12 
Dr. Ro get’s description of a new instrument for 
be performed on their corresponding numbers. Thus it will 
be found, that the portion of the scale extending from 1 to 3, 
added to that extending from 1 to 4, is equal to that between 
1 and 12 : showing that the logarithm of 3, added to that of 
4, is equal to the logarithm of 12 : or that the ratio of 1 to 3, 
added to that of 1 to 4, composes the ratio of 1 to 12: or 
that 12 is the product of 3 and 4. The excess of the interval 
between 1 and 24, over that between 1 and 6 , or, what is the 
same thing, the interval between 6 and 24, will be equal to 
that between 1 and 4 ; showing, by a similar process of rea- 
soning, that 4 is the quotient of 24 divided by 6. This com- 
parison of the intervals between the numbers on Gunter’s 
scale is effected with great ease by the addition of another 
scale, which may be called the slider, exactly equal in length 
to the former, and bearing the same divisions, but capable of 
being moved by its side, so as to allow of any part of the one 
being applied to any part of the other. In this form it con- 
stitutes the common sliding-rule, the utility of which is so 
generally known in resolving all questions that require the 
simple operations of multiplication and division, or relate to 
the finding of any term of a proportion. Supposing the two 
scales originally to coincide, the sliding scale being the un- 
dermost, by advancing the slider any given distance, each of 
its divisions will be brought under those of the fixed scale, 
which before were respectively situated farther forwards by 
an interval equal to that given distance. Every number in 
the upper scale will therefore have to the number standing 
under it on the slider, the same constant ratio ; a ratio indi- 
cated by the number under which the unity, or commence- 
ment of the scale, of the slider has been placed. The former 
