they are of the same or related groups of ele-
ments. See Periodic Law.
When a substance has been found to form crystals of more than one kind it is said to be dimorphous, trimorphous, or polymorphous, the term dimorphous being used in a general sense to describe substances which exhibit three or more as well as two kinds of crystals. Sulphur crystallizes from fusion in long needle-like cr3"s- tals of monoclinic symmetry, but from a solution in carbon bisulphide in orthorhombic crystals. Under other special conditions it assumes other kinds of sjTiimetry. Carbonate of lime, which is generally found crystallized in nature as hex- agonal (trigonal) crystals (calcite), is less fre- quently found in crystals belonging to the ortho- rhombic system, and with different physical properties from those of calcite. As explained above, calcite belongs in an isomorphous series with carbonate of magnesia, carbonate of iron, carbonate of zinc, etc. Aragonite, on the other hand, is a member of a different isomorphous group in which are carbonate of strontium, car- bonate of barium, and carbonate of lead. A double group of this kind connected by a dimor- phous substance (carbonate of lime as calcite and aragonite) is knovn as an isodimorphous group or series. See Cbystallography ; Chem- istry ; Atomic Weights.
ISOPERIMETRIC FIGURES (from Gk. hot, isos. equal -|- inplij^Tpov, perimetrori, perimeter, from Tepl, peri, around + lUrpov. metron, meas- ure). Plane figures having equal perimeters. In the seventeenth century all problems which de- manded the statement of a maximum or minimum property of functions were called isoperimetric problems. To the oldest problems of this kind belong especially those in which one curve with a maximum or minimum property was to be found from a class of curves of equal perimeters. That the circle, of all isoperimetric figures, gives the maximum area is said to have been known to Pythagoras. In the writings of Pai)pus a series of propositions relating to figures of equal perimeters is found. In the fourteenth century the Italian mathematicians also worked on prob- lems of this kind. But Bernoulli (1696) and Euler (1744) applied the calculus of variations to these problems, and Euler gave a purely ana- lytic treatment in his celebrated work, Methodus Inveniendi Lineas Ctirvas. . . . This theory culminated in the calculus of variations, La- grange supplying the appropriate notation. An illustration of problems of this class is that of Jakob Bernoulli — of all curves of the same length described on a given base, to determine one such that the area of a second curve, each of whose ordinates is a given function of the cor- responding ordinate or arc of the first, may be a maximum or a minimum. See Maxima and illXIMA.
ISOP'ODA (Xeo-Lat. nom. pi., from Gk. 1<to!,
isos, equal + irofJs, pons, foot). An order of
malacostracous crustaceans of the section Ar-
throstraca, mostly aquatic — some marine, some
inhabitants of tresh waters — but some terres-
trial, inhabiting damp places, as the wood-louse
and the like. They are easily recognized by the
fact that the body is flattened dorso-vent rally,
and many of them — e.g. the 'sowbug* or 'pillbug'
(Porcellio) — have the habit of rolling up into
a ball with the head tucked safely inward. The
first segment of the thorax is fused with the
head, but the remaining seven are free, and bear
limb-like appendages without gills. In females
the basal joints of several of these appendages
bear laraellfe, which form a brood-pouch for the
eggs. There is never any carapace. The maxil-
lipcds, of which there is only a single pair, usu-
ally fuse to form a sort of lower lip. The ab-
dominal appendages are hiramose, and serve for
swimming and breathing; the most anterior pair
are usually thick, and form an operculum which
serves to protect the more delicate appendages
behind. The heart is situated chiefly in the ab-
domen, but extends forward a short distance into
the thorax. While most qf the species lead a
free life, some of the marine forms (Cymothoa,
etc. ) are parasitic on fishes or on other crusta-
ceans, or bore into wood, etc. See illustration
under Gbibble.
One group (Bopyridse) are parasitic, living under the carapace of various shrimps. The fe- males of Bopyrus palwmoneticola (Packard) are many times larger than the males, and are much degenerated, the head being without eyes and appendages; they retain their position on their host by means of the sharp, hook-like legs around the edge of the body. The male in general ap- pearance shows but slight modifications and is about one-fifth as large as the female, and is lodge^d partly out of sight under the ventral plates of its consort.
Some of these forms are notably degenerate. The Isopoda are a comparatively small group, and are generally small individuals, few species reaching a length of one inch, except in the colos- sal deep-sea Bathynomiis giganteus, dredged in the Caribbean Sea from a depth of nearly a mile. The colors are usually dull, blackish, gray, or brown ; but some of the marine forms are highly colored, red or brown, according to the hue of the seaweed they rest on.
Fossil isopods, though of little geological im- portance, are knowTi from rocks as early as the Upper Devonian and Carboniferous ; also from the .Jurassic limestones of Bavaria and other Jlesozoic formations. Most of them have some superficial resemblance to the marine Sphiieroma, and to the t-errestrial wood-lice of modern time. See Cri'stacea.
I'SOQUIN'OLINE. See QrixoLijfE.
ISOSPONDYLI. I'so-spon'dMi ( Neo-Lat. nom.
pi., from Gk. liros, isos, equal + o-Trii-Si/Xos. spon-
dglos, vertebra ) . An order of teleost fishes, the
soft-rayed fishes. They have the anterior verte-
brse simple, unmodified; the mesocoracoid arch
is always well developed, and the strong shoulder-
girdle is connected with the cranium. There are
no auditory ossicles. The scales usually are
cycloid, the ventral fins abdominal. It is a
large group, comprising the tarpons, lady- fishes,
herrings, shads, sardines, anchovies, menhadens,
salmons, trouts, whitefishes. and related fami-
lies, and, in the opinion of some, the Iniomi
(q.v.) also. Consult Jordan and Evermann,
Fishes of Northern and Middle America (Wash-
ington, 1896).
ISOTHERAL (i-soth'er-al) LINES, or ISOTHERÆ (from Gk. fo-os. i.50.s, equal + S^pot,
tberos. summer). Lines that connect together
places that have the same mean summer tem-
perature.
