VARIANCE. that set forth in the phadings, the variance is fatal. Consult the works of Stephen and Chitty on Plcadiiiij. VARIATION (Lat. variotio, from varmre, to change, vary). Structural or functional de- viations from tlui ])arciit form or type. Varia- tions, which are apparent to all, are attracting the careful attention of workin;; naturalists, whose tendencies are to cease theorizing and to bend all their energies toward the discovery aiul classification of facts and of t!ie causes producing variation. Species are une(|ually variabU>; there are plastic as well as rigid ones. Nature pre- vents over-variation by competition; otherwise crowding of s]H'cies would result. The greatest range of variation occurs in cultivated plants and domestic animals; yet the turkey does not vary, whether living in America or Europe, nor does the guinea-fowl in America depart from the African type; and the cat varies much less than the dog. Wide-ranging, much ditTused, and com- mon species vary most, and those of large genera more frequently vary than those of genera con- taining but one or onh* a few species. Persistent or ancient and cosmopolitan forms have not varied all through the immense periods of their history. There has been much discussion as to whether variation is fortuitous or definite. It was claimed by Darwin that variation is by ehanee, though he adds that this is 'a whidly incorrect expression,' for in nature there is no such thing as chance, the expression serving "to acknowledge plainly our ignorance of the cause of each par- ticular variation;" and he states that "the direct action of changed conditions leads to definite or indefinite results." But it is more probable that, though variations may in some cases seem to be fortuitous, in general throughout geological time variation has been regulated by changes in the physical and biological conditions of the environ- ment along certain determinate lines, the varia- tions becoming permanent when they prove useful. That the direction of variation is in accordance with and dependent on the surroundings is shown by the atrophy of eyes in animals living in dark- ness, the reduction in the visual organs varying in degrees dependent on the length of time and on the number of generations the animals have lived in darkness. The reduction in the number of limbs and toes is conditioned by the mode of life. The variation in the colors of animals is in direct relation with the varying amount of light and shade to which they are exposed. Sec Pi!o- TECTivE Coloration. The causes of variation are in the main ob- scure, but primarily variation is due to the changes of the environment, i.e. to the differences in atmospheric pressure, electricity, gravit.y, light, to changes of temperature (heat and cold), and of the mechanical and chemical state of the water or air, as well as the kind and amount of food. The causes are mainly external, but some are apparently internal, such as reproduction. These physical agents have been called the primary factors of organic evolution (q.v.) operating on the most primitive and plastic one- celled forms of life, whieh in the beginning led to the origin of the difTerent t^'pes of life or lines of development. NoMEKCL.TOBE. A variant is one of the dis- 15 VARIATION. similar conditions of form in which an organ ap- pears; thus the variants of the number of rays of a scallop-shell are 1.3, 14, 1,5, etc. A variant must be sharply distinguished from a variety, which is a group term for individuals that breed true to one another, and resemble one another in color, size, and other characteristics less broad and general than specific ones. A variate is one of the varying units of study; each scallop-shell is, in respect to the number of its rays, a variate, and in 1000 scallops there may be, for example, 200 variates (ray-numbers) falling in the variant class of 16 rays. Each different variant thus usually includes a number of variates. Variates are of two sorts: counted and measured ('inte- gral' and 'graduated'). For example, the number of ra.ys on a scallop-shell (15, 16, 17, etc.) is an integral variate; the diameter of the shell is a graduated variate. The data of variation may be classified in various ways, but two main types are (1) slight variations and (2) sport variations. Slight variations are such apparently trivial dif- ferences as distinguish one adult male of a homogeneous community from another male of this community, one grain of wheat from another grain of wheat, the number of grains on one head of rice from the number on a second head of rice. It is the noticed and yet unnoted form of variation. Sport variations are the relatively rare occurrence of great differences cro]i])ing out in a community. These are sometimes incom- patible with life, and are then known as 'mon- sters;' but when sports persist, and are bred from, they may impress themselves with peculiar strength; e.g. Ancon sheep, and the hair- less peaches called nectarines. Variable char- acters may also be classified as 'integral' and 'graduated.' They play a nearly equal part in evolution, for some species have differentiated chiefly along the line of multiplication or reduc- tion of the number of parts, wdiile other species have varied in size, color, and other qualities of parts. Again variates may be either individual or organal. Individual variates belong to dif- ferent individual animals or plants, whereas or- ganal variates are found in the multiple organs of one and the same individual, e.g. the length of a fish is an individual variate; the diameter of one of its scales as compared with that of the others is an organal variate. According to Huxley's definition, "a race is a propagated variety." These terms, variant, variety, i-ace, species, are by no means fi.ed, since in many in- stances gradations may be found which more or less completely link them. Variation with age is a matter of daily observa- tion. First of all the absolute size of the body and its organs tends to increase with age up to a limit. Secondly, the proportions change. Some organs are developed precociously, for instance, the child's head; others are retarded, e.g. the length of the child's legs. Careful measurements of the .shell of a crab have shown that the shell grows larger in proportion to its breadth as it grows older. Especially at the time of sexual maturity in most animals special features de- velop greatly that are earlier latent. Not only the size, but also the variability of organs, changes with age. Thus the standard deviation of the stature of the 5year-old child is 3 inches ; of the 7-year-old child 2.85 inches. Variation with
