AN EASY PROOF FOR SUMS IN MULTIPLICATION.
As boys are always interested in short cuts in arithmetical processes, it may be well to insert for the benefit of those who are studying multiplication, a method of proving their examples which I learned a short time ago from an old banker of New York. This rule is simply to add the digits of both multiplicand and multiplier, divide both answers by 9, and multiply the remainders; divide this product by 9 and the remainder will be, if the example is correct, the same as that obtained by adding the digits of the product and dividing that answer by 9. For instance, suppose after multiplying 4359 by 2786 we have 12144174 for the answer; now instead of performing this operation over a second time to make sure our answer is correct, we simply add the digits in 4359 and divide the sum 21 by 9, we find we have 3 left. As it is the only remainder we have to deal with, we need not keep the other figures. By adding the digits in the multiplier we obtain 23, which divided by 9 gives 2 and 5 remainder. Now, multiplying the first remainder by the second we have 15: this product divided by 9 gives 1 and 6 remainder. If the product 12144174 is correct, the sum of its digits divided by 9 will leave 6 for a remainder. Performing the operation, we find the sum of its digits is 24, divided by 9 equals 2 and 6 remainder. As both the remainders correspond, the answer was correct. After a little practice you will find you can prove your examples very quickly by this method, and where a number of sums are given without the answers it will be of invaluable assistance, besides saving you a great amount of labor.
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THE SELF-RECTIFYING DART.
The dart, and its larger brother the javelin, were among the earliest weapons used in warfare, and were very skilfully thrown, not only by the Roman soldiers, but by the Goths and other savage tribes who lived in the regions north of them.
These javelins were large affairs, measuring some six or seven feet in length; the handle, a tough piece of wood, was generally four and one-half feet in length, and an inch in diameter, while the rest of the length was taken up by the barbed triangular-shaped head.
Ever since those days children of all nations and climes have made toy implements, resembling those in general appearance, but varying much in size and materials used.
