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the head indicate the figures of the Quotient. — 
The Quotient 4 just found must, therefore, he taken 
down. After haying subtracted the number 39592 
from 41868 we add to the remaining 2276 the 
next figure of the Dividend, 5, and seek then 
for the number 22765, thus obtained, the Product 
next to it in size, which proves to be 19796, 
in column 2. This figure 2 is added to the 
Quotient 4, set down first, and the process then 
continued in the same order, which will yet pro 
duce, as third and last figure of the Quotient, the 
number *3, and with that we shall have the re 
quired Quotient 423. 
Written down the example will assume the 
following form: 
39592 
22765 
19796 
29694 
29694 
The Division on the Russian abacus is to be 
effected in the following manner. The Dividend, 
for instance, 4,186,854, is counted on the abacus, 
and the Products 39592, 19796, and 29694, are 
subtracted from it in the same order as in the 
written calculation. The figures of the Quotient 
thus produced, are thrown out, one under another, 
on the empty bar of the abacus. 
From the above solution of the question it is 
evident, that the Quotient is contained in the 
Tables ready-made, and that a simple process of 
subtracting only is needed to complete the calcu 
lation. 
On the whole, the object of these Tables is 
to reduce Multiplication to mere Addition, and 
Division, to Subtraction. 
Note. 
The author, of these Tables who has spared neither 
labour, nor money, to make them as practical and useful 
as possible, and thereby to introduce them to general use, 
begs to draw the reader’s attention especially to the follow 
ing hints which will greatly facilitate the use of the 
Tables : 
1. Each Table contains 99 numbers which, in system- 
order, fill up the middle column. Thus we find in 
the first Table the numbers from 1 to 99, 
„ second „ „ „ , „ 101 „ 199, 
„ third „ „ „ „ 201 „ 299 
and so on. 
By this uniform arrangement of the Tables, the 
searching and finding of any required number will be 
greatly facilitated. 
2. On the margin of each leaf the number of the 
hundreds is printed with Avhich the left hand Table begins; 
so that by cutting off the lower blank part of the margin 
an index will be obtained by which it is possible to find 
out at once the page containing the required number, with 
out being obliged to turn over the leaves in search for it. 
3. The prime numbers (Multiplicand, or Divisor) are 
contained in the middle column, just between the numbers 
of five and six-fold value. By this arrangement an easy 
and quick survey of the Tables is afforded, the eye getting 
soon accustomed to look for numbers of from two to five 
fold value on the left, and for those of from six to nine 
fold value on the right hand of the middle column. 
4. The Products in the Tables do not always appear 
in their complete form; but whilst one lino shows the 
Product in its entireness, the next shows only the increase 
in the units and tens, omitting the hundreds and thou 
sands. In the next following line, however, the Product 
is again printed in its complete form, and so on alternately. 
In this way the dazzling effect of long rows of compact 
numbers is lessened. It prevents the eye from becoming 
weary, or wandering into a wrong line. 
16 
18 
20 
22 
24 
26 
28 
30 
32 
34 
36 
38 
40 
42 
44 
46 
48 
50 
52 
64 
56 
58 
60 
62 
64 
66 
68 
70 
72 
74 
76 
78 
80 
82 
84 
86 
88 
90 
92 
94 
96 
98 
100 
102 
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