This is specially true of the reasoning about arithmetical facts in life. "Will 3-1/2 yards of this be enough for a dress?" Reason directs you to learn how wide it is, what style of dress you intend to make of it, how much material that style normally calls for, whether you are a careful or a wasteful cutter, and how big the person is for whom the dress is to be made. "How much cheaper as a diet is bread alone, than bread with butter added to the extent of 10% of the weight of the bread?" Reason directs you to learn the cost of bread, the cost of butter, the nutritive value of bread, and the nutritive value of butter. In the arithmetic of the school this feature of reasoning appears in cases where some fact about common measures must be brought to bear, or some table of prices or discounts must be consulted, or some business custom must be remembered or looked up. Thus "How many badges, each 9 inches long, can be made from 2-1/2 yd. ribbon?" cannot be solved without getting into mind 1 yd. = 36 inches. "At Jones' prices, which costs more, 3-3/4 lb. butter or 6-1/2 lb. lard? How much more?" is a problem which directs the thinker to ascertain Jones' prices. It may be noted that such problems are, other things being equal, somewhat better training in thinking than problems where all the data are given in the problem itself (_e.g._, "Which costs more, 3-3/4 lb. butter at 48¢ per lb. or 6-1/2 lb. lard at 27¢ per lb.? How much more?"). At least it is unwise to have so many problems of the latter sort that the pupil may come to think of a problem in applied arithmetic as a problem where everything is given and he has only to manipulate the data. Life does not present its problems so. The process of selecting the right elements and attaching proper weight to them may be illustrated by the following problem:--"Which of these offers would you take, supposing that you wish a D.C.K. upright piano, have $50 saved, can save a little over $20 per month, and can borrow from your father at 6% interest?" A A Reliable Piano. The Famous D.C.K. Upright. You pay $50 cash down and $21 a month for only a year and a half. _No interest_ to pay. We ask you to pay only for the piano and allow you plenty of time. B We offer the well-known D.C.K. Piano for $390. $50 cash and $20 a month thereafter. Regular interest at 6%. The interest soon is reduced to less than $1 a month. C The D.C.K. Piano. Special Offer, $375, cash. Compare our prices with those of any reliable firm. If you consider chiefly the "only," "No interest to pay," "only," and "plenty of time" in offer A, attaching much weight to them and little to the thought, "How much will $50 plus (18 × $21) be?", you will probably decide wrongly.