SOME PRACTICAL PROBLEMS.

"Do you mind taking my class in arithmetic for a half hour?" inquired my friend Jones one morning when I was visiting his school.

I assured him it would be a pleasure to me, and inquired where they were working. "They are just reviewing square measure. Give them a few practical examples out of your head," said he.

Then he left me alone with the class, and I began: "We will do a little practical problem in papering. My room is twenty feet

long, sixteen feet wide, and ten feet high. Paper it with paper two feet wide, and thirty feet in a roll, at twenty cents a roll."

Now, I will leave it to the average teacher if that is not about the way he might have given an ordinary question in papering. It is very much like one I saw in an arithmetic, anyway. I had hardly given out my problem before a twelve year old boy said: "They don't have wall paper two feet wide and thirty feet long. There isn't a roll like that in my father's store, and he has the biggest wallpaper store in Tacoma." Well, we reduced the paper to the proper width,

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and stretched it out to the right length, and then another hand went up. "Shall we paper the ceiling?" I had not thought of that, but I said the ceiling should be papered, and then thought my trials over. But a lad asked me if I was going to have a border, and how wide the border would be, for with a wide border we would put the paper farther down the wall. He had hardly finished this before another rascal wanted to know how many doors and windows I had, and how big they were. "And I suppose there is a baseboard," he remarked. "And how often does the paper match?" asked another small villain. I had never before realized that papering was so abstruse a problem.

I said we would put flooring on that room at the rate of $45 a thousand. "That is too much to pay for flooring here in Tacoma," remarked a lumberman's boy. I claimed this was extra fine flooring, and despite the fact that he said that I could have the pick of his father's yard for less than half the price I stuck to my price. "Are you going to put on three-inch, four-inch, or six-inch tongue and groove?" was the next query.

"You know there is less waste in the wide lumber, but the narrow makes the best floor," he remarked. I did not know it, but soon learned that 320 feet of lumber would not cover the floor, and that six-inch flooring was not six inches wide.

Then I started to have them carpet the same room, and I got carpet of a width different from any that ever came to Tacoma, the girl whose father was a carpet dealer assured me, and I failed miserably when I tried to tell them how often the figures matched, and I overlooked the fact that it would have to be turned under, and that it took more carpet if put one way of the room than the other way; and when I told the price and was asked what kind of a carpet it was I was afraid to answer.

Then I started to have a roof put over that room, and the carpenter's boy snickered when I gave them the length of the rafters, and to this day I can not see what was funny in my telling that every shingle was four inches wide, and lay six inches to the weather. I am sure that is the way I saw it in the book.

I got afraid of original examples, so I opened the book and began to read a prob

lem where the soldiers got 8 oz. of rations a day, and a girl who belonged to the Tacoma Girls' Brigade wanted to know if the men were shut up in a fort and starying. And then the whole class looked at me, as though I was responsible for those short rations. You can't imagine how glad I was to see Jones return and take the class out of my hands.-Northwestern Journal of Education.

FUNNY FIGURES.

A professor, who dreams in figures, has evolved the following curious specimen of figure gymnastics:

1 time 9 plus 2 equals 11 12 times 9 plus 3 equals 111 123 times 9 plus 4 equals 1111 1234 times 9 plus 5 equals 11111 123456 times 9 plus 7 equals 1111111 1234567 times 9 plus 8 equals 11111111 12345678 times 9 plus 9 equals 111111111 1 time 8 plus 1 equals 9 12 times 8 plus 2 equals 98 123 times 8 plus 3 equals 987 1234 times 8 plus 4 equals 9876 12345 times 8 plus 5 equals 98765 123456 times 8 plus 6 equals 987654 1234567 times 8 plus 7 equals 9876543 12345678 times 8 plus 8 equals 98765432 123456789 times 8 plus 9 equals 987654321

THE EDUCATIONAL VALUE OF
MATHEMATICS.

Professor W. H. Metzler, of Syracuse (N. Y.) University, claims for the study of mathematics, when properly pursued, that its facts, particularly those of elementary arithmetic, "are of the utmost importance to every individual"; that it develops the power of concentration; that it trains to clearness of thought and expression; that it engenders the habit of distinguishing essentials from nonessentials; that it develops the power to reason accurately and logically; that it trains the student in good judgment; that it, particularly geometry and trigonometry, aids the imagination; that it builds up rational memory; that it tends to make one liberal-minded; that it forms good mental habits; that it leads one to appreciate the beautiful in form and thought; that it promotes a scholarly spirit; that it trains

SOLUTION.

=

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(a) Take as the independent variable x the angle FAB through which the boat must be turned up stream. Then AF-3 sec x, and the time on water: = sec x. FP, the downward drift, at 3 miles per hour, sec x. Now PC, the distance on land, = BC+FPBF 5sec x 3 tan x; and the time on land=1+1 sec x – tan x. Adding the two expressions for time we have t=1+ sec x

Differentiating

dt 6 sin x

dx 5 cos2 x

tan x.

3

5 cos2 x

Substituting these values in the expression for PC we find

PC 53, or 5.86603.

He should turn his boat 30° up stream and land at a point 5.86603 miles below the city. S. P. Shull, Kouts.

(b) Let A be the position of the man on the water, B the city. Since C is up stream he must row against the stream and must attempt to reach a point up stream from the point at which he lands. Let F be the point of landing if there were no current.

4B 3 miles

=

BC = 5 miles

B

Then