The modern form of slide rule, variously styled the Gravêt, the
Tavernier-Gravêt, and the Mannheim rule, is frequently made of boxwood,
but all the leading instrument makers now supply rules made of boxwood
or mahogany, and faced with celluloid, the white surface of which brings
out the graduations much more distinctly than lines engraved on a
boxwood surface. The celluloid facings should not be polished, as a dull
surface is much less fatiguing to the eyes. The most generally used, and
on the whole the most convenient size of rule, is about 10½in. long,
1¼in. wide, and about ⅜in. thick; but 5 in., 8 in., 15 in., 20 in., 24
in. and 40 in. rules are also made. In the centre of the stock of the
rule a movable slip is fitted, which constitutes the slide, and
corresponds to the lower of the two rules of our rudimentary examples.
[Illustration: FIG. 5.]
From Fig. 5, which is a representation of the face of a Gravêt or
Mannheim slide rule, it will be seen that four series of logarithmic
graduations or scale-lines are employed, the upper and lower being
engraved on the stock or body of the rule, while the other two are
engraved upon the slide. The two upper sets of graduations are exactly
alike in every particular, and the lower sets are also similar. It is
usual to identify the two upper scale-lines by the letters A and B, and
the two lower by the letters C and D, as indicated in the figure at the
left-hand extremities of the scales.
Referring to the scales C and D, these will each be seen to be a
development of the elementary scales of Fig. 3, but in this case each
principal space is subdivided, more or less minutely. The principle,
however, is exactly the same, so that by moving the slide (carrying
scale C), multiplication and division can be mechanically performed in
the manner described.
The upper scale-line A consists of two exactly similar scales, placed
end to end, the first lying between IL and IC, and the second between IC
and IR. The first of these scales will be designated the _left-hand A
scale_, and the second the _right-hand A scale_. Similarly the
coinciding scales on the slide are the _left-hand B scale_ and the
_right-hand B scale_. Each of these four scales is divided (as finely as
convenient) as in the case of the C and D scales, but, of course, they
are exactly one half the length of the latter.
The two end graduations of both the C and D scales are known as the
_left-_ and _right-hand indices_ of these scales. Sometimes they are
figured 1 and 10 respectively; sometimes both are marked 1. Similarly IL
and IR are the left- and right-hand indices of the A and B lines, while
IC is the centre index of these scales. Other division lines usually
found on the face of the rule are one on the left-hand A and B scales,
indicating the ratio of the circumference of a circle to its diameter, π
= 3·1416; and a line on the right-hand B scale marking the position of
(π)/(4) = 0·7854, used in calculating the areas of circles. Reference
will be made hereafter to the scales on the under-side of the slide, and
we need now only add that one of the edges of the rule, usually
bevelled, is generally graduated in millimetres, while the other edge
has engraved on it a scale of inches divided into eighths or tenths. On
the bottom face inside the groove of the rule either one or the other of
these scales is continued in such a manner that by drawing the slide out
to the right and using the scale inside the rule, in conjunction with
the corresponding scale on the edge, it is possible to measure 20 inches
in the one case, or nearly 500 millimetres in the other. On the back of
the rule there is usually a collection of data, for which the slips
given at the end of this work may often be substituted with advantage.