In general we may say of the soft-rayed fishes that very few of them are inhabitants of tropical shores. Of these few, some which are closely related to northern forms have fewer vertebræ than their cold-water analogues. In the northern species, the fresh-water species, and the species found in the deep sea the number of vertebræ is always large, but the same is true of some of the tropical species also. =The Flounders.=--In the flounders, the halibut and its relatives, arctic genera (_Hippoglossus_ and _Atheresthes_), have from 49 to 50 vertebræ. The northern genera (_Hippoglossoides, Lyopsetta_, and _Eopsetta_) have from 43 to 45; the members of a large semi-tropical genus (_Paralichthys_) of wide range have from 35 to 41; while the tropical forms have from 35 to 37. In the group of turbots and whiffs none of the species really belong to the northern fauna, and the range in numbers is from 35 to 43. The highest number, 43, is found in a deep-water species (_Monolene_), and the next, 40, in species (_Lepidorhombus, Orthopsetta_) which extend their range well toward the north. Among the plaices, which are all northern, the numbers range from 35 to 65, the higher numbers, 52, 58, 65, being found in species (_Glyptocephalus_) which inhabit considerable depths in the arctic seas. The lowest numbers (35) belong to shore species (_Pleuronichthys_) which range well toward the south. =Spiny-rayed Fishes.=--Among the spiny-rayed fishes the facts are more striking. Of these, numerous families are chiefly or wholly confined to the tropics, and in the great majority of all the species the number of vertebræ is constantly 24,--10 in the body and 14 in the tail (10+14). This is true of all or nearly all the _Berycidæ_, _Serranidæ_, _Sparidæ_, _Sciænidæ_, _Chætodontidæ_, _Hæmulidæ_, _Gerridæ_, _Gobiidæ_, _Acanthuridæ_, _Mugilidæ_, _Sphyrænidæ_, _Mullidæ_, _Pomacentridæ_, etc. In some families in which the process of reduction has gone on to an extreme degree, as in certain _Plectognath_ fishes, there has been a still further reduction, the lowest number, 14, existing in the short inflexible body of the trunkfish (_Ostracion_), in which the vertebral joints are movable only in the base of the tail. In all these forms the process of reduction of vertebræ has been accompanied by specialization in other respects. The range of distribution of these fishes is chiefly though not quite wholly confined to the tropics.