In order to show the use of this Abacus, let tis sup pose it required to add 8 to 7. In the groove inn of units, place the sharp point upon the cross stroke of the ivory slip opposite 8, and pressing with the sharp point till it conies to n, the number 8 will appear in the line of units to the left hand of II. When this is done, place the sharp point in the cross stroke opposite 7, and bring it also down to n. Instead of 7, a 0 will appear in the line of units at II, and a 1 in the line of hundreds, as the slip which contains the line of hun dreds has been brought down one spree by the catch in the slip of units. Keeping the sharp point still at n, in the stroke which was opposite 7, move the slip up wards till the point readies the very top in, and a 5 will now appear in phi( c of 0, in the line of units at II ; so that the figures in the Opening G11 will he now 15, the sum of 7 and 8. Whenever a blank space or a 0 ap pears in the opening, the slips of ivory must always be carried up to the very top of the groove.
In subtraction, we must put the greater number, sup pose 123, in the opening Er, and if the lesser number be 34, we must, by means of the sharp point placed in the cross stroke opposite 4, bring this figure in the line of units to the bottom of the groove inn, and also the figure 3 in the line of tens, to the bottom of the groove up. Instead of the number 123 in the opening Er, we shall now have 89, the difference between 123 and 31.
It must be attended to, however, that whenever there is a 0 in the greater number, we must take 1 from thy. line of tens, if the 0 is in the line of units, and 1 from the line of hundreds, if the 0 is in the line of tens : Thus, if we want the difference between 92 and 150, the Aba cus will give 68 instead of 58 ; and if we want the dif ference between 1500 and 264, the Abacus will give 1346 instead of 1236.
In multiplication, the same process is necessary :Li in addition. If, for example, the product of 15 and Is were required, we bring 5 times 5, which is 25, into the lower opening, by means of the sharp point, as before, and we afterwards bring one times 5, or 5, in the line of tens, to the opening ; and one times i, or 1, in the line of hundreds, to the opening. When this is done, the number 225 will appear in the opening, Its the product of 15 by 15.
In the figure, we have, for the sake of distinctness, represented only one of the slips with teeth and a catch ; but all the slips, except the last kg, have a catch ; and all of them, except the first ta, have teeth. A descrip tion and drawing of the ancient Roman Abacus, may bi seen in F. Urzin. loser. Duillian,e ; and in Ant. Augustin, Numisni. ; Dial. 9. For an account of other arithmetical machines, see ARITIIMETtc, Part III. G UN