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146 Bibliography. 
smaller than we would prefer; but for trigonometrical tables, where it 
is necessary to oe sixty lines into a page, larger type would have 
been inconvenie 
In a volume of tables like the present, the — problem is to com- 
press the greatest amount of valuable matter into a given space, and so 
to arrange the materials as to furnish every possible facility to the com- 
uter. We shall be the better able to judge of the merits of Prof. 
Stanley’s tables, st comparing them with those which have hitherto 
een most esteemed. We will then compare Stanley’s table of loga- 
rithms of pellets ern that of Hutton. The former extends to 100,000; 
the latter to 108,000. There is some convenience in the latter part of 
Hutton’s table, particularly i in computing compound interest for long 
periods of time, and in other problems of a like kind. But Prof. Stan- 
ley has given in half a page at the end of the volume, i numbers 
most useful for this purpose, and has thus effected a saving of sixteen 
pages of numbers. ‘The arrangement of Stanley’s table is very similar 
to that of Hutton, except that the former has sixty lines to a page, 
while the latter has but fifty. Prof. Stanley has a more effectual mode 
Vith respect to 40 ogarithmic sines and on er we think the vapesk 
ority of Stanley’s tables as compared with those of Hutton is still more 
decided. Hutton gives sines and tangents to every second of t ‘first 
two degrees; but for the remainder of the quadrant he gives them 
only for each minute, with differences for 60”. In order then to find 
the correction for seconds, it is necessary to divide the tabular differ- 
ence by 60, and multiply the quotient by the given number o 
This operation is so laborious that we presume no mathem atician en 
ged in nice computations, ever long used Hautton’s trigonometrical 
tables, provided he could find better ones. That a trigonometrical table 
extending to seven places of decimals, should give simply differences to 
60”, when the differences for 100” would occupy no more room, is fi 
donable. On this account we long since discarded Hutton’s’ table of 
sines and tangents. Prof. Stanley gives sines, tangents and 
for every 10” for one-third of the quadrant, with differences to Hi. 
or the remaining ae thirds of the quadrant, he gives them only to 
Single minutes, but with differences to 1”. There is also a eo 
* pats for the frat ti iwo degrees, furnishing with pares - 
he last decimal place, the sine, tangent, etc., by means of sar ron 
f the arc expressed in seconds. Callet gies snes ee 1 every a 
