height in man also influences growth in bone.

The mean increase in weight at the respective ages, normal cadet records occurring first and gymnastic cadet records second below, was as follows: At 17, 3.6 and 8.8 k.; at 18, 3.2 and 6.6 k.; at 19, 2.4 and 6.6 k.; at 20, .7 and 6.6 k.; and at 21, .2 and 6.4 k. The total mean increase was, for the normal cadets, 10.1 k., while that for the gymnastic cadets was 35 k. These figures indicate a great increase in weight due to exercise, the greatest increase being in the year from 16 to 17, as was true of height. But, as was not true of height, the additions in weight per year from 17 to 21 were practically uniform; 35 kilos, or 77 pounds, is a much larger proportionate increase in weight than was noticed in regard to height. The inference from this fact is that growth in weight is much more easily influenced by exercise than is growth in height. It is true, however, that weight is easily and quickly lost, while height does not decrease materially.

The mean increase in lung capacity at the respective ages, the records occurring in the order employed in the discussion of weight, was as follows: At 17, 250 and .658 liters; at 18, .167 and .540 liters; at 19, .152 and .462 liters; at 20,

.083 and .376; at 21 the normal cadets had no record, while the increase of the gymnastic cadets was .340 liters. The total mean increase for the normal cadet was .652 liters, while that of the gymnastic cadets was 2.374 liters. The data shows a very great increase in lung capacity over the normal cadets on the part of the gymnastic cadets and that the annual value steadily diminishes in both classes of cadets. A comparison of this data with that pertaining to height and weight shows that the ratio is more constant in reference to the table of heights than to the table of weights. This showing is not satisfactory from the standpoint of hygiene according to Demeny's law of "vital-index," which holds that vital-index is equal to lung capacity divided by weight. It is evident that if weight increases out of proportion to lung capacity, the "vital-index" is lowered. Further studies may show, since increase in strength results in increase in weight but not in a corresponding increase of lung capacity, what system, or combination of systems of gymnastic work, is best adapted to bring the individual to the highest in him and yet keep all of the conditions hygienically perfect; that is, keep the "vital-index" rising, or, at least, holding its own. (To be continued.)

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reviewing. This is not justice. If there were no other reasons why she should not do this the fact that she was living in the month of May would be a sufficient

one.

All the world outside is awake, it is thrilling with new new life and beauty. Should the work of the school because of its quantity or routine be divorced from this awakening?

The children from the youngest to the oldest should be sent to the fields or the woods for observation, and by this we do not mean that a story of everything they are likely to see be told to them before they start. Their observation should be independent. The help which they need will be better help if it be given in the form of a question rather than in the form of a statement.

The children of our school should be taught to observe. Facts observed are of great educational value, but the habit of observing is of greater value. When the children of our schools by independent observation know how the blue birds build their nests, that on some trees the blossoms come before the leaves are out, and why the seed stalk of the dandelion is so long, then they have taken a long step towards self-development. These are very simple facts, but the processes by which these were gained will lead to selfactivity and independent study.

If teachers or pupils have been unconcerned of all around them save the room in which they gather each day, the books and the facts which are contained in them, each has lost a great deal. The windows of such a school should be kept open and May should be allowed to come in with her perfume of apple blossoms, her bird choir, the beauty of her flowers and the tender sacred memories of Memorial Day.

Four special days should be kept in this month of May: (1) May Day, (2) Bird Day, (3) Flower Day and (4) Memorial Day.

In one primary room the children were asked to bring on May first all the flowers they could. After these had been arranged the room was beautiful with blossoms. At the opening of school they

were told of the May day as it is kept
over the sea. The words-
"Rise and call me early,

Call me early, mother dear,
For I'm to be the Queen of the May,
I'm to be the Queen of the May"—

kept the interest from lagging. The recess time was happy because of the May pole which the teacher provided for the occasion, such fun as the little child had as he skipped about the pole. That recess will be long remembered.

When the day was ended and the flowers had been placed in the dainty paper baskets which had been the manual work for the afternoon, carefully and proudly the children carried the May greeting home.

that their ends might be gained. Their courage was as great as that shown by those who have died on battlefields. In giving either of these ideals of patriotism we are not belittling the other. Memo

rial day should be filled with reverence, and we honor those who have died for our country when we teach the children how good and honorable it is to live for our country.

EASY MATHEMATICS.

Under the above title Sir Oliver Lodge of the University of Birmingham has written a very interesting and helpful book. As the author states, it is "a collection of hints to teachers, parents, self-taught students and adults." The book deals chiefly with arithmetic, although algebraic and geometric notions are freely used, when they help to simplify the treatment.

The book will be a great help to teachers because of its suggestiveness. The author believes that "dullness and bad teaching are synonymous terms." He also thinks that "A subject may easily be over-taught or taught too exclusively and too laboriously." The student of this book will surely improve his teaching and will be saved from over teaching the unimportant, and from laboring too hard upon the important.

The first few chapters are devoted to counting and the fundamental operations. The hints for teaching are full of common sense. In speaking of the use of terms, he says: "I see no reason for troubling about the names addition and subtraction, nor yet for artificially withholding them. If they come naturally and helpfully, let them come. Nothing is gained by artificial repression at any stage. Premature forcing of names is worse than artificial withholding of them, but both are bad."

Many teachers and many text-books make the treatment of concrete numbers very difficult. The chapter upon this subject is excellent. He takes the very sane and mathematical view that the most complicated operations may be performed with concrete numbers, provided the result can be intelligent y of the troubles

ted

in arithmetic would be avoided if this notion were taught from the start.

The discussion of large and small numbers is very interesting. Many school children labor long and hard to get a money result expressed to a thousandth of a cent, when the nearest cent is the only possible accurate result in practice. The matter of practical accuracy belongs to judgment. It is necessarily relative.

The book as a whole is a notable one. It will be read with pleasure and profit by students and teachers. The experienced mathematical teacher will find it full of pleasant surprises. It is published by the Macmillan Company of New York.

SEAT WORK IN ARITHMETIC.

For middle grade classes interesting and valuable drills can be devised in the form of missing figure puzzles. These may be used occasionally for variety. There is in this a kind of thinking that is akin to that which is developed by algebraic problems. The missing figure is an unknown quantity to be found by "working back" from the result, and which when supplied will fulfill the conditions as determined by the given result.

Try the following yourself and observe the kind of thinking required for their solution. They are not mere puzzles; far from it.

14. See April number for statement of problem.

The locus of the points fulfilling the given condition would be the surface of a sphere whose center would be the position of the foot of the ladder and whose radius would be the distance from that point to the top of either pole.

In the figure let A B C be an equilateral triangle, each side being 200 feet; AE, the pole erected at A, 50 feet high; BF, at B, 30 feet high, and CG at C, 40 feet high. Pass a plane through EF and G. Let P be the center of the circumscribed circle. Then PG is the radius of a small circle of the sphere whose center we are seeking. Through C, G and P pass a plane. Then this plane is perpendicular to the plane of A B C. L, the required point, lies in the plane A B C. Through PG pass a plane perpendicular to the plane E F G. Then L lies in this plane also or in the line of its intersection with A B C. Let D be the

projection of the point P on the plane A B C, and P K be perpendicular to the line K T. Through K and PR a perpendicular to FG at its middle point R pass a plane, and through PR pass a plane PRSL perpendicular to the plane E F G. Now L lies in the plane A B C, in the plane P Q T K, and in the plane PRSL. Therefore it must lie at L, their point of intersection. L G would be the length of the ladder and LC the distance of L from CLA the distance of L from A and LB the distance of L from B.

By drawing through F a line parallel to AB we form a right-angled triangle whose short arm is 20 feet and whose long arm is

E

M

B

200 feet. Solving this for the hypothenuse, we find E F to be 201.494. In the same way we find FG and EG each to be 200.249. Thus EFG is an isosceles triangle. Find P the center of the circumscribed circle. Then P lies in the perpendicular bisector of EF, which also passes through G. By solving the triangle FGQ for its longer leg we find GQ=173.205. The triangles FGQ and PGR are similar. Therefore FG:PG::QG: RC.

Solving PG=115.758. Solving PGR for PR-58.089. In the trapezoid ABFE, Q is the middle point of the now parallel side EF and QH is parallel to AE and BF, and is equal to one-half their sum, or 40 feet. Therefore HCGQ is a rectangle and PD is equal to 40 feet. The plane triangle angle HQT PDK, their sides being parallel and is similar to EQM, their acute angles be

ing equal. Therefore MQ:HQ::EQ:TQ. Solving TQ or PK-40.198, the value of MQ being found in solving the triangle EQM. EQ being EF and EM being equal to 50-30 or 10 feet. R being the middle point of FG and RV being parallel to BF and CG, is equal to their sum, or 35 feet. The triangle KPL is similar to PRN, their sides being perpendicular each to each. PN=5. Wherefore by solving PRN, RN-58.089. PK:NR::PL:PR whence PL-40.35. Solving triangle PLG, GL the length of the ladder= 122.588 feet, CL the distance of C from L= 115.879, AL the distance of A from L= 111.928, BL the distance of B from L= 118.861.

C. W. Caldwell, Delaware.

16. See April number for the statement of the problem.

Let x = radius of one of the equal circles. πX2

Area of the three sectors

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