September, 1902.] 



KNOWLEDGE 



201 



ptjrraets de vous signaler, et doat 1' interpretation rationelle 

 est encore a trouver. C'est uu grand eirele exoruti' eu 

 mosaique dans un pavement antique a El-Husn, daus la 

 Palestine trans-jordaniqiie. II est d'epoque relativement 

 basse peut-Otre bjzantine.' 



After briefly describing this nionunient, and referring 

 specially to the fact that the number 11<I had evidently 

 been desiguedly omitted, he adds : ' Je livrc ue petit 

 problt'ni a votre sagaoiti'.' I append a cojjv of the circle of 

 El-Husu, and, following M. Clermout-Gaunoau's example, 



Fig. 2.— The Circle of EMIusn. 



have iuKcrted in brackets the uumerical values of the 

 Greek letters. As every division of a circle mu.st, either 

 expressly or by implication, begin with 1 and proceed 2, 3, 

 etc., and as the numbei-s in this circle are not consecutive 

 but range from 6(3 to 180, advancing by tens, except in the 

 instance of 110, which is omitted, it is evident that two or 

 more divisions of the circle are here shown in combination. 

 In the abstract, a circle divided into 12 segments could be 

 accommodated to the representation of 60, 120, 240, 360 

 or 480 parts (degrees), inasmuch as these several numbers 

 are all divisible by 12. We have seen that two or more 

 divisions of the circle must be shown by the Circle of 

 El-Husn ; and, as only 12 numbers were to be used, the 

 problem before the circle-maker was how to express as 

 many divisions of the circle as possible with these materials. 

 The segments themselves showed the number 12, and the 

 single number 69 sufficed to show by implication the division 

 of the circle into 60', commencing with Sec. Pn — 5°, 

 PO — 10°, and so on. A lower number than 60 could not 

 liave been used, (1 ) on account of economy in numbers, 

 there being only altogether 12 numbers available to express 

 all the ideas ; and (2) because in a circle of 60° only, each 

 segment must have been 5^, and such a segment would 

 have prevented the harmonious expression of the other 

 numerical circles. Hence the circle begins with 60'. 



Now, had the numbers proceeded from 60 liy increase 

 of 10 without any omission, the total of the circle would 

 have been 1 70', an amount altogether inadmissible in any 

 division of the circle. One decade (110) is therefore 

 omitted, and at such a place as to bring 120 opposite 00, 

 each on the line of one half of the circle. The 60, there- 

 fore, also represents the half of a circle of 120°, which 

 latter is shown liy commenciug with PA — IC, PM — 20', 



and so on. Similarly, the 120 suggests the half of a circle 

 of 240 \ and the 180, which is also arranged to fall at the 

 half circle, the half of a circle of 360°. Thus, the circle of 

 El-Husu, by the use of only 12 numbers, expresses circles 

 of 12, 60, 120, 240 and 360 degrees. 



Such, then, are the Euphratean divisions of the circle 

 which have come down to us, and thus do Euphratean 

 concepts and principles connected with it still rule our 

 world of to-day. 



ASTRONOMY WITHOUT A TELESCOPE. 



By E. Walter Maunder, f.r.a.s. 

 XVII.— STARS BY DAYLIGHT; AND THE SUM 



OF STARLIGHT. 

 Ake the stars visible to ordinary sight in the daytime ? 

 There is a widespread tradition that they are ; that if an 

 observer places himself at the bottom of any deep shaft — 

 as of a mine, a well, or a factory chimney — which may 

 shut off scattered light and reduce the area of sky 

 illumination acting on the retina, he will be able to discern 

 the brighter stars without difficulty. The tradition is one 

 of a respectable anticjuity, for Aristotle refers to persons 

 seeing stars in daylight when looking out from caverns or 

 subterranean reservoirs, and Pliny ascribes to deep wells 

 a similar power of rendering visible the stars the light of 

 which would otherwise be lost in the overpowering 

 splendour of the solar rays. 



The tradition, well founded or not, has often been 

 adopted for literary effect. It seems almost sacrilegious 

 to hint that no star known to astronomers could have 

 shone down unceasingly upon poor Stephen Blackpool 

 during his seven days and nights of agony at the bottom 

 of the Old Hell Shaft ; that at best he could only have 

 caught a glimpse of it for a few minutes in each twenty- 

 four hours as it passed across the zenith. Dickens indeed 

 does not absolutely say that Stephen watched the star by 

 daylight. It is only a natural inference from his descrip- 

 tion ; but Kipling adopts the tradition in its extremest 

 form when he writes of : — 



" The gorge that shows tlie stars at noonday clear." 



But is the tradition true ? Of course everyone knows 

 that Venus from time to time may be seen even at high 

 noon ; but then Venus at her brightest is many times over 

 brighter than Sirius. Then, again, the assistance of a 

 telescope enables the brighter stars to be discerned at mid- 

 day ; but the telescope not only directs the eye and greatly 

 limits the area from which the skylight reaches the 

 observer, but it enormously increases the brightness of the 

 star relative to that sky illumination. The naked-eye 

 observation of true stars in full sunlight stands in quite a 

 ditferent category. 



Humboldt, who was much interested in the question, 

 repeatedly tried the experiment in mines, both in Siberia 

 and in America, and not only failed himself ever to detect 

 a star, but never came across anyone who had succeeded. 

 Much more recently an American astronomer set up a tube 

 for the express i.urpose of seeing the Pleiades by daylight, 

 also with no effect. It has been supposed that Flamsteed, 

 the first Astronomer Royal, sank a well at Greenwich 

 Observatory for the purpose of observing Gamma Draconis, 

 the zenith star of Greenwich, in this manner. The 

 existence of the well is undoubted, though Sir George 

 Airy, the late Astronomer Royal, was uuable to find it, but 

 Flamsteed marks it on more than one of his plans of the 

 Observatory, and there is a drawing extant of the well 

 itself, showing the spiral staircase that ran down it. But 

 its purpose seems to have been, not to have furnished the 



