Page:The American Cyclopædia (1879) Volume XIII.djvu/738

 718 PORCUPINE ANT-EATER PORISMS Australia and Tasmania. The snout is long, slender, and naked, and the tongue protractile, very long, and slender, as in the ant-eaters proper ; the opening of the mouth small ; the upper part of the body covered with spines and hairs intermixed ; legs short and powerful ; all the feet with five well developed toes with large nails, the fore feet formed for burrowing, and the hind feet in the male with a horny spur as in the ornithorhynchus ; tail Very short, and hidden by the spines. The best known species, the E. aculeata (Shaw), is about a foot long, with a stout body, spiny above, and the head, limbs, and lower parts with brownish black coarse hair ; inner toe of the hind feet with a broad rounded nail, the others with long curved claws, that of the second very long. It is considerably larger than the com- mon hedgehog, is powerfully built, and espe- cially adapted for burrowing. The food con- sists of ants and other small insects, which it captures like the ant-eaters with its tongue, by means of a viscid matter secreted by two large submaxillary glands extending from behind the Porcupine Ant-Eater (Echidna aculeata; . ear to the fore part of the chest ; there are no teeth in the jaws, but the palate is armed with several rows of horny spines directed back- ward, and the upper surface of the tongue is furnished with numerous small corneous warts. The skull in shape has been compared to the half of a pear cut lengthwise, being 4 in. long by If in. wide at the posterior portion, ending in a point anteriorly ; nostrils near the end of snout ; eyes small and black ; ear cavity in the form of a long tube, with its S-shaped opening on the back of the head. The spines are dirty white tipped with black, sharp, about If in. long, directed backward, and on the back in- ward, crossing each other on the mesial line. The hind feet in the natural position rest on their inner side, the concave surface looking outward, thus keeping the claws unworn for casting aside the earth loosened by the fore claws. In captivity it is stupid, slow-moving, avoiding the light, and active only in burrow- ing, which it does with astonishing rapidity; specimens have been kept alive at the London zoological gardens, where they were fed on bread and milk ; when irritated or asleep they roll themselves in a ball, the head between the fore legs. It can sink into loose sand directly downward, presenting only its spiny back to its enemies ; in spite of its defensive armor, it often falls a prey to the thylacine and other carnivorous marsupials. Its common name is inappropriate, as it is neither a rodent like the porcupine nor an edentate proper like the ant- eater, though it has the spiny covering of the one and the toothless jaws of the other; in some districts it is called the hedgehog, which is equally inapplicable, as the dentition of the insectivora is not represented in this animal ; perhaps, however, the name here given, origi- nally imposed by Shaw, is the best that could be selected. It is now very rare. PORGY. See SCUPPAUG. PORISMS (Gr. 7ropio/na, from Tropi&iv, to sup- ply or deduce), a class of geometric proposi- tions treated by the ancient Greek geometers, the precise nature of which is a matter of dis- pute. The only original authorities we have upon the subject are the seventh book of the " Mathematical Collections " of Pappus and the commentary on Euclid's " Elements " by Pro- clus. In both authors the language is so vague and the text so corrupt that they have served rather to stimulate the curiosity and exercise the ingenuity of scholars than to afford any real insight into the subject. Euclid is said to have written three books of porisms, but our information in regard to them is substantially confined to the imperfect account of Pappus above mentioned. According to this, a porism is a proposition intermediate between a theorem and a problem. "A theorem," says Pappus, "is a proposition requiring demonstration, a problem one requiring construction, a porism one requiring investigation." This is too vague to afford much assistance in the restoration of this class of propositions. The first important step in this direction was made by Robert Simson in a work published in 1776, after his death. His definition was substantially the same as that afterward given by PI ay fair in a paper contained in the " Transactions of the Royal Society of Edinburgh," vol. i., which we quote: " A porism is a proposition affirm- ing the possibility of finding such conditions as will render a certain problem indeterminate or capable of innumerable solutions." The most important recent work on the subject is by M. Chasles, Les trois livres de porismes cTEuclide retablis (Paris, 1860). According to him, "a porism is an incomplete theorem expressing certain relations between things varying ac- cording to a common law indicated in the enunciation. The theorem would be complete if the magnitude and position of certain things which result from the hypothesis were deter- mined, but which the enunciation of the porism does not explain." Other views have been presented by mathematicians of great ability, and the subject must still be considered as in- volved in obscurity.