HOMCEOPATHY. 177 HOMOLOGY. therapeutics and practice, and as a result all the earlier, and for many years most of the well- equipped, native American physicians were graduates of the regular school. Finally, homoeo- pathic medical schools were established, in which all the branches of medicine were taught, and the inexplicable terms 'homoeopathic surgeon' and 'homoeopathic obstetrician' came into use. The inlluence of the school has been waning for some years. In 1883 the Hahnemannmn Monthly said:' "A few years ago the editors of the .Yeii; "iorl: Medical Times dropped from the title of their journal the distinctive word 'Homwo- patliic' ; now they boldly urge the renunciation of the word as applied to our school of medicine. If we are emancipated from the thraldom of sect, we shall not only save our school from im- minent dissolution, but shall also become an in- tegral part of the medical profession of the day, honored as true, broad, liberal, progressive phy- sicians. But if we cling to a name which by no means represents the catholicity and spirit of the new school, we are oloomed to annihilation." In the large cities of the Eastern States, "fieat numbers of graduates of homoeopathic medical schools have taken courses of study in post-graduate departments of regular medical colleges, and afterwards, while retaining the term homoeopathic, practice medicine principally ac- cording to the regular principles, using 'old- school' drugs in 'old-school' dosage. The editor of the 'Seto York Medical Times (homoeopathic) asserted that there are only two 'pure' homoeo- pathic practitioners in that city. Whether due to its influence or not, since the advent of homoeopathy the repulsiveness in taste and appearance as well as the size of the dose of old-school remedies have been greatly modi- fied ; and in a vast number of cases suggestion and encouragement together, perhaps, with placebos, have taken the place of active medi- cinal treatment, and natural recuperative power has worked the cure. It is certainly true that without the resort to and adoption of regular 'old-school' remedies homoeopathy would have died out e.xcept among those who love mystery and prefer magic to medicine. Few and rare to- day are the practitioners who adhere to the po- tentization tenets of Hahnemann, or who are content to treat symptoms in ignorance of the disease present. The terms 'allopathy' and 'allopathic' came in- to use after the invention of the words "homoe- opatliy' and 'honui>opathic.' and were used by the adherents of the new school in designating the old school and its practitioners, through a mis- taken idea. The terms are etymologically incor- rect. See H.MIXFMANN. HOMCEOPATHY, American Institute of. The oldest national medical organization in the United States, its first session having been held in New York City, on .pril 10, 1.S44. Its ob- jects are the reformation and augmentation of the JIateria iledica, and the furthering of the ]irineiples of honueopathy. It has two thousand members, divided into liureaus on various lines of medicine and siirgery, and meets annually in the large cities of the country. The institute publishes annual volumes of "Transactions," in- cluding reports and original papers. HO'MOGENEITY. L.w of. The product of two homogeneous integral functions of the nith and the nth degree, respectively, is a homogeneous, integral function of the (»i + n)th degree. The value of this principle in checking the process of multiplication oi homogeneous functions is evi- dent. The notion of homogeneity may be extended to irrational and fractional functions. In this ease the degree is determined by introducing a factor A; into each variable, and observing the degree of the factor k in the resulting function. HOMOIOtrSION, ho'nioi-oo'sl-on. .See Ho- iiooisiox. HOMOL'OGA'TION (from ML. homologare, to homologate, from Gk. ofioXiytlf, homoloijein, to agree, from o/jAXoyos, homologos, agreeing, from ojiuSs, homos, same -f- A70s, logos, word, from yt:iv, Icjeiit, to say). In the civil law, the judicial confirmation of an award, or of an ac- counting, or of any other administrative or judicial proceeding. In Scotch law, an act or course of conduct which confirms or approves of something which otherwise might be invalid. Thus, an informal deed, though useless in itself, yet if acted on by one or both parties, will be set up and made valid as against the party ho- mologating. To constitute homologation, a clear knowledge of what the party is doing is neces- sary. Cf. E.STOPPEL. HOMOL'OGOTJS SERIES. See hydrocar- BOXS. HOMOL'OGY (from Gk. o/wXayla, homologia, conformity, from 6/i6oyos, homologos, harmoniz- ing, from 6/i6i, hmnos, same -|- -oyla, -logia, account, from yei.p, legein. to say). (1) In biology, a term used to indicate structural corre- spondence based on blood-relationship, as op- posed to analogj', which is a])plied to functional resemblance, such as that between the wings of a bird and tho.se of a butterfly. Different sorts of homology have been recognized. There is the homology of the diflerent parts of the body; namel.v, serial homolog}'. as of the front and hind paired fins of fishes, or the arms and legs of man; antimeric homologv', as of the petals of a flower or the right and left sides of the body. There is homology of corresponding or- gans in different individuals. This is most cer- tain in individuals of the same species; some- what less certain between gcneia and families; often dinibtful l)etween orders and classes ; u.su- ally si)eculative between phyla. The criteria of homology- are: (a) The <'ri(erion of connections. A part having similar relations in two s])ecies. and making similar connections is homologous in the two cases, (b) The criterion of structure. Homologous parts have a fundamental similarity of structure, (c) The criterion of development. Homologous organs arise from the same germ- layer in corresponding parts of the body and develop in the same fashion. Despite these clear-cut criteria, homologies are practically often very difliculf of determination, particu- larly beyond the limits of a class. (2) In geometry, figures which are in per- sjieetive are often spoken of as homologous, be- cause the centre and axis nf jierspective intro- duced by Poncelet were called i)y Chasles centre and axis of homology. ( l^ee the articles Centre; Axis.) The term is used in another sense to signify the relation of reciprocity or duality (q.v.) which exists between geometry and al- gebra. Law of Homology. Given two sets of con-
