>nic. [500 
501] 
95 
say, for shortness, 
4.67, 12.45, and 
of the 8 points, 
question passes 
onic through the 
leous factor 2—6, 
i writing therein 
-12 z] 
-27 z] 
throwing this out 
2, 3, 4, 5, 6, 7, 8. 
1234 - 812345} : 
it the final result, 
h twice repeated: 
>f y 2 they destroy 
; of y~ contains 
and this contains 
501. 
REVIEW. Tables de Logarithmes vulgaires à dix décimales construites d'après un nouveau 
mode par S. Pineto, approuvées par l’Académie des Sciences de S. Pétersbourg. 
S. Pétersbourg, 1871. 
[From the Quarterly Journal of Pure and Applied Mathematics, vol. xi. (1871), 
pp. 375—376.] 
The tables occupy 56 pages—the principal one being a table in 44 pages, the 
22 left-hand pages containing the 10 figure logarithms of the numbers from 1,000,000 
to 1,010,999, and the 22 right-hand pages the proportional parts •01/02,... ‘99 of the 
differences. A like table 100,000 to 999,999 would occupy 3600 pages. By means of 
an auxiliary table of 3 pages, and of a slight increase of the numerical calculation, 
the table of 44 pages does the work of the table of 3600 pages. To explain how this 
is: the auxiliary table gives for any number A the initial four digits of which are 
equal to or exceed 1011, a multiplier M, such that in the product MA the initial 
four digits are between 1000 and 1011; this multiplier M contains only 1, 2 or 3 
figures, and when there are 3 figures, then in general either the middle figure is 0, 
or two of the figures are equal; the table gives also log ^ decimals; and 
there is a third column, as will be explained. Hence A being as above, the auxiliary 
table gives M, we form the product MA, obtain the logarithm thereof from the 
principal table, and adding thereto log-^-, we have the required log A. Conversely, 
when there is given a logarithm B the first five digits in the mantissa of which are 
not included between 00000 and 00474 (being the limits of the first five digits of 
the logarithms in the principal table), the auxiliary table by means of its third 
column gives M; adding log ~ to B, we have a logarithm included in the limits of