.Voz>. i8, 1875J 



NATURE 



47 



This statement is not perfectly correct. 



The expression of the Chamberlain of the Corporation, as 

 recorded in the official register, and as correctly reported in the 

 principal newspapers, was : — 



" When the national standards of measure and ponderosity 

 were by accident lost to the nation, you were applied to for the 

 accomplishment of their restoration with that mathematical exac- 

 titude which was indispensable." 



The statement in Nature will be made correct by erasing 

 the word " Metric " and substituting " National. " 



G. B. AiRV 



The Origin of our Numerals 



Mr. Doxisthorpe's ingenious construction of our numerals 

 by corresponding numbers of lines (Nature, vol. xii. p. 476) 

 innuces me to offer a few remarks on this subject, which has a 

 literature of its own. There can be no doubt, I believe, that 

 our forms were derived directiy from the Arab series called 

 Gobar j that the Arabs had them from the Indians, and the 

 Indians from the Chinese. My esteemed friend Dr. WUson, of 

 Bombay, published a " Note on the Origin of the Units of the 

 Indian and European numerals," in 1858,* in which he showed 

 the derivation of some of our nimierals from ancient Indian 

 forms found on cave inscriptions of Western India, on the Bhilsa 

 Topes, and on coins. IVIy remarks are founded wholly on the 

 forms given in this note, which is little known, I believe, in 

 England. 



Dr. Wilson obtains our first four numeral forms from the 

 Chinese, traced through different Indian script characters nearly 

 as supposed by Mr. Donisthorpe. One, two, three horizontal 

 bars and a square for 4. He also hnds the eight in the forms 



n n C^J , and QO ""^ *^® '^^^'^ inscriptions. 



Before proceeding to the other numerals I \vish to notice a 

 rule which may be deduced from the consideration of the changes 

 in the forms of numerals in passing from one people to another, 

 that the same form may be turned through angles of 90" or 180% 

 and may be inverted or reversed without altering its value. 

 Even the same people have uied a form tiimed in different ways 

 for the same numeral. The Arabs used their 2, 3, and 4 in two 

 ways, making angles of 90" with each other ; the 2, 4, and 5 of 

 Sacro Bosco and Roger Bacon were the Indian script Modi (and 

 ours) turned through 180^, or upside down ; other examples will 

 be noticed. 



The most important derivation by Dr. Wilson is that from 



the Chinese ■+— ten ; this is found on the Bhilsa Topes with a 



circle round it (Dr. Wilson thinks to distinguish it from the 

 oldest form of K foimd on the cave inscriptions). The nine 



is found on the Bhilsa Topes as ® , or one tmder ten, and on 

 old coins thus : ^3. The Indian caves give half of ten -^ , 

 ^, for five (as V is the half of the Roman ten, X). It is from 

 this form that Dr. Wilson derives the Indian Modi and Nagari 

 fives ^ , "5 , "^ . It is here that I venture to differ slightly 



from Dr. WDson. One of the cave forms of fom: is ^. , which 



Dr. Wilson interprets (as in the case of nine) one imder five, or 

 five less one ; now this form without the under bar, as well as 

 the other forms of iive, are, it seems to me, the halves not of 



the cross i -U \ merely, but of the cross £nd circle thus : 

 y^;, i^, ^J:> which are as nearly as possible two half dia- 

 meters and half circumference. The form Nl is, I believe, the 



origin of our four, and not the Chinese or Indian square, as 

 supposed. This I think will be evident when we compare the 



Aiab four y H^ ) with the Indian four above. The Arab four 



s also employed thus : ^^ , which inverted gives ^^ , a suffi- 

 ciently near approximation to our four. 

 Dr. Wilson has not been able to find the origin of our seven, 



but this is obtained from his Arab seven /\ , by turning it 



rotmd ( ^ ) and making one leg shorter than the other, nearly 



* See " India Three Thousand Years Ago." By John Wilson, D.D., 

 F.R.S. (Bombay : Smith, Elder, and Co., 1858.) 



resembling the Gobar seven O . We may also find an earlier 



source in the Chinese seven turned round 1 80°, ^^ , which is 

 almost exactly the German written seven. Neither six nor seven 

 is to be found on the cave inscriptions. In Dr. W^ilson's Arab 

 series the Indian five (/ is used for six, and the Gobar six, as 



well as ours, may be taken from the Nagari seven m . We 



may also find an origin m the Chinese six ■Jt-- , by omitting the 



horizontal bar, as in the case of the seven. That such liberties 

 were taken is evident on a consideration of the five of Sacro 



Bosco and Roger B^con ( y ), the Indian five witkaut the bar, 



and turned round 180°. If there is any merit in these sugges- 

 tions it belongs to Dr. Wilson. 



John* Allan Broun 



On the Cup-shaped Joints in Prismatic Basalt 

 The difference between Mr. Mallet (Nature, vol. xiii. p. 7) 

 and myself is simply this. He asserts, as necessary to his 

 theory, that the "convexities" should always project in the 

 direction in which the cooling and consequent " splitting is pro- 

 ceeding" ("Proceedings of the Royal Society," No. 158, 

 p. 182). I referred him to the beautiful specimen, in the hall of 

 the Geological Society's Museum, of three columns, one of which 

 exhibits an articulation in the shape of a double- concave lens ; 

 the adjacent convexities consequently pointing, in this case, in 

 opposite directions. 



Mr. Mallet's reply to this is, that the cooling must have 

 proceeded, in this instance, in different directions, and met in 

 the biconcave-lens-shaped articulation. Now, inasmuch as this 

 articulation is only a few inches (three or four) thick, and shows 

 no sign of seam or separation across it, and ilr. Mallet himself 

 declares (in the article mentioned above) that the plane which 

 separates the part cooled from above, from that which cooled 

 from beloTiVj "consists of irregular Segments, ' I maintain that 

 his explanation is inadmissiole and self-contradictory. Any 

 geologist who takes sufficient interest in the question to examine 

 the columns for himself will be easily satisfied on this point. 

 Nov. 8 G. P. SCROPE 



A Nev7 Palmistry 



The proportions of the fingers in the two hands are not, I 

 think, always the same. W^ith me the index finger of the left 

 hand is considerably longer than the ring ; in the right they are 

 very nearly equal R. A. Pryor 



Hatfield, Nov. 12 



OUR ASTRONOMICAL COLUMN 



The Minor Planets. — ^The discovery of No. 154 

 by M. Prosper Henry at the Observatory of Paris, on 

 November 6th, is announced in M. Leverrier's Bulletin 

 and by circular with the " Astronomische Nachrichten ;" 

 and that of No. 155 by Herr Palisa at Pola on the 8th 

 inst, in the Paris Bulletin of the 13th. They are of the 

 same magnitude (twelfth) as the three previously detected 

 during the present month. 



The rapid increase in the number of small planets must 

 soon occasion serious difificulty, not only in predicting 

 their positions with sufficient approximation to allow of 

 their being recognised without considerable expenditure 

 of time and trouble, but likewise in securing observations, 

 especially on the meridian, according to the system pur- 

 sued for some years past at Greenwich and Paris, by 

 agreement between the Astronomer Royal and M. 

 Leverrier. 



As regards the preparation of ephemerides, it is well 

 known that the conductor of the " Berliner Astronomis- 

 ches Jahrbuch," Prof. Tietjen, makes it a speciality of his 

 work, with the aid of a numerous body of astronomers in 

 various parts of Europe and in the United States, and 

 hitherto he has succeeded in providing observers with an 

 ephemeris of nearly every small planet detected to within 

 a short time of publication. Thus, in the Jahrbuch for 



