and the right-hand side can be developed in whatever form is most convenient for the particular case.
References.—For general formulae, with particular applications, see the Text-book of the Institute of Actuaries, part ii. (1st ed. 1887, 2nd ed. 1902), p. 434; H. L. Rice, Theory and Practice of Interpolation (1899). Some historical references are given by C. W. Merrifield, “On Quadratures and Interpolation,” Brit. Assoc. Report (1880), p. 321; see also Encycl. der math. Wiss. vol. i. pt. 2, pp. 800-819. For J. D. Everett’s formula, see Quar. Jour. Pure and Applied Maths., No. 128 (1901), and Jour. Inst. Actuaries, vol. xxxv. (1901), p. 452. As to relative accuracy of different formulae, see Proc. Lon. Math. Soc. (2) vol. iv. p. 320. Examples of interpolation by means of auxiliary curves will be found in Jour. Royal Stat. Soc. vol. lxiii. pp. 433, 637. See also [Differences, Calculus of].
(W. F. Sh.)
INTERPRETATION (from Lat. interpretari, to expound, explain, interpres, an agent, go-between, interpreter; inter, between, and the root pret-, possibly connected with that seen either in Greek φράζειν, to speak, or πράττειν, to do), in general, the action of explaining, or rendering the sense of an obscure form of words or an unknown tongue into a language comprehended by the person addressed. In legal use the word “interpretation” is employed in the sense of ascertaining the meaning of the language of a document, as well as its relation to facts. It is also applied to acts of parliament, as pointing out the sense in which particular words used therein are to be understood. The interpretation of documents and statutes is subject to definite legal rules, the more important of which will be found in the articles [Contract], [Statute], [Will], &c.
INTERREGNUM (Lat. inter, between, and regnum, reign), strictly a period during which the normal constituted authority is in abeyance, and government is carried on by a temporary authority specially appointed. Though originally and specifically confined to the sphere of sovereign authority, the term is commonly used by analogy in other connexions for any suspension of authority, during which affairs are carried on by specially appointed persons. The term originated in Rome during the regal period when an interrex was appointed (traditionally by the senate) to carry on the government between the death of one king and the election of his successor (see [Rome]: History, ad init.). It was subsequently used in Republican times of an officer appointed to hold the comitia for the election of the consuls when for some reason the retiring consuls had not done so. In the regal period when the senate, instead of appointing a king, decided to appoint interreges, it divided itself into ten decuries from each of which one senator was selected. Each of these ten acted as king for five days, and if, at the end of fifty days, no king had been elected, the rotation was renewed. It was their duty to nominate a king, whose appointment was then ratified or refused by the curiae. Under the Republic similarly interreges acted for five days each. When the first consuls were elected (according to Dionysius iv. 84 and Livy i. 60), Spurius Lucretius held the comitia as interrex, and from that time down to the Second Punic War such officers were from time to time appointed. Thenceforward there is no record of the office till 82 B.C., when the senate appointed an interrex to hold the comitia which made Sulla dictator (Appian, Bell. civ. i. 98). In 55, 53 and 52 interreges are again found, the last-mentioned being on the occasion when Pompey was elected sole consul.
The most noteworthy use of the term “Interregnum” in post-classical times is that of the Great Interregnum in German history between the death of Conrad IV. (1254) and the election of Rudolf of Habsburg (1273). See [Germany]: History.
INTERSTATE COMMERCE. The phrase “interstate commerce,” as used in the United States, denotes commerce between the citizens of different states of the Union. The words “interstate” and “intrastate” are not found in the constitution nor, until comparatively recently, in decisions of the courts or in legislative acts (probably being first used officially in 1887 in the Interstate Commerce Act). The constitution of 1789 uses the phrase “commerce among the states,” and the first official decision interpreting the phrase says that “it may very properly be restricted to that commerce which concerns more states than one” (Chief Justice Marshall in Gibbons v. Ogden, 9 Wheaton 194). Commerce among the states is there distinguished from “commerce which is completely internal, which is carried on between man and man in a state, or between parts of the same state, and which does not extend to or affect other states.” It was declared (Lehigh case, 145 U.S. 192) that commerce between two persons in the same state is not interstate even when there is a temporary deviation to the soil of another state; but later (Hanley case, 187 U.S. 617, distinguishing the Lehigh case) it was declared that as to transportation, such commerce is interstate. The courts have interpreted commerce to denote not merely a mutual selling or traffic, but as “a term of the largest import,” including intercourse for the purposes of trade in any and all its forms (Gibbons v. Ogden, 9 Wheaton 194, and Welton v. Missouri, 91 U.S. 280). Thus have been included not only the actions of trading, navigation, transportation, and communication, but also the instruments and agents employed, including even telegraph messages and, in the extremest cases, lottery tickets.[1]