THE ARITHMETICAL PROBLEM.

Colonist, Volume XII, Issue 1243, 24 August 1869, Page 3

THE ARITHMETICAL PROBLEM.

The proposer ofthe problem, G.T., Takaka, or rather the resuseitator, for it is very old, sends several calculations. We print the following as ho putß it:— "If £1 in a certain number of years becomes £19 19s. llfd., what will £19 19s. lijd become in the same period? —Answer : £399 19s. 2 " First reduce all into farthings. The fourth term is obtained by multiplying tha second and third terms together, and then dividing by the first, which will give you 383960 r J- ff which reduce to pounds. Answer. £ £ s. d. £ s. d. £ s. d. As 1 : 19 19 11J :: 19 19 11$ : : 399 19 2^ £1 £19 19s. lljd. 20 20 20 399 12 12 240 4799 4 4 960 19199 19199 172791 172791 19199 172791 19199 960) 368601601 4) 383960 ¥^ 12) 95990 20) 7999 2 399 19 Answer as above, £399 19s. 2^-ijjd." Another correspondent sends us the following calculated by tho decimal process:—■ £19 19s. Od. = 19-95 0 0 6 = *025 0 0 3= *0125 0 0 2= -00833333 0 0 Ok = -00208333 0 0 Oi = -00104166 £19 19s. llfd= 19*99895833 19*99895833 5999687499 5999687499 15999166664 9999479165 17999062491 15999166664 17999062497 17999062497 17999062497 1999895833 399*9583342850763889 20 19*1666857015277780 12 20002284183333360 4 •0309136733333440 Answer: £399 19s. 2 TC {hn,d. '• Boy," gives the following answer—£379 lis. 3id. The whole thing so far as it relates to anything actually practical, as raeaniug the multiplication of a sum of money by a sum of money, unless in the way of principal aud'interest, is a simple absurdity. Take G-.T's own position, ancl instead of making the sum £19 19s. llfd., which necessitates reduction to farthings, let us make the sum one farthing more, and say £20, thus:—lf £1 give £20, how much will £20 yield? It is a rule of three sum; the £1 represents the principal, or say the original prico of a share in an Auckland gold-raining claim, and the £20 is the monthly profit arising from it; the answer i 3 £400, which is the product of twenty shares at a profit of £20 each. So far back bb 1856 a correspondent wrote on the subject to the Weekly Dispatch, which, in its answers to correspondents, gave the following reply : —

" It is impossible to multiply a sum of money by another sum. The question is frequently asked us, and we think it worth while to show the grounds of our assertion. Number and value are distinct abstract ideas, and cannot, without committing a logical absurdity, be contused. To multiply is to repeat a certain number of times, and it is obviously impossible to bring value into the question. Value 13 arbitrary; number is fixed. Put it in this way, and the absurdity is evident: —One pound is equivabnfc to 20 shillings, or 240 pence, or 960 farthings. In value there is no difference whatever ; but what aa enormous difference between multiplying by 1, 20, 240, or 960! The so-called problem of multip yiDg £19 19s. llf d. by the same may be treated f ucfcionally, considering the shillings and pence as fractions, and the multiplieator would read 19 959 960th's. This, though a long process, iis perfectly possible, but the idea of value is entirely lost. A little reflection will satisfy 'John' and others that they are pursuing a shadow."