schoolroom work. With this may be coupled the use of the analytic rather than the synthetic method in many subjects. The most important example of this is the word-method in teaching reading, according to which the child learns first to recognize the written or printed word and later analyzes it into letters. This is after the analogy of the learning of spoken language, where we begin with words rather than with phonic elements. The sentence-method goes one step further in beginning with whole sentences, later analyzing them into words and letters. So, too, in learning a language the analytic method endeavors to get the learner to use the language immediately and later to analyze out its grammatical principles and forms. All these are founded on the discovery that the child begins with a complex experience and later analyzes it. (See Child-Studr.)

Psychology has led to a better comprehension of the laws of memorizing (q. v.) and of habit. It has emphasized the fact that learning is always through and for the sake of doing. Indeed, in the investigation of the motor-powers psychology has been especially helpful. The development of control over the body has been carefully studied. The sequence of random, spontaneous acts, experimental efforts, followed by the gradual elimination of such as are undesirable and the fixation of the rest as habitual responses to certain stimuli has been shown to be the regular sequence in developing skill of any sort. The general principle that larger fundamental muscles are brought under control before the smaller accessory ones and that, therefore, the muscles of the arm should be practiced before those of the fingers has been made clear. The importance of imitation, especially in the development of self-consciousness and the. social and moral sense, has been traced out. and the effect of suggestion analyzed. The training of the mental powers has been shown to consist m storing the memory with useful material and the practice in its use, together with the formation of such habits as make for efficient thinking. Thus the conception of formal discipline has been discredited. (See Mental Discipline.)

Physiological psychology has done a little toward determining the laws of fatigue. More careful observation and experiment have shown the existence of wide individual differences among children and the consequent danger that class-teaching may fa<l to reach many. The importance of testing children for power and kind of memory, motor-ability, hearing and sight, capacity to attend etc. has been shown. It has become evident that schools need the supervision both of medical and of psychological experts, that the unhealthy and the abnormal may be singled out for special treatment.

Finally, child-study has done much to determine the nature and order of development of the instincts to which teachers must appeal and the general history of physical and mental growth from infancy to manhood. See Adolescence, Apperception, Association of Ideas, Child-Study, Feeling, Interest, Memorizing, Mental Discipline, Teaching, Method op, and Modern Education. Consult Talks to Teachers on Psychology by James, Principles of Teaching by Thorndike; Fundamentals of Child-Study by Kirkpatrick; and The Educative Process by Bagley.

Pteridophytes (tcr'-dof-ts), one of the four great groups of plants, which includes the ferns, the scouring rushes or horsetails and club-mosses. The ferns are the most abundant and representative forms, containing about 4,000 species; the club-mosses are represented by a little over 400 species; but the horsetails only by 25 living species. The group as a whole is characterized by having a leafy, and vascular sporophyte, in this way decidedly differing from the bryo-phytes (mosses) and resembling the sperma-tophytes (seed-plants). From the seed-plants the group differs in that its members do not produce seeds. The group as a whole is most extensively developed in the tropics, where especially the ferns and "little club-mosses" (Selaginella) are luxuriant both in forms and numbers. The three great divisions of pteridophytes differ exceedingly from one another in external appearance, but all are held together by important similarities. One of their important characteristics in common is the possession of a large, coiled and multiciliate sperm, very distinct from the simple, biciliate sperm of the bryophytes. See Equisetales, Filicales and Lycopo-diales.

Ptolemy (tT-mĭ),Clau'diusPtolemae'us, an eminent mathematician and astronomer. He was born probably either in 70 or 77 A. D., and died at Alexandria in 147 A. D. As a mathematician he is especially to be remembered as having written the first treatise on trigonometry, a branch of mathematics invented by Hipparchus. In astronomy he wrote a complete treatment upon the entire subject as known in his time. This volume, The Almagest, remained a standard work until the time of Copernicus. Ptolemy assumed that the earth is spherical, is placed in the center of the spherical heavens and is a mere point compared with the distances of the fixed stars. As a geographer, Ptolemy was the first to point out the fftct that the position of any point on the earth's surface can be accurately stated only after its longitude and latitude have been determined. In addition to these works he wrote a volume on optics, in which he stated the correct laws of reflection for plane surfaces and for concave mirrors as well as [ the law of refraction. Ptolemy must be