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ANAGNI 159 ANALYSIS and in painful affections of limited areas of the body. It depends upon a paralysis of the sensory nerves of the part, and may be induced by the ap- plication of cold, or of medical agents. Of medical agents the best is cocaine, prepared from the coca shrub of Peru (erythr-oxylon coca). Eucaine, thymol, menthol, aconite, belladonna, chloroform (the last three as the well-known A. B. C. liniment), phenol, chloral, and Indian hemp, have also a local anaesthetic action if rubbed on the skin, or applied to abraded surfaces, but most are too irri- tating to be of any great value. ANAGNI (an-an'ye), a town of Italy, on a hill, 40 miles E. S. E. of Rome. The seat of a bishop since 487, it has an old, but much modernized cathedral, and was the birthplace of four popes — Innocent III., Gregory IX., Alexander IV., and Boniface VIII. The chief city of the Hernici, it was a place of importance during the whole period of Roman his- tory. Vergil calls it "wealthy Anagnia." Pop. about 10,000. ANAHEIM, a city of California, in Orange co., about 27 miles S. E. of Los Angeles. It is on the Southern Pacific and the Atchison, Topeka and Santa Fe railroads. The center of an important fruit-growing country, it has also im- portant trade interests in oil, oranges, farm and dairy products. Pop. (1910) 2,628; (1920) 5,526. ANALOGY, similitude of relations be- tween one thing and other. The thing to which the other is compared is preceded by to or with. When both are mentioned together they are connected by the word between. In logic, the resemblance of relations, a meaning given to the word first by the mathematicians. As more commonly used it is a re- semblance of any kind on which an argu- ment falling short of induction may be founded. If an invariable conjunction is made out between a property in the one case and a property in the other, the argument rises above analogy, and be- comes an induction on a limited basis; but if no such conjunction has been made out, then the argument is one of analogy merely. Metaphor and allegory address the imagination, while analogy appeals to the reason. The former are founded on similarity of appearances, of effects, or of incidental circumstances; the latter is built upon more essential resemblances, which afford a proper basis for reasoning. In biology, an analogy is the relation between parts which agree in function, as the wing of a bird and that of a but- terfly, the tail of a whale and that of a fish. ANALYSIS, in ordinary language, the act of analyzing; the state of being an- alyzed; the result of such investigation. The separation of anything physical, mental, or a mere conception into its constitutent elements. It is also applied to a syllabus, conspectus, or exhibition of the heads of a discourse; a synopsis. a brief abstract of a subject to enable a reader more readily to comprehend it when it is treated at length. In mathematics, the term analysis, signifying an unloosing, as contradis- tinguished from synthesis=a putting to- gether. The analytical method of in- quiry has been defined as the art or method of finding out the truth of a proposition by first supposing the thing done, and then reasoning back step by step till one arrives at some admitted truth. It is called also the method of invention or resolution. Analysis in mathematics may be exercised on finite or infinite magnitudes or numbers. The analysis of finite quantities is the same as specious arithmetic or algebra. That of infinites, called also the new analysis, is particularly used in fluxions or the differential calculus. But analysis could be employed also in geometry, though Euclid preferred to make his immortal work synthetic; it is, therefore, a de- parture from correct language to use the word analysis, as many do, as the anti- thesis of geometry; it is opposed, as already mentioned, to ssntithesis, and to that alone. In chemistry, the examination of bodies with the view of ascertaining of what substance they are composed, and in what proportion these substances are contained in them. The former is called qualitative and the latter quantitative analysis. Chemical analysis is classified into blowpipe, qualitative, gravimetrical, and volumetric analysis; and the proxi- mate and the ultimate analysis of or- ganic bodies. 1. Blow-pipe analysis. 2. Qualitative analysis is employed to find out the composition and properties of any unknown substance, and to sepa- rate different substances from each other. 3. Gravimetrical analysis, or quanti- tative analysis by weight, is the method of separating out of a weighed quantity of a compound its constituents, either in a pure state or in the form of some new substance of known composition, and ac- curately weighing the products; from the results of these operations the per-