102 Transactions. — Miscellaneous. 



dicated by the number of ciphers and those of the major 

 radix by the number of groups, the index-prefixes " bi," 

 " tri," &c., agreeing with the power. By this plan, and this 

 alone, the comma dividing the groups becomes a significant 

 arithmetical sign as well as an aid to legibihty. Both the 

 British system and the French are defective in starting from 

 the million, which, though itself a square number, has not a 

 square for its radix. In the British scheme, however, the 

 terms " billion," " trillion," &c., representing as they do the 

 successive powers of the greater radix, are correctly used ; 

 but the French nomenclature, in which a thousand millions 

 is called a " billion " and a thousand " billions " a " trillion," 

 is worse than meaningless — it is misleading. If we seek the 

 root of the British billion, the cube-root of the trillion, and so 

 on, we shall always come back to the starting-point — the 

 million, or 10**. Applying the same process to the French 

 table, we have a series of anomalous results — the root of the 

 "billion" is 31622777 with an endless decimal fraction; the 

 cube-root of the " trillion " is 10,000. The fact that the French 

 have their own specific word, " milliard," for their modern 

 "billion" seems to indicate that the numeration scheme has 

 undergone alteration ; and, in fact, I find it explicitly stated 

 by one authority that in France the " older writers " use the 

 same system as our own. I have been unable to ascertain 

 whether the change was made as recently as the revolution 

 at the close of the eighteenth century, so few writers concern 

 themselves with the historic aspects of the question ; but I 

 am inclined to think it belongs to a remoter period. Unfor- 

 tunately for the English-speaking world, the French method 

 has become prevalent in the United States, causing such 

 confusion in the interchange of newspaper items and literature 

 in general that one meeting with a i-eference to a " billion " 

 in print, unless assisted by the context, can never be sure 

 whether a thousand millions or a million millions is in- 

 tended. Stranger still, the French notation was most un- 

 warrantably introduced into at least one important Eng- 

 lish text-book — the Sandhurst Military College Arithmetic 

 — but appeared, 1 am informed, in one edition only. Its 

 temporary adoption in this academy, however, has led 

 to serious confusion. When the present Education Act 

 came into force the Department found both systems being 

 taught to the children of New Zealand, certain provincial 

 Inspectors apparently preferring the French method, and it 

 became necessary to issue a special direction insisting on the 

 uniform use of the British notation in all the public schools. 

 Apart from scientific defects, a low base of computation, 

 especially when combined with a low unit of currency, is not 

 in keeping with the dignity of a great people. Mark Twain 



