44' to 23° 49'? From 1750 a.d. to 250 B.C. is 

 2000 years. At the rate of 48" diminution per century 



I the obliquity would be 



', 23= 28' 18" -f 48" X 20 = 23' 44'. 



The observation of Eratosthenes at Alexandria is then 

 authentic, and moreover very precise. That of Syend 

 presents an error of only 5'. 



There remains the geodetic operation. Egypt was the 

 only country of antiquity which rejoiced in a survey. The 

 valley of the Nile was very populous at that epoch, as far 

 as Syend, and no doubt the survey extended thus far. 

 Eratosthenes must have had every facility for procuring 

 the necessary documents. He must have taken into 

 account the difference of longitude of 2° 59' which exists 

 between the two cities, without having had to determine 

 it directly. I regard, then, the distance of 5000 stadia, in 

 round numbers, as being quite as accurate as the other 

 parts of his operation, and as applying to the arc of 

 meridian comprised betvreen the parallels of the two 

 cities. 



We finally conclude from this 694'4 stadia for the 

 degree. The Greek astronomer ga\e, in round numbers, 

 700 stadia. AYbat was this stadium ? 



To reply to this question I calculate the arc of meridian 

 from Alexandria to the parallel of Syend, with the actual 

 element of the terrestrial ellipsoid. It is 797,760 metres. 

 At the rate of 5000 stadia we find I59'55 metres for the 

 stadium. At the rate of 600 feet for the stadium, the foot 

 adopted by Eratosthenes would be o'266 metres. This 

 was then the ancient Egyptian foot, which we now 

 reckon at 0^27 metre ; and in fact it was with this foot 



that the survey of Egypt must ha\e been made. By this 

 reckoning the 50CX) stadia give — 



5000 X 600 X o 27 = 810,000 metres, 

 showing a difference of 12,240 metres, partly owing to 

 that of the points of departure, partly to the error which 

 we perhaps make in the length of the Egyptian foot in 

 carrying it to 0-27 metre. Thus the measurement made 

 in Egypt, more than 2100 years ago, by an able Greek 

 astronomer, is as good as authentic. All the existing 

 causes of uncertainty do not alter it more than one-sixth. 

 It is certainly not from this quarter that the error can 

 come for which we seek. 



Nor is it in the measurement of Ptolemy, for he tells 

 us he went through the same operations and found the 

 same results ; only he gives 500 stadia to the degree 

 instead of 700. This difference is evidently due to the 

 fact that Ptolemy, who lived 400 years after Eratosthenes, 

 under another domination, did not make use of the same 

 foot. In fact he employed the stadium of 600 Phileterian 

 feet, and as this foot is about o'36 metre, while the 

 ancient Egyptian foot was only 0-27 metre, he had to 



reduce the 700 stadia of his predecessor to 700 X — 



= 525, or 500 in round numbers. 



These estimates are confirmed, finally, by the Arabian 

 astronomers, v.'ho measured, in 827 A.D., an arc of 1° in 

 the plains of Mesopotamia. They found fifty-six miles, 

 and concluded that they had thus verified the numbec of 

 Ptolemy. The Arab mile being 2100 metres, the arc 

 measured is found to be 117,600 metres, which corre- 

 sponds to a stadium of 235 metres. This is very nearly 

 the Phileterian stadium of 216 metres, except *'" --*^'' °| 

 the measurements seven times nior>» - -.-"^'6 on so small 

 an axis, and the unr-'v -^ "' ""V^'^'/^'?" ^^'^^'^ "^ 

 the Ai-"^-— """^ '" '^ '"^^ of the Kalif Almamoun. 



■po resume : the estimate of Ptolemy is only a sort of 

 conversion of the excellent measurement of P-ratosthenes 

 in units of another epoch and of different length. It 

 would thus lose a little of its first precision ; but, such as 

 we find it in Ptolemy, the English geographers were fully 

 justified in taking it for the basis of a valuation of the arc 

 of i' and of offering it to the navigators of their country. 

 Only, and it is here the mistake lies, they believed that 

 the great Greek astronomer of Alexandria must have 

 made use of the Greek foot. This is one and a half 

 hundredths larger than the English foot. If the English 

 geographers of the sixteenth century had strained this 

 valuation ever so little, and had carried it to ycoths, they 

 would have found 630 English feet for the stadium, which 

 they believed to be 600 Greek feet, and these 630 feet or 

 210 yards, multiplied by 500, would give them 105,000 

 yards for the degree, and exactly 1760 yards for the mile. 

 The English mile, then, has evidently been deduced from 

 the measure of Ptolemy ; its error of one-sixth is solely 

 due to the fact that the Greek foot has been confounded 

 with the Phileterian foot. 



LAURENTIAN GNEISS OF IRELAND 

 T N 1863 Dr. T. Sterry Hunt pointed out the resemblance 

 ■l of some specimens of rocks and minerals from 

 Donegal which he had examined to those of the Lauren- 

 tian series of North America. These rocks and minerals 

 have been described by Dr. Haughton and Mr. R. H. 

 Scott, who have pointed out that the " typical Donegal 

 granite " is really a metamorphic bedded rock, containing 

 m some places bands of crystalline limestone or marble. 

 Outside the granite district .are the newer series of schists, 

 quartzites, and limestones, which occupy the whole of the 

 Promontory of Innishowen, and were identified by the 

 late Prof Harkness with the Lower Silurian metamorphic 

 series of the Highlands of Scotland. These two groups 

 are shown on Griffith's Geological Map of Ireland, and it 



