TEACHING ETHICS. If one is inclined to preach and moralize at all in school he is likely to do too much of it. Too little is altogether better than too much, and the "unconscious tuition" of the teacher's own conduct and personality is of more value than many sermons. The argumentum ad hominem may, however, occasionally be used with. excellent effect. The interest of children like that of grown persons is easily enlisted in the discussion of conditions which they can themselves illustrate from experience and observation. Kate Douglas Wiggin says in Patsy, "We had our morning hymn and familiar talk in which we always outlined the policy of the day, for the children were apt to be angelic and receptive at nine o'clock in the morning, the unwillingness of the spirit and weakness of the flesh seldom overtaking them till an hour or so later." A three minutes' talk of this kind with the teacher assuming an intimate, kindly, sympathetic attitude toward the pupils, reviewing the mistakes of the preceding day, finding out the causes and the best way to correct them; three minutes thus spent are worth hours of keeping in at night when both teacher and pupils are tired, fretted perhaps, and irritable with a day's work in the vitiated air of the schoolroom. Keeping in is perhaps a necessary evil, as a temporary expedient it must occasionally be resorted to. It is productive of no permanent good whatever, and the best schools reduce it to the least possible minimum. BRUDDER BROWN'S BLESSING. O Mahsr! let dis gath'rin' fin' a blessin' in yo' sight! Don't jedge us hard fur what we does-you knows it's Christmas night; Ef dancin's wrong, O Mahsr! let de time excuse de sin! We labors in de vineya'd, wukin' hard an' wukin' true; Bekase, nex' week, we'll start in fresh, an' labor twict as well. Remember, Mahsr-min' dis now-de sinfulness ob sin Is 'pendid' 'pon de sperrit what we goes an' does it in; It seems to me—indeed it do—I mebbe mought be wrong— -From Irwin Russell's "Christmas Night in the Quarters." BIOGRAPHY SOPHUS LIE. MATHEMATICS. ROBERT J. ALEY, BLOOMINGTON, Ind. IV. Mathematical scholars are numerous the world over. All civilized nations have possessed them, and possess them now. England, for example, has among her educated men a vast number of mathematical scholars, men whose knowledge of, and training in higher mathematics is unsurpassed. Such men have added greatly to the science; they have tinted the frescoes and completed the niches; they have finished the structures only indistinctly projected. Occasionally, however, in a century there appears quite a different kind of mathematician, one whose intuition seems to comprehend the known scope of mathematics, or at least that of certain fields, one whose brain is afire to see beyond the known limits of mathematical knowledge, one who penetrates the unknown. Such a man may be called a mathematical genius, and such was Sophus mathematical genius, and such was Sophus Lie. This remarkable man was a Norwegian, educated at the University of Christiania, receiving his doctorate in 1865 at the age of twenty-three. During his connection with the University as an undergraduate student Lie attracted no especial attention. as an original worker in mathematics; in fact, he anticipated his career to be either philology or engineering, with a possibility of mathematics. A course of lectures on algebraic substitutions by Professor Sylow at the University of Christiania, and a careful study of Plücker's Line Geometry inspired Lie to the highest mathematical activity. From 1868 to 1872 his genius had full sway, unhampered by the details of everyday life. It was during this brief period that the foundations for his farreaching and epoch-making discoveries. were conceived. The remainder of his life was devoted to the amplification of this program. The fundamental product of Lie's genius embraced a general and systematic treatment of the theory of differential equations. For this purpose he devised the theory of transformation groups, the scope of which embraces not only the theory of differential equations, but manifold other applications, including invariants, covariants, differential invariants, as well as problems in mechanics, physics and astronomy. Lie's career as a professor of mathematics extended over a period of twenty-one years. A special chair of mathematics was created for him in the university of Christiania in 1877. He held this position until his call to the university of Leipzig in 1886. While connected with the university of Leipzig he held the chair of geometry. His fame spread far and wide; students from Germany, Russia, Greece, Italy, France, England, America, attended his lectures. These lectures were, as a rule, very informal, being interspersed by questions, informal remarks and illustrations. This method of instruction was, as a source of inspiration, far superior to the formal lecture of the ordinary German professor. Lie was a giant physically and mentally, odd in habits, fearless in thought and action, kind to his friends, intolerant of his real or fancied enemies. During the last few years of his life the fancied enemies gave him a source of annoyance that was entirely avoidable. He gradually grew discontented with his surroundings at Leipzig, and resigned in the summer of 1898 to accept his old position at the university of Christiania, where he died in February, 1899, at the age of fifty-six. GRAPHICAL REPRESENTATION. By a graph is meant a drawing used to represent or illustrate some numerical or statistical fact. It is used very freely in the public press. It has a wide applica tion, not only in the diffusion of general knowledge, but in the schoolroom as a help in all lines of mathematical work. The first essentials in a graphical representation are the lines of reference, technically known as the axes. These are two arbitrary lines at right angles to each other, the horizontal one being known as the X-axis, or the axis of abscissas, and the other the Y-axis, or the axis of ordinates. The intersection of the axes is called the origin. Anything that can be located with respect to these axes is capable of graphic representation. An example will make the matter clear. Suppose that in crossing a field 20 rods long, a man walks in a path described as follows: He crosses in 80 sec., starting at southwest corner. At the end of 4 sec. he is 1 rd. from south fence, 8 sec. 2.rds., 12 sec. 3 rds., 16 sec. 2 rds., 20 sec. 1 rds., 24 sec. 1 rd., 28 sec. rd., 32 sec. 1 rd., 36 sec. 2 rds., 40 sec. 3 rds., 44 sec. 5 rds., 48 sec. 2 rds., 52 sec. 2 rds., 56 sec. 1 rd., 60 sec. 4 rds., 64 sec. 3 rds., 68 sec. 5 rds., 72 sec. 4 rds., 76 sec. 3 rds., 80 sec. 1 rd. On the OX line let the spaces each represent 4 seconds. Then at each of these points erect perpendiculars which shall be proportional to the distance he is. at that time from the south fence. A line through the tops of these perpendiculars represents his path. Such a diagram shows more at a single glance than can be gained by several minutes' study of the mere figures. (See fig. 1.) The temperature from 7 a. m. to 5 p. m. on a certain day was as follows: 7 a. m. 70, 8 a. m. 75, 9 a. m. 78, 10 a. m. 80, 11 a. m. 82, 12 m. 85, 1 p. m. 88, 2 p. m. 90, 3 p. m. 85, 4 p. m. 81, 5 p. m. 78. To show this in a graph we will represent the hours on the horizontal line and the temperature by the perpendiculars. A similar diagram may be used to show the price of wheat for the months of a year. Represent the months on the horizontal line and price for each month by a perpendicular proportional to it. The growth of a town or state may be shown graphically in the same way. Represent the time on the horizontal line and the population by the perpendiculars. SOLUTIONS. 35. The volume of a cylinder is 196.35 cu. ft. Its height is 10 ft. What is the area of the base of a similar cylinder whose volume is 27 times as great? Similar solids are to each other as the cubes of their like parts. Volume of second cylinder is 27 × 196.35=5301.45. 196.35: 5301.45 = (10)3 : x3. x=30, the altitude of second cylinder. 5301.4530176.715, base of second cylinder. Lizzie Lilly, Pierceton. = 4 8 36. (1) x + 2y + 3z (2) 2x+3y+4z=6 (3) 3x+4y+5z Eliminating x from (1) and (2), the result is y+2z=2. Eliminating x from (1) and (3), the result is 2y+4z=4. The second of these results is twice the first, hence a definite solution is not possible; but if y+2z=2, y can be 0 and z=1 or 2 and z = =0. y Similar triangles are to each other as the squares of their like parts. The triangles, therefore, are to each other as а V3 } 2 2 3a2 A. F. Wood, Mitchell. 38. Find the equated time for the payment of the balance of a debt of $1.250, which was to run one year, without interest, one-half of it having been paid at the end of 3 months; one-fourth of the remainder at the end of 6 months; and one-fourth of that remainder at the end of 9 months. The various payments are $650, $156.25 and $117.1875. The balance unpaid is $351.5625. Interest on $625 for 9 mo. at 6 % $28 125. = Lizzie Lilly, Pierceton, 35; R. E. Lind, Sandborn, 35, 36, 37, 38, 39; A. F. Wood, Mitchell, 37, 39; Lefevre Du Bois, Rochester, 37, 38, 39; L. M. Neher, N. Manchester, 35, 36, 39; W. W. Wells, Tipton, 39; O. V. Wolfe, Walkerton, 35, 37, 38; Howard Kesler, Clark's Hill, 38; Myrtle Skinner, Gaston, 39; Clinton Moornow, South Bend, 35, 36, 37; Colonel Sentman, Stone Bluff, 35, 36, 37, 39; Ethel Bennett, Peru, 35, 37, 39; Lillian Carter, Acton, 38; 0. F. Krieger, Carthage, 37, 38; E. J. Metz, Columbia City, 35, 37, 39; R. H. Baumunk, Saline City, 37; G. E. Combs, Linton, 35; Clara Coombes, Borden, 35, 36, 37, 38, 39; P. G. Huston, Weirtown, 35, 37, 38, 39; Jos. R. Westhafer, Washington, 35, 37, 38, 39; Anna B. Partridge, 35, 37, 39; Ernest Applegate, Thorntown, 35, 36, 37, 39; F. J. Conboy, Wanatah, 35, 39; Edward Morgan, Aroma, 35, 36; R. C. Whitted, Pinhook, 35; R. L. Modesitt, Atherton, 35, 39; Olin Norman, Heltonville, 35, 37; C. O. Mitchell, Eaton, 35, 38; L. W. Clements, Elnora, 38; Flora J. Scott, Fairmount, 35; H. H. Pleasant, Tower, 35, 38; V. W. Martin, Carbon, 37, 38, 39; F. W. Donahue, Boonville, 37; John T. Campbell, Rockville, 39; Charles B. Austin, Winchester, 35; J. J. Gorhinger, Anderson, 35, 36, 37, 38, 39; A. R. Melick, Etna Green, 35; E. L. Penn, Remington, 37; Emma B. Miller, Don Juan, 35; D. W. Werremeyer, Jasper, 35; J. B. Murphy, Georgetown, 35, 36, 37, 38, 39; Ethelbert Woodburn, Ambia, 35, 36, 37, 39; Perry Snethen, Walkerton, 35, 39; Michael Kappes, Kelso, 35, 38, 39. |