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these two students be unequal and shall vary rlirectlv as the sizeof the pocket-books. - \ Three meals of a boarding school are always less than a square meal. Propositions. The loci of the daily paths of all students must intersect at one point. Proof:-lf these paths did not intersect we would thus have a collegestudent going without his dinner -which is absurd. Two boarding schools are equal if the president of one equal the president of the other. Proof:-Place the board- ing school A on the boarding school B, so that the president of A shall fall on the president of B. Then the faculty of A will fall on the faculty of B, because, by an axiom, the faculty must take the direction of the president. For a similar reason the students of A will fall on those of B. Hence the boarding schools coincide throughout and are equal. Exercises. 1. Calculate the income of the father of a student, if the pull of that student be such that the president will permit him to leave town without consulting the faculty. How much, if the student will not be dcmeritcd for going down town? 2. How many desserts will be given a week, if the presi, dent intends to erect a building 100 ft. long, 50 ft. deep and two floors high? 3. What is the average weight of the students in problem 2' 4. Construct a boarding school in which the decreesof the faculty are pleasing to the students. Hint:-Let d=eO, where d is the number of decrees. --J- 167 +-