s calcium oxalate, practically insoluble in
water and dilute acetic acid, but readily soluble in nitric or hydrochloric
acid. Calcium is generally estimated by precipitation as oxalate which,
after drying, is heated and weighed as carbonate or oxide, according to the
degree and duration of the heating.

CALCULATING MACHINES. Instruments for the mechanical performance of
numerical calculations, have in modern times come into ever-increasing use,
not merely for dealing with large masses of figures in banks, insurance
offices, &c., but also, as cash registers, for use on the counters of
retail shops. They may be classified as follows:--(i.) Addition machines;
the first invented by Blaise Pascal (1642). (ii.) Addition machines
modified to facilitate multiplication; the first by G.W. Leibnitz (1671).
(iii.) True multiplication machines; Leon Bolles (1888), Steiger (1894).
(iv.) Difference machines; Johann Helfrich von Mueller (1786), Charles
Babbage (1822). (v.) Analytical machines; Babbage (1834). The number of
distinct machines of the first three kinds is remarkable and is being
constantly added to, old machines being improved and new ones invented;
Professor R. Mehmke has counted over eighty distinct machines of this type.
The fullest published account of the subject is given by Mehmke in the
_Encyclopaedie der mathematischen Wissenschaften_, article "Numerisches
Rechnen," vol. i., Heft 6 (1901). It contains historical notes and full
references. Walther von Dyck's _Catalogue_ also contains descriptions of
various machines. We shall confine ourselves to explaining the principles
of some leading types, without giving an exact description of any
particular one.

[Illustration: FIG. 1.]

Practically all calculating machines contain a "counting work," a series of
"figure disks" consisting in the original form of horizontal circular disks
(fig. 1), on which the figures 0, 1, 2, to 9 are marked. Each disk can turn
about its vertical axis, and is covered by a fixed plate with a hole or
"window" in it through which one figure can be seen. On turning the disk
through one-tenth of a revolution this figure will be changed into the next
higher or lower. Such turning may be called a "step," _positive_ [Sidenote:
Addition machines.] if the next higher and _negative_ if the next lower
figure appears. Each positive step therefore adds one unit to the figure
under the window, while two steps add two, and so on. If a series, say six,
of s