ISO 



ISO 



crooked lines, made by the edges of im- 

 perfect plates. 



What appears very singular in the 

 structure of this body is, that all the sur- 

 faces are placed in the same manner, and 

 consequently it will split off into thin 

 plates, either horizontally or perpendicu- 

 larly ; but this is found, on a miscroscopic 

 examination, to be owing to the regularity 

 of figure, smoothness of surface, and nice 

 joining of the several small parallelepiped 

 concretions, of which the whole is com- 

 posed ; and to the same cause is probably 

 owing its remarkable property in refrac- 

 tion. See OPTICS, and REFRACTION. 



It is very soft, and easily scratched with 

 the point of a pin ; it will not give fire on 

 being struck against steel, and ferments, 

 and is perfectly dissolved in aquafortis. 

 It is found in Iceland, from whence it has 

 its name ; and in France, Germany, and 

 many other places. In England, fragments 

 of other spars are very often mistaken for 

 it, many of them having in some degree 

 the same property. 



ISNARDIA, in botany, so named in 

 memory of Mons. Antoine Danti d'Isnard, 

 member of the Academy of Sciences, a 

 genus of the Tetrandria Monogynia class 

 and order. Natural order of Calycan- 

 themx. Salicariae, Jussieu. Essential 

 character : calyx four-cleft ; corolla none ; 

 capsule four-celled, covered by the calyx. 

 There is but one species, viz. I. palustris, 

 which bears a great resemblance to pep- 

 lis portulaca ; it is creeping and floating ; 

 the flowers are axillary, opposite, sessile, 

 and green. It is a native of Italy, France, 

 Alsace, Russia, Jamaica, and Virginia, in 

 rivers. 



ISOCHRONAL, ISOCHROXE, or ISO- 

 CHRONOUS, is applied to such vibrations of 

 a pendulum as are performed in the same 

 space of time as all the vibrations or 

 swings of the same pendulum are, whe- 

 ther the arches it describes be longer or 

 shorter : for when it describes a shorter 

 arch, it moves so much the slower, and 

 when a long one, proportionably faster. 



ISOCHRONAL line, that in which a heavy 

 body is supposed to descend without any 

 acceleration. 



M. Leibnitz shows, that an heavy body, 

 with a degree of velocity acquired by the 

 descent from any height, may descend 

 from the same point by an infinite num- 

 ber of isochronal curves, all which are of 

 the same species, differing from one 

 another only in the magnitude of their 

 perimeters; such are all the quadi*ato- 

 cubical paroboloids, and consequently 

 similar to one another. He shows also 

 there, how to find a line in which a heavy 



body descending shall recede uniformlj 

 from a given point, or approach uniformly 

 to it. 



ISOETES, in botany, a genus of the 

 Cryptogamia Filices class and order. Na 

 tural orde* of Filices, or Ferns. Essentia 

 character : male, anther within the base 

 of the frond : female, capsule two-celled 

 within the base of the frond. There arc 

 two species, viz. I. lacustris, common 

 quillwort, and I. coromandelina, Coroman 

 del quillwort, both natives of mountair 

 lakes, and in wet places that are inun- 

 dated in the rainy season. 



ISOPERIMETRICAL figures, in geo 

 metry, are such as have equal perimeters 

 or circumferences. 



Isoperimetrical lines and figures have 

 greatly engaged the attention of mathe- 

 maticians at all times. The fifth book oi 

 Pappus's Collections is chiefly upon this 

 subject ; where a great variety of curious 

 and important properties are demon, 

 strated, both of planes and solids, some ol 

 which were then old in his time, and 

 many new ones of his own. Indeed, it 

 seems, he has here brought together into 

 this book all the properties relating to 

 isoperimetrical figures then known, and 

 their different degrees of capacity. The 

 analysis of the general problem concern- 

 ing figures, that, among all those of the 

 same perimeter, produce maxima and 

 minima, was given by Mr. James Ber- 

 noulli, from computations that involve the 

 second and third fluxions. And several 

 enquiries of this nature have been since 

 prosecuted in like manner, but not al- 

 ways with equal success. Mr. Maclaurin, 

 to vindicate the doctrines of fluxions 

 from the imputation of uncertainty or 

 obscurity, has illustrated this subject, 

 which is considered as one of the most 

 abstruse parts of this doctrine, by giving 

 the resolution and composition of these 

 problems by first fluxions only ; and in a 

 manner that suggests a synthetic demon- 

 stration, serving to verify the solution. 

 See Maclaurin's Fluxions. Mr. Crane 

 also, in the Berlin Memoirs for 1752, has 

 given a paper, in which he proposes to 

 demonstrate, in general, what can be de- 

 monstrated only of regular figures in the 

 elements of geometry, viz. that the circle 

 is the greatest of all isoperimetrical 

 figures, regular or irregular. We shall 

 now mention a few of the properties of 

 isoperimetrical figures. 



1. Of isoperimetricul figures, that is 

 the greatest that contains the greatest 

 number of sides, or the most angles, and 

 consequently a circle, is the greatest of all 

 figures that have the same ambit as it has 



