1896-97'] COUNTING AND TIME RECKONING. 317 



Probably the most familiar use of letters, as numerals, was found as 

 practised by the Romans. With them C, which was the initial letter 

 for Centum, stood for lOO, and M from Mille represented i,ooo. There 

 seem, however, to have been older forms in use instead of these. 

 Thus, a circle divided vertically (J) stood for i,ooo, and horizontally 

 9 for 100. From the sign for i,ooo, disparted thus, (/), still 

 occasionally found in prints, comes D for 500. Another symbol used 

 by them for 100 was C which has been suggested as the mode of 

 cancelling ten X^, just as X, in the same manner, may have been the 

 way the ten upright strokes for ten were cancelled, thus, r^^^S^. The 

 bi-section of this symbol for 100 ( C ) gives F, or L for 50, and of X, 

 V for 5. Further improvements in course of time were introduced ; IV 

 being used for IIII ; IX instead of Villi ; XL for 40 ; CD for 400; 

 CM for 900, etc. Here, as will be seen, when the smaller number is 

 placed in front, it has a subtractive force ; when placed behind the 

 larger it has an additive force. By the multiplication of the symbol for 

 1,000 (C 1 3), we get CCl 3 3= 10,000 ; CCC I 30 3= 100,000, and the bi- 

 section of these, 13 3 = 5,000, and 1333 = 50,000. In a Clavis Homerica 

 which I have, the date of publication is given thus, CI 3 1 3 CIV, being 

 1604. On the nth May, 1850, an inscription on a brass plate inserted 

 in the foundation stone of New College, London, has this date 

 CI 3 DCCCL. 



The introduction of the Arabic numbers worked a marvellous revolu- 

 tion in the modern systems of notation. It is now generally agreed that 

 they were of Indian origin and not Arabic, and were invented by the 

 Brahmins some time before the Christian Era. The Arabs themselves 

 lay no claim to the honour of having invented them, but ascribe them 

 to the Hindoos, while we are told that the Hindoos ascribe the inven- 

 tion of the nine digits {anca) to the beneficent Creator of the universe. 

 They were probably first introduced into Europe in the loth or nth 

 Century, but it was long before their use was sufficiently appreciated. 

 In manuscripts of the 14th Century,these "new numerals" (called Gobar), 

 seem to have been only partially understood, as we find Roman and Arabic 

 numerals hopelessly mixed together, nor was the value of zero (o) at 

 that time known. Thus, we have X, Xi, X2, X3, etc., for 10, n, 12, 13,, 

 and we find in regular sequence XXX, XXX i, 302, 303, for 30, 31, 32, 

 33. We come across also such combinations as X4 for 14, and MD58 

 (1558), and MDX47 (1647). The first calendar in the English lan- 

 guage in which the Arabic numbers are used has the date 1431. The 

 first English book which bears its date in the Arabic numerals was 

 printed in 1478. We find also a curious practice of dividing 8 so as to 



