ISOMERISM

(Yunanca köken — orijinale bakınız.) Compounds which contain the same elements in the same ratio, and yet exhibit distinct chemical qualities, are said to be isotneric. The cyanic and fulmlnlc acids are isomeric compounds of nitrogen, oxygen, and carlion. The distinctions thus arising are probably referable to the different ways in which the same elementary atoms are gropued in the compound. ISOMORPHISM. {Gr. la-oi, and /xoi<pv,for7n.) Substances which resemble each other in their crystalline forms, but differ in their component parts, are said to be isomorphous. Thus the phosphate and biphosphate of soda have the same form, or are isomorphous, with the arseniate and binarsenlate of soda; and in regard to other bases, such as potash and ammonia, each arseniate has a corresponding phosphate po e ed of the same form. la these cases there is nece arily an analogy in the atomic constitution of the compounds, which are observed to po e the same number of equivalents of acid, alkali, and water of crystallization, and differ in nothing except that the one series contains an atom of arsenic, and the other an atom of phosphorus. ISOPERIMETRICAL FIGURES (Yunanca köken — orijinale bakınız.), are such as have equal perimeters or circumferences. The term i so perl me tricar problems, in modern analysis, designates a very extensive and difficult cla .of problems, the solution of which requires the application of a peculiar analysis. The general problem is this: — Among all curves having the same length, to determine that of which some a igned property is a maxhnuni or a minimum; for example, among all curves having the same perimeter, to find that which has the greatest area. This is the simplest question of the kind, and the curve to which the property belongs is proved by elementary geometry to be a circle. In all Isoperimetrical problems there are two conditions to be fulfilled: according to the first of which a certain property is to remain constant, or to belong to all individuals of the species; and according to the second, another property is to be the greatest or least po ible. In the problems of this kind which first attracted the particular attention of mathematicians, the constant quantity was the perimeter of a certain curve; and hence the origin of the term, which is now applied to all problems indifferently in which the question is to find curves having a property of maximum or minimum, with or without the condition of equality of perimeters. James Bernoulli was the first who discovered the true principles on which questions of this kind depend, and the circumstances which render the ordinary methods of maxima and minima inapplicable to them. The Immediate subject of his researches was the problem of the Brachystochrone (see the term), or curve of quickest descent, celebrated in the early history of the calculus on account of the controversy to which it gave rise between the two brothers, James and John Bernoulli. The analysis of the former. Analysis magni Problem at is I so perimetric i, was published at Basle in 1701, and in the Leipsic Acts of the same year. Solutions were afterwards given by Taylor In his Method us Incremcntoruin; by John Bernoulli in the Memoirs of the Academy of Sciences foV 1718; and by Euler in the Petersburg Memoirs. Euler afterwards gave a complete and general solution of the problem In ills Method us Invicndi Lineas Curvas Maximi Minimive proprietate gaudentes, a work of which Lagnmge has said that tliere is perhaps no other which can De of mvre use [s. 627]