(12) _Ambiguities and falsities._--Consider the ambiguities and false reasoning of these problems. 1. If you can earn 4 cents a day, how much can you earn in 6 weeks? (Are Sundays counted? Should a child who earns 4 cents some day expect to repeat the feat daily?) 2. How many lines must you make to draw ten triangles and five squares? (I can do this with 8 lines, though the answer the book requires is 50.) 3. A runner ran twice around an 1/8 mile track in two minutes. What distance did he run in 2/3 of a minute? (I do not know, but I do know that, save by chance, he did not run exactly 2/3 of 1/8 mile.) 4. John earned $4.35 in a week, and Henry earned $1.93. They put their money together and bought a gun. What did it cost? (Maybe $5, maybe $10. Did they pay for the whole of it? Did they use all their earnings, or less, or more?) 5. Richard has 12 nickels in his purse. How much more than 50 cents would you give him for them? (Would a wise child give 60 cents to a boy who wanted to swap 12 nickels therefor, or would he suspect a trick and hold on to his own coins?) 6. If a horse trots 10 miles in one hour how far will he travel in 9 hours? 7. If a girl can pick 3 quarts of berries in 1 hour how many quarts can she pick in 3 hours? (These last two, with a teacher insisting on the 90 and 9, might well deprive a matter-of-fact boy of respect for arithmetic for weeks thereafter.) The economics and physics of the next four problems speak for themselves. 8. I lost $15 by selling a horse for $85. What was the value of the horse? 9. If floating ice has 7 times as much of it under the surface of the water as above it, what part is above water? If an iceberg is 50 ft. above water, what is the entire height of the iceberg? How high above water would an iceberg 300 ft. high have to be? 10. A man's salary is $1000 a year and his expenses $625. How many years will elapse before he is worth $10,000 if he is worth $2500 at the present time? 11. Sound travels 1120 ft. a second. How long after a cannon is fired in New York will the report be heard in Philadelphia, a distance of 90 miles? GUIDING PRINCIPLES The reader may be wearied of these special details concerning bonds now neglected that should be formed and useless or harmful bonds formed for no valid reason. Any one of them by itself is perhaps a minor matter, but when we have cured all our faults in this respect and found all the possibilities for wiser selection of bonds, we shall have enormously improved the teaching of arithmetic. The ideal is such choice of bonds (and, as will be shown later, such arrangement of them) as will most improve the functions in question at the least cost of time and effort. The guiding principles may be kept in mind in the form of seven simple but golden rules:--