596 Royal Irish Academy, 



astrological influences, viz. Aries = good ; Taurus = evil ; Gemini 

 = evil ; Leo = evil ; Virgo = evil ; Libra = good ; Sagittarius 

 = good ; Capricomus = evil ; Aquarius = good. The others are 

 said to neutralize their influences. 



" In the Philosophical Transactions of the Royal Society of Lon- 

 don*, Dr. Ward has given an account of a date in Arabic numerals 

 found on a stone in Ireland, which he considered to belong to the 

 twelfth century. Professor Peacock, however, in his History of 

 Arithmetic, has ably confuted this conjecture. 



" The Liber Niger of Christ Church, Dublin, is said to contain 'a 

 curious treatise on arithmetic, exhibiting the state of that science 

 before the introduction of Arabic numerals f.' I much question the 

 accuracy of this statement, and should be rather inclined to think 

 that it is merely an account of the numbers of algorism, so common 

 in manuscripts of this class. The same volume also contains a trans- 

 cript of the French poetical treatise entitled Imago Mundi, one of 

 the most curious unpublished scientific tracts of the middle ages. 

 This latter treatise is now in the progress of publication, by the His- 

 torical Society of Science. 



" But by far the most curious document that I have met with re- 

 lating to the early science of Ireland, is a manuscript in the posses- 

 sion of C. Wright, Esq. of Cambridge, who has kindly allowed me 

 to make use of it, and has also furnished me with a translation of 

 the greater part, which has been of great assistance to me. This 

 MS. consists of six foHo leaves on vellum, slightly injured by damp, 

 apparently belonging to the early part of the fifteenth century, and 

 containing the following articles : — 



" 1. A brief treatise on arithmetic. 



" This unfortunately commences imperfectly in the account of the 

 rule of duplation ; ' In duplation only one order of figures is neces- 

 sary : in the three preceding kinds, we commenced from the right 

 and from a smaller figure ; but in this and the following kinds, we 

 commence from the left and from a larger figure. For if you M'ish to 

 double from the first figure, it happens that you must double it twice. 

 And if you can in any other manner commence from the right-hand, 

 the operation and construction will be much more difficult. If, there- 

 fore, you wish to double any number, that number must be written 

 by its diff'erences, and the last number must be doubled. From that 

 duplation, therefore, either results a digit, an article, or a composite. 

 If a digit, it must be written in the place of the other blotted out. 

 If an article, a must be written in the place of the other blotted 

 out, and the article must be removed towards the left-hand. If a 

 composite number, the digit which is a part of that composite must 

 be written in the place of the other blotted out, and the article be 

 removed to the left-hand. This being done, the last figure must be 

 doubled, and whatever thence arises must be dealt with as before ; 

 but if a cipher turns up, it must be left untouched. We prove 

 duplation by means of mediation.' 



* For the year 1745, p, 283. 



t Report on the Public Records of Ireland, p. 307. 



