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Appendix.

existing between miles and hours? Do not be disheartened by your two friends' sarcastic remarks on your "roundabout ways." Their short method, of adding 12 and 8, has the slight disadvantage of bringing the answer wrong: even a "roundabout" method is better than that! M. A. H., in (2), makes the travellers count "one" after they met, not when they met. Cheshire Cat and Old Maid get "20" as answer for (1), by forgetting to strike out the train met on arrival. The others all get "18" in various ways. Bog-Oak, Guy, and R. W. divide the trains which the westerly traveller has to meet into 2 sets, viz., those already on the line, which they (rightly) make " 11," and those which started during her 2 hours' journey (exclusive of train met on arrival), which they (wrongly) make "7"; and they make a similar mistake with the easterly train. Bridget (rightly) says that the westerly traveller met a train every 6 minutes for 2 hours, but (wrongly) makes the number "20"; it should be "21." G. E. B. adopts Bo-Peep's method, but (wrongly) strikes out (for the easterly traveller) the train which started at the commencement of the previous 2 hours. Mary thinks a train, met on arrival, must not be counted, even when met on a previous occasion.

The 3, who are wholly right but for the unfortunate "Clara" theory, are F. Lee, G. S. C, and X. A. B.

And now "descend, ye classic Ten!" who have