Elementary arithmetic, with brief notices of its history... by Robert Potts.

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sack of 3 bushels, and the chaldron of 12 sacks; they are now measured by weight, the ton being employed as the unit of weight.
MEASURES OF LIQUID SUBSTANCES.
Ale, Beer, fc.
2 pints are equal to 1 quart
4 quarts,, 1 gallon
9 gallons,, 1 firkin
2 firkins,, 1 kilderkin
2 kilderkins,, 1 barrel
3 kilderkins,, 1 hogshead
2 hogsheads,, 1 butt.
Wines, Spirits, ic.
2 pints are equal to 1 quart
4 quarts,, 1 gallon
63 gallons,, I hogshead
2 hogsheads,, 1 pipe
2 pipes,, 1 tun.
There were other measures of wine in use, such as the anker of
10 gallons, the runlet of 18, the tierce of 42, and the puncheon of 84.
Any quantity expressed in terms of a larger unit of measure, can
also be expressed in terms of a smaller unit which is some subdivision
of that measure, and conversely. The units of larger magnitude are
changed to units of smaller magnitude of the same kind by multiplying
the number of larger units by the number of smaller which make one
of the larger; and conversely, the units of smaller magnitude are
changed to those of a larger of the same kind by dividing the smaller
by as many of the smaller as make one of the larger.
ANGULAR AND CIRCULAR MEASURES.
8. The invention of the sexagesimal division of the circumference of
the circle is attributed to Ptolemy by his commentator Theon, but it is
clear from the language of Ptolemy himself that this mode of division
was known long before his time. It is more probable that the improvement made by Ptolemy was the extension of that mode of division to
the radius or the chord of a circle which subtends an arc equal to onesixth of the whole circumference.
It has been conjectured that the division of the circumference of a
circle into 360 equal parts was suggested by the fact that the sun
appears to move once round the whole circle of the heaven in the.
period of about 360 days; but whether this or the converse be the
truth, it is quite impossible to affirm. This division of the circumference
has come down from very early times.
Angles are measured by the arcs of circles. If a circle be described
with any radius from the angular point as a centre, the arc intercepted
between the lines which contain the angle may be assumed to be the