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2io                          THE  MACHINE-SHOP
parts. Each subdivision on the vernier is thus shorter than those on the
rule by TWIT in. Hence the rule: Note how many inches, tenths, and parts
of tenths the zero point on the vernier has been moved from the zero on the
rule. Count upon the vernier the number of divisions, until one is found
which coincides with one on the rule. This division will correspond to the
number of thousandths to be added to the distance read off on the rule.
Fixed Gauges.—Some fits in mechanisms must be tight and others
easy. Differences made in dimensions for the various kinds of fits are termed
" allowances ". The very minute variations that are permissible are called
" tolerances ". The term " limits " includes allowances and tolerances, and
gives the name to the " limit " gauges, which are generally guaranteed to be
correct within o-oooi in. Usually the hole is taken as the basis for measure-
ment, and the allowance is made on the shaft, but this is not invariable.
For many years after the introduction of gauges, the Whitworth cylindrical
forms only were used—the " plug " and the " ring ".    No attempt was
,                                 made at first to include limits.    The plugs fitted their rings exactly on the
f                                 application of the merest film of oil with the finger.    Tight and easy fits
!                                 were made by the exercise of judgment.    These have largely given place,
!                                 except for tapers, to the flat " snap " gauges, partly because these show a
dimension more finely than the others, and also because they can be used
k                                 on pieces that are not cylindrical.    In some forms there is a gauge, fixed by
\                                 two opposing jaws, at one end of the instrument that should pass over the
{                                work, and at the other a pair of jaws that must not.    They are called " go "
I                                and " not-go " gauges.    In large gauges the instruments are separate or
f                                combined.
|                                      The Johansson System.—In this system, end measuring blocks of
t                                rectangular  shapes   are   employed.     A   set  comprises   eighty-one  blocks
'                                divided into four series.   The first ranges from o-iooi to 0-1009 in. by
I                                increments of o-oooi in., the second from o-ioi to 0-149 *n- ^7 °'OOi in.,
f                               the third from 0-050 to 0-950 in. by 0-05 in., the fourth measure i in.,
^                               2 in., 3 in., and 4 in.    The blocks in the first series will divide up the spaces
f                               between those of the second series, and series three and four can be divided
\                               by the first and second series.    By means of combinations of the eighty-one
I                               gauges, 80,000 different sizes can be obtained.   These combinations are of
I                               much value in providing a ready method of checking the accuracy of a number
?                               of fractional dimensions.    They are used both for checking work directly,
I                              and for testing other measuring instruments, as calipers, limit gauges, measur-
I                              ing rods, jig parts, &c.    Various holders are provided.   The most remarkable
feature of these gauges is that the blocks adhere to each other by reason of
the fine accuracy of their surfaces.