Page:The New International Encyclopædia 1st ed. v. 10.djvu/820

* INVOICE. 730 IODIDES. inform the consignee that the goods invoiced have been ship|)e<l to him, and may become liis upon payment of the prices named in accordance Vith the conditions named in or accompanying the bill of lading. An invoice is not a document of title, and its pos.session does not indicate that the holder is tlm owner of the goods therein described. Nor is it a written contract of sale. It is a mere memorandum, always susceptible of explanation by parol evidence. It may be a sullicient memorandum under the sUitute of frauds (q.v. ) if it contains all the material terms of the oral sale conlnut and is signed by the party to be charged. Invoices of imported goods are required by the tariff regulations of some countries to be verified before one of their consuls or to be vouched for by him. Consult tho authorities rcfiTrcd to under S.LES; Baii.me.nts. IN'VOLU'CRE ( Lat. iinolucriim, wrapper, from i>ivolicre, to wrap, from in, in + i)o/i;ere, to roll ; connected with Goth, iralwjan, AS. loeal- iCTan, Eng. icullow). As a rule, each llower in a cluster (inflorescence) is sul)tcnd(il by a bract. In case the (lowers or their i>edicels are close to- gether, the bracts are thrown into a rosette, which is called an 'involucre.' Such inflorescences as the umbel of Umbellifcrte and the head of Com- positie have very characteristic involucres. Sec INFLOHFSCKNCK. INVOLUTION AND EVOLUTION. In mathematics, the raising to powers and the ex- traction of roots, respectively. The result of taking a number twice as a factor is called the square of the number; the result of taking it three times as a factor, its cube; four times, its fourth power, and so on; e.g. 3 . 3 = 3", or 9 is the square of 3 ; 3 • 3 • 3 = 3', or 27 is the cube of 3; a • a • a • a ^ a* y the fourth power of a. This process is called involution. Evolution is the inverse of involution, or it is the process which undoes involution. The square root of a number is one of the two equal factors of the number, the cube root one of the three equal factors, and so on; e.g. the square root of 16, or '/, is either 4 or — 4, since 4 • 4 = 16, and — 4 ■ — 4 = 16; the cube root of 27, or ^'ey.is either 3 or — 3( — ^(<±V2 V—3) sineo each of these cvibed equals 27. The nth root of a perfect jith power is one of the n equal fac- tors of that power. A number which is not a perfect »ith power has not n equal factors. It is, however, said to have an «th root to any re- quired degree of ap|)roximatinn. Thus the nth root of m to 0.1 is that number of tenths whose nth power difTers from m by less than the nth power of any other number of tenths. When the nundKT whose root is sought is a perfect power, the process of factoring is one of the most practical methods except the use of tables. In the case of numbers which are not perfect powers, and of certain algebraic expres- sions, the binomial formula is usually employed where tables are not available. Thus a' + 2ab + 6", the square of a -- b, may be applied to extract the square root of a number or of an alge- braic expression, since the root can always be expressed as a binomial whose square the power contains. The older methods of square and cube root, depending upon the sections of a square and of a cibe, were inferior, since they could not be extended to higher roots. The binomial formula is, however, of general application, and may be extended so as to extract the jith root. The detail of these processes can best be obtained from text- books. I'ractically to obtain the square or culie root of a number, reference is usually made to tables of roots or of logarithms. Sec LooA- BITIIM. In geometry two collinenr ranges, three points each, are .said to form an involution, when the anharmonic ratios (q.v.) of any four, not two pairs of conjuqalc points, is equal to the anhar- monic ratio of their fotir conjugates. Thus, in the figure ABC C B' A' A. U, C, C, B', .' form an involution, A. B, C being conjugate to A', B', t" and (A BOB') = (A' B' C B). This form of involution is due to Desargues (1639). Involutions of higher degrcM have been developed by Poncelet (1843) and Mobius (18.55). 10, i'A ( Lat., from Gk. 'Iii) . In Greek legend, the daughter of Inachus or lasus. and priestess of Hera at Argos. She was loved by Zeus, who, on account of Hera's suspicions, changed her into a white cow. Ucra, having obtained of him the cow as a present, sot the hundred-eyed Argus to watch her. Hermes, by command of Zeus, killed Argus and released her. Hera then sent a givd- tly, which ))ursued lo until in her wanderings she reached Egypt, where she was restored to her original form, and became the mother of Epa- phus. . somewhat dilfcrcnt account of this myth is found in the I'iomcllieu» of .Eschylus. In the early Greek art lo is represented as a cow; about n.c. 500 it became customary to represent her as a maiden with horns on her forehead; later still there is a return to the earlier method. Various attempts have been made to explain the myth by natural phenomena, but none have obtained any general acceptance. Consult. Engelman, De lone (Halle, 1868) ; id., in Roscher, l.rxikon der (irkchischen und rtimischrn Miilholorjic (I.eipzig, 1890-94) ; Plew, Xcue Jahrbiicher fiir I'hilologiv, vid. cii. (Leipzig, 1870). I'ODIDES ( from iodine, from Gk. ii>Sriz, iOdfs, like a violet, from lov, ion, Lat. viola, violet). The salts of hydriodie acid (q.v.). The iodides of potassium, sodium, ammonium, strontiiim, and zinc, are used in medicine. They are extensively employed in the lertiarj' stages of syphilis, caus- ing the rapid absorption of syphilitic deposits. The iodide of potassium is further beneficial in gonorrhieal rheumatism, in certain joint diseases, in pleurisy, Bright's disease, asthma, and as an expectorant in brondiitis; it is also used in cases of chronic lead and mercury poisoning. The other iodides have much the same effect as that of potassium, and the iodides of sodium and strontium are even beMeved to be preferable. Overdoses of iodides, and :ven moderate doses in the case of some people, may give rise to certain symptoms that are collectively known as iodism : there is an eruption on the skin, running at the nose and mouth, .sore throat, and even larj'ncitis and bronchitis. In such cases the dose should Ik' diminished, and. if necessary, the administration of the salt entirely discontinued. Potassium iodide sometimes causes great gen- eral depression : if so, it may be replaced by the