ADAPT THE MUSIC TO THE CHILD.

A plan of music for the child-and for the teacher as well-should be more than a logical development of the science of music. It should be psychological in its adaptation to the development of the child, appealing in the highest degree to every quality of mind and heart. And does it not seem that inasmuch as the child's intelligence and independent power grow by observation from memorizing and imitating, that his training in music should begin with songs committed to memory and related in construction and thought to sight reading exercises and studies? If the power of song is to be used as a starting point and the child's efforts at musical understanding are to be prompted by the inspiration of song, it follows that only the very best songs should be selected; the character of the material itself is of first importance.

WHY STUDY MUSIC?

The value of education to the individual must be found in its effect on the soul; in its influence as an element in character-forming. No consideration of ultimate values is adequate unless it weighs the well-being of the immortal part of man. As educators we assume that the formation of worthy character is the ultimate object of all education.

Music is of the highest value in education, because it supplies in an attractive and effective manner the very elements that are so often wanting in modern life. The average American boy is born with the notion that the most important thing in the world is to make money; that all his time should be given to preparing himself to work for wages: and that if he does prepare himself to fill a position that will bring him a livelihood, he is doing all that should be expected of him, In other words, he places the skill of his eyes or his hand above his own worth, and makes what he can do of more importance than what he is. . . . I take the position that music educates the child, not to make him bring a higher price in the labor market, but to make him a broader, better man in mind and heart. . . . The things that really move and mold humanity are, after all, the things that touch the common heart and lay hold of the great common feelings of mankind.

Nothing that is the common property of man does this so completely as music. The exact character and influence of its operation can be explained no more than you can exactly explain the influence of a noble picture, of a garden of beautiful flowers, of a park of lofty forest trees, or of a grand outlook whence may be seen the glories of a lovely sunset, or of a broad stretch of river and forest and landscape. . . . All the lessons in all the books are not so important as to learn to live happily, drawing pleasure from the free gifts of the universe. Teach a child to love the sun and the breezes, the sunset and coming of the night bringing the moon and the stars, all the beautiful gifts of God, and you make this world an abode of happiness, and his life a benefaction to himself and his fellows.

It is this element of nature, this message from the heart of God, that music puts into the school course, puts into the church service, and puts into the home. You can not tell what this element is nor describe its working, but we all feel it swaying our emotions, speaking for our heavengiven intuitions, appealing to the best that is in our beings.-P. C. Hayden at N. E. A.

Music is what awakes in you when instruments are played.— Whitman.

MUSIC IN EDUCATION.

One of the best things a musician can do for his art is to bring before the people the position that music should occupy in the general scheme of education. Music stands as the representative of the esthetic life in general. The world at large often gives to the term "education" in general the meaning of simply a collection of facts and theories, to the neglect of the esthetic sense. But when we exploit the real place of music in the scheme of education, we are opening the way for all that goes to make up a higher and better esthetic life.-The Etude.

When he is old and past all singing,

Grant, kindly Time, that he may hear The rhythm through joyous nature ringing, Uncaught by any duller ear.

-H. C. Bunner.

· HISTORY OF ARITHMETIC.

XX-THE CALENDAR.-(Continued). The mistake of Numa's reign was finally corrected by an edict which commanded that every third period of eight years, instead of having four extra months should only have three of twenty-two days each. This made the average year 3654 days each. The announcements and arrangements of the extra months were left to the pontiffs. With the usual corruptness of the times, the extra months, Mercedimii, were hurried or retarded as might best suit the ruling pontiff. At the time of Julius Cæsar the calendar was three months wrong.

days.

Cæsar decided to take a new start. He decreed that the year should consist of 365 This was to be accomplished by making the ordinary years consist of 365 days, and every fourth year of 366 days. The new reckoning began January 1, 45 B. C. The months of January, March, May, July, September and November, each consisted of thirty-one days, and all the others of thirty except February which had twenty-nine in ordinary years, and thirty in leap years. August was increased to thirty-one to gratify the vanity of Augustus. In order to prevent three long months in succession, September was reduced to thirty days, then November was also so reduced, and October and December, increased to thirty-one days. The extra day for August was taken from February.

The Julian year was too long by about eleven and one-fourth minutes. This amounted to a whole day in about 128 years. Some unknown Persian astronomer suggested that the extra day in every thirty-second leap year be omitted. Had this suggestion been followed, it would have reduced the error to less than one day in 100,000 years. It is worthy of mention that Losigenes, the mathematician who made the calculations for Julius, knew that his rule made the year too long.

The error in the Julian calendar accumulated until in the sixteenth century it amounted to about ten days; that is, the seasons arrived ten days earlier than they should. In 1582 Gregory XIII. corrected this by omitting ten days from that year, and decreeing that the even centuries should be leap years only when divisible by 400. This made the year contain 365.2425 days. The

error in this is so small that it will take about 3,300 years for it to amount to one day.

The new calendar met with much opposition. Roman Catholic countries, in general, adopted it at once. The change was not made in England until 1752, when it was necessary to omit eleven days from that year. Scotland made the change in 1600, and the German Lutheran States in 1700. Russia and the Greek church still adhere to the Julian calendar.

All Mohammedan countries use the year of twelve lunar months, or 354 days. Such a year, of course, has no connection whatever with the seasons.

The Gregorian change in the calendar was not made for scientific reasons, but solely to keep Easter at the proper season of the year. In 325 the Nicene council decreed that Easter Sunday should be the first Sunday after the first full moon next following the vernal equinox. It was very important that the church all over the world should celebrate Easter on the same date. It is also important to know in advance what that date is to be. Many mathematicians have worked out rules by which the date of Easter can be determined. The best rule is that of Gauss corrected by Delambre. The rule for the next 200 years is as follows: (1) "Divide the given year by 4, 7, 19; and let the respective remainders be a, b, c. (2) Divide 19c+24 by 30; and let the remainder be d. (3) Divide 2a+4b +6d+5 by 7; and let the remainder be e. Then, if de is not greater than 9, Easter Sunday will be on (22+d+e) th of March; and, if (d+e) is greater than 9, Easter Sunday will be on (d+e— 9) th day of April, unless d=29, e=6, in which case Easter Sunday will be on April 19, and not on April 26, or unless d=28, e=6 and c>10, in which case Easter Sunday will be on April 18 and not on April 25." For the year 1900: a=0, b=3, c=o, 19c+24=24, and d=24. 2a+4b+6d+ 5=161, and e=0. d+e=24, which is greater than 9, hence Easter is the (24-9) th=15th of April. The two exceptions to the general rule mentioned above will occur in 1954 and 1981.

SHORT CUTS-IV.

MULTIPLICATION.-(Continued).

15. To find the product of two numbers which differ by 2. From the square of the intermedi

First, the multiplicand is multiplied by 9, then this product is doubled to give the product of the multiplicand by 18, and then this last product is doubled to give the product of the multiplicand by 36, proper attention being given in each case to the position of the partial products. This method is of frequent application, and insures greater accuracy than ordinary multiplication.

17. To square by supplement or complement. The supplement of a number is its excess above the next lower number of tens; e. g., 4 is the supplement of 64; 3 is the supplement of 83, etc. The complement of a number is the difference between the number and the next higher order of tens; e. g., 1 is the complement of 49; 2 is the complement of 68, etc. The base in each case is the number of tens considered.

To the number to be squared add its supplement, multiply the sum by the base and add the square of the supplement; e. g., 632 (63+3)X60 +3=3969. 84=(84+4)X80+4=7056.

From the number to be squared subtract its complement, multiply the difference by the base and add the square of the complement; e. g., 492 (49—1) 50+12=2401; 872= (87—3) X90+32= 7569.

=

Prob. 23, page 327. This problem has been solved in these columns, but John S. Williams of Mt. Vernon sends so good a solution that we gladly give it space. The problem reads, "At what point shall a triangular board 12 ft. long and 12 in. wide, be sawn into two equivalent boards?" The larger circle has a radius of 12 ft. If the inner circle is just one-half as large as the outer, then the triangle O L S will be just one-half the triangle O K T. (Fig. 1.)

122×3.1416-452.3924 area of larger circle. 452.3924÷2=226.1962 area of smaller circle. 226.1962.7854-16.96+ diameter of smaller circle 16.962=8.48+ radius of smaller circle, and so the point of section of the triangle. Mr. Williams also sends a similar solution to the 24th problem on page 327.

Problem 33, page 327.

A road two rods wide about a circular field contains one acre. What is the area of the

circle?

2 rods width of road.

1 a. or 160 sq. rds. =area of road. 1602 80 rds., average length or length of middle M'. (Fig. 1.)

80 rds.÷3.1416=25.464+rds., diameter of M'. Diameter of I is 2 rods less than dia. of M'. 25.464+rds.-2 rds.-23.464+rds. dia. of field, I. 23.464+2.7854-432.41+sq. rds. Area of field.