CLASS LIST.
i.
At Spes Infracta.
ii.
Addlepate.
Problem 2.—L makes 5 scarves, while M makes 2: Z makes 4 while L makes 3. Five scarves of Z's weigh one of L's; 5 of M's weigh 3 of Z's. One of M's is as warm as 4 of Z's: and one of L's as warm as 3 of M's. Which is best, giving equal weight in the result to rapidity of work, lightness, and warmth?
Answer.—The order is M, L, Z.
Solution.—As to rapidity (other things being constant) L's merit is to M's in the ratio of 5 to 2: Z's to L's in the ratio of 4 to 3. In order to get one set of 3 numbers fulfilling these conditions, it is perhaps simplest to take the one that occurs twice as unity, and reduce the others to fractions: this gives, for L, M, and Z, the marks 1, 25, 43. In estimating for lightness, we observe that the greater the weight, the less the merit, so that Z's merit is to L's as 5 to 1. Thus the marks for lightness are 15, 53, 1. And similarly, the marks for warmth are 3, 1, 14. To get the
