..81 to the Construction of Xeper's Rods : suppose the common table of multipli cation to be made upon a plate of metal, ivory or paste-board, and then conceive the several columns (standing downwards from the digits on the head) to be cut asunder ; and these are what we call Ne per's rods for multiplication. But then there must be a good number of each ; for as many times as any figure is in the multiplicand, so many rods of that species (i. e. with that figure on the top of it) must we have p though fix rods of each species will be sufficient Tor any ex ample in common affairs : there must also be as many rods of O's.
But, before we explain the way of using these rods, there is another thing to be known, cis. that the figures on every rod are written in an order. differ ent from that in the table. Thus, the little square space, or division, in which the several products of every column are written, is divided into two parts, by a line across from the upper angle on the right to the lower on the left; and if the product is a digit, it is set in the lower division ; if it has two places, the first is set in the lower, and the second in the upper division ; but the spaces on the top are not divided ; also there is a rod of digits not divided, which is called the index-rod, and of this we need but one single rod.
Multiplication by Xeper's Rods. First lay down the index-rod ; then on the right of it set a rod, whose top is the figure in the highest place of the multi plicand: next to this, again, set the rod whose top is the next figure of the mul tiplicand ; and so on in order, to the first figure. Then is your multiplicand tabu lated for all the nine digits ; for in the same line of squares standing against every figure of the index-rod, you have the product of that figure, and there fore you have no more to do but to transfer the products and sum them. But in taking out these products from the rods, the order in which the figures stand obliges you to a very eusy and small addition : thus, begin to take out the fi. gure in the lower part, or unit's place, of the 'square of the first rod on the right : add the figure in the upper part of this rod to that in the lower part of the next, and so on, which may be done as fast as you can look on them. To make this practice as clear as possible, take the following example.
Example. To multiply 4,768 by 185.
Having set the rods together for the number 4,768 against 5 in the index, I find this number, by adding according to the rule 23,840 Against 8, this number . . 38,144 Against 3, this number . . 14,304 Total product 1,835,680 ississmei To make the use of the rods yet more regular and easy, they are kept in a flat square box, whose breadth is that of ten rods, and she length that Of one rod, as thick as to hold six (or as many as you please) the capacity of the box being di vided into ten cells, for the different spe cies of rods. When the rods are put up in the box, (each species in its own cell, distinguished by the first figure of the rod set before it on the face of the box near the top) as much of every rod stands without the box, as shews the first figure of that rod ; also upon one of the flat sides without and near the edge, upon the left hand, the index-rod is fixed : and along the foot there is a small ledge, so that the rods, when applied, are laid upon this side, and supported by the ledge, which makes the practice very easy ; but in case the multiplicand should have more than nine places, that upper face of the box may be made broader. Some make the rods with four different faces, and figures on each for different purposes.
Division by Neper's Rods. First tabu late your divisor ; then you have it mul tiplied by all the digits, out of which you may choose such convenient divisors as will be next less to the figures in the di vidend, and write the index answering in the quotient, and so continually, till the work is done. Thus 2,179,788, divided by 6,123, gives in the quotient 356.
Having tabulated the divisor, 6,123, you see that 6,123 cannot be had in 2,179; therefore take five places, and on the rods find a number that is eqtral, or next less to 24/97, which is 18,569 ; that is, three times the divisor, wherefore set 3 in the quotient, and subtract 18,369 from the figures above, and there will remain 3,428 ; to which add 8, the next figure of the dividend, and seek again on the rods for it, or the next less, which you will find to be five times ; therefore set 5 in the quotient, and subtract 30,615 from 34,228, and there will re main 3,673, to which add 8, the last 6 pre in the dividend, and finding it to be just six times the divisor, set 6 in the quotient.
6123)2179788(356 18369 34288 30615 36738 36738 00000 15S11