11 
performing the involution and evolution of numbers. 
subtraction of one logarithm from another will, in like man- 
ner, give the logarithm of the quotient resulting from the 
division of the number corresponding with the second, by the 
number corresponding with the first. The multiplication of 
a logarithm by any number will change it into another loga- 
rithm, which will answer to that power of the number cor- 
responding with the former logarithm, which has this multi- 
plier for its exponent. 
But it will be seen that even in the simplest and most direct 
applications of this invention some exertion of arithmetical 
skill and some share of mathematical knowledge are requi- 
site. Even this species of labour may, however, be avoided 
by the employment of lines as the representatives of loga- 
rithms ; so that by the simple admeasurement of these lines, 
with their sums, differences, or multiples, on a given scale, 
the result of any of the above mentioned operations may be 
obtained within a certain degree of accuracy. A farther im- 
provement consists in graduating a line of a convenient length 
logometrically , that is, dividing it so that the distance of each 
division from the beginning of the line, which is marked with 
unity, shall measure, on a given scale of equal parts, the 
logarithm of the number which is affixed to it. A line so 
divided is known by the name of Gunter’s scale. 
The divisions which are situated at equal distances, being 
marked by numbers whose logarithms have equal differences, 
it follows that the spaces intervening between any two num- 
bers are proportional to the differences between their respective 
logarithms ; or are measures of the ratios between each of these 
numbers. The same use may therefore be made of such r 
scale, as of a table of logarithms with regard to operations to 
C 2 
