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 crystallizing in monoclinic prisms, and occurring in various natural waters, as an efflorescence in limestone caverns, and in the neighbourhood of decaying nitrogenous organic matter. Hence its synonyms, “wall-saltpetre” and “lime-saltpetre”; from its disintegrating action on mortar, it is sometimes referred to as “saltpetre rot.” The anhydrous nitrate, obtained by heating the crystallized salt, is very phosphorescent, and constitutes “Baldwin’s phosphorus.” A basic nitrate, Ca(NO3)2·Ca(OH)2·3H2O, is obtained by dissolving calcium hydroxide in a solution of the normal nitrate.

Calcium phosphide, Ca3P2, is obtained as a reddish substance by passing phosphorus vapour over strongly heated lime. Water decomposes it with the evolution of spontaneously inflammable hydrogen phosphide; hence its use as a marine signal fire (“Holmes lights”), (see L. Gattermann and W. Haussknecht, Ber., 1890, 23, p. 1176, and H. Moissan, Compt. Rend., 128, p. 787).

Of the calcium orthophosphates, the normal salt, Ca3(PO4)2, is the most important. It is the principal inorganic constituent of bones, and hence of the “bone-ash” of commerce (see ); it occurs with fluorides in the mineral (q.v.); and the concretions known as  (q.v.) largely consist of this salt. It also constitutes the minerals ornithite, Ca3(PO4)2·2H2O, osteolite and sombrerite. The mineral brushite, CaHPO4·2H2O, which is isomorphous with the acid arsenate pharmacolite, CaHAsO4·2H2O, is an acid phosphate, and assumes monoclinic forms. The normal salt may be obtained artificially, as a white gelatinous precipitate which shrinks greatly on drying, by mixing solutions of sodium hydrogen phosphate, ammonia, and calcium chloride. Crystals may be obtained by heating di-calcium pyrophosphate, Ca2P2O7, with water under pressure. It is insoluble in water; slightly soluble in solutions of carbonic acid and common salt, and readily soluble in concentrated hydrochloric and nitric acid. Of the acid orthophosphates, the mono-calcium salt, CaH4(PO4)2, may be obtained as crystalline scales, containing one molecule of water, by evaporating a solution of the normal salt in hydrochloric or nitric acid. It dissolves readily in water, the solution having an acid reaction. The artificial manure known as “superphosphate of lime” consists of this salt and calcium sulphate, and is obtained by treating ground bones, coprolites, &c., with sulphuric acid. The di-calcium salt, Ca2H2(PO4)2, occurs in a concretionary form in the ureters and cloaca of the sturgeon, and also in guano. It is obtained as rhombic plates by mixing dilute solutions of calcium chloride and sodium phosphate, and passing carbon dioxide into the liquid. Other phosphates are also known.

Calcium monosulphide, CaS, a white amorphous powder, sparingly soluble in water, is formed by heating the sulphate with charcoal, or by heating lime in a current of sulphuretted hydrogen. It is particularly noteworthy from the phosphorescence which it exhibits when heated, or after exposure to the sun’s rays; hence its synonym “Canton’s phosphorus,” after John Canton (1718–1772), an English natural philosopher. The sulphydrate or hydrosulphide, Ca(SH)2, is obtained as colourless, prismatic crystals of the composition Ca(SH)2·6H2O, by passing sulphuretted hydrogen into milk of lime. The strong aqueous solution deposits colourless, four-sided prisms of the hydroxy-hydrosulphide, Ca(OH)(SH). The disulphide, CaS2 and pentasulphide, CaS5, are formed when milk of lime is boiled with flowers of sulphur. These sulphides form the basis of Balmain’s luminous paint. An oxysulphide, 2CaS·CaO, is sometimes present in “soda-waste,” and orange-coloured, acicular crystals of 4CaS·CaSO4·18H2O occasionally settle out on the long standing of oxidized “soda- or alkali-waste” (see ).

Calcium sulphite, CaSO3, a white substance, soluble in water, is prepared by passing sulphur dioxide into milk of lime. This solution with excess of sulphur dioxide yields the “bisulphite of lime” of commerce, which is used in the “chemical” manufacture of wood-pulp for paper making.

Calcium sulphate, CaSO4, constitutes the minerals (q.v.), and, in the hydrated form, selenite,  (q.v.),  (q.v.), and also the adhesive plaster of Paris (see ). It occurs dissolved in most natural waters, which it renders “permanently hard.” It is obtained as a white crystalline precipitate, sparingly soluble in water (100 parts of water dissolve 24 of the salt at 15°C.), by mixing solutions of a sulphate and a calcium salt; it is more soluble in solutions of common salt and hydrochloric acid, and especially of sodium thiosulphate.

Calcium silicates are exceptionally abundant in the mineral kingdom. Calcium metasilicate, CaSiO3, occurs in nature as monoclinic crystals known as tabular spar or wollastonite; it may be prepared artificially from solutions of calcium chloride and sodium silicate. H. Le Chatelier (Annales des mines, 1887, p. 345) has obtained artificially the compounds: CaSiO3, Ca2SiO4, Ca3Si2O7, and Ca3SiO5. (See also G. Oddo, Chemisches Centralblatt, 1896, 228.) Acid calcium silicates are represented in the mineral kingdom by gyrolite, H2Ca2(SiO3)3·H2O, a lime zeolite, sometimes regarded as an altered form of (q.v.), which is itself an acid calcium silicate containing an alkaline fluoride, by okenite, H2Ca(SiO3)2·H2O, and by xonalite 4CaSiO3·H2O. Calcium silicate is also present in the minerals:, , , , , , (qq.v.).

Detection and Estimation.—Most calcium compounds, especially when moistened with hydrochloric acid, impart an orange-red colour to a Bunsen flame, which when viewed through green glass appears to be finch-green; this distinguishes it in the presence of strontium, whose crimson coloration is apt to mask the orange-red calcium flame (when viewed through green glass the strontium flame appears to be a very faint yellow). In the spectroscope calcium exhibits two intense lines—an orange line, ( 6163), a green line , ( 4229), and a fainter indigo line. Calcium is not precipitated by sulphuretted hydrogen, but falls as the carbonate when an alkaline carbonate is added to a solution. Sulphuric acid gives a white precipitate of calcium sulphate with strong solutions; ammonium oxalate gives 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; Léon Bollés (1888), Steiger (1894). (iv.) Difference machines; Johann Helfrich von Müller (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 Encyclopädie 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.

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 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 such figure disks be placed side by side, their windows lying in a row, then any number of six places can be made to appear, for instance 000373. In order to add 6425 to this number, the disks, counting from right to left, have to be turned 5, 2, 4 and 6 steps respectively. If this is done the sum 006798 will appear. In case the sum of the two figures at any disk is greater than 9, if for instance the last figure to be added is 8 instead of 5, the sum for this disk is 11 and the 1 only will appear. Hence an arrangement for “carrying” has to be introduced. This may be done as follows. The axis of a figure disk contains a wheel with ten teeth. Each figure disk has, besides, one long tooth which when its 0 passes the window turns the next wheel to the left, one tooth forward, and hence the figure disk one step. The actual mechanism is not quite so simple, because the long teeth as described would gear also into the wheel to the right, and besides would interfere with each other. They must therefore be replaced by a somewhat more complicated arrangement, which has been done in various ways not necessary to describe more fully. On the way in which this is done, however, depends to a great extent the durability and trustworthiness of any arithmometer; in fact, it is often its weakest point. If to the series of figure disks arrangements are added for turning each disk through a required number of steps,