As a hydrate, orthophosphoric acid should be expressed, after the fashion of other hydrates, as containing three water residues (hydroxyl groups), _i.e._ as PO(OH)_{3}. This method of expression indicates that the type PX_{5}, seen in PH_{4}I, is here preserved, with the substitution of X_{2} by oxygen and X_{3} by three hydroxyl groups. The same type appears in POCl_{3}, PCl_{5}, PF_{5}, &c. And if we recognise phosphoric acid as PO(OH)_{3}, we should expect to find three anhydrides corresponding with it: (1) [PO(OH)_{2}]_{2}O, in which two of the three hydroxyls are preserved; this is pyrophosphoric acid, H_{4}P_{2}O_{7}. (2) PO(OH)O, where only one hydroxyl is preserved. This is metaphosphoric acid. (3) (PO)_{2}O_{3} or P_{2}O_{5}, that is, perfect phosphoric anhydride. Therefore, _pyro- and metaphosphoric acids are imperfect anhydrides_ (or anhydro-acids) _of orthophosphoric acid_.[19] [19] In this sense the ortho-acid itself might be regarded as an anhydro-acid, counting P(HO)_{5} as the perfect hydrate, if PH_{5} existed; but as in general the normal hydrates correspond with the existing hydrogen compounds with the addition of up to 4 atoms of oxygen, therefore PH_{3}O_{4} is the normal acid, just as SH_{2}O_{4} and ClHO_{4}; while NHO_{3}, CH_{2}O_{3} are meta-acids, or higher normal acids (NH_{3}O_{4} and CH_{4}O_{4}) with the loss of a molecule of water. In order to see the relation between the ortho-, pyro-, and metaphosphoric acids, the first thing to remark in them is that the anhydride P_{2}O_{5} is combined with 3, 2, and 1 molecules of water. In the absence of data for the molecular weight of ortho- and pyrophosphoric acids it is necessary to mention that all existing data for metaphosphoric acid indicate (Note 21) that its molecule is much more complex and contains at least H_{3}P_{3}O_{9} or H_{6}P_{6}O_{18}. The explanation of the problems which here present themselves can, it seems to me, be only looked for after a detailed study of the phenomena of the polymerisations of mineral substances, and of those complex acids, such as phosphomolybdic, which we shall hereafter describe (Chapter XXI.) A similar instance is exhibited in the solubility of hydrate of silica (produced by the action of silicon fluoride on water) in fused metaphosphoric acid, with the formation, on cooling, of an octahedral compound (sp. gr., 3·1) containing SiO_{2},P_{2}O_{5}. A certain indication (but no proof) that ordinary orthophosphoric acid is polymerised is given by Staudenmaier (1893), who obtained a salt, K_{5}H_{4}P_{3}O_{12}, by the action of a solution of KH_{2}PO_{4} upon K_{2}CO_{3}; and a compound, KH_{3}P_{2}O_{8}, corresponding to the doubled molecule of H_{3}PO_{4}, by the action of KH_{2}PO_{4} upon H_{3}PO_{4} itself.