## Saturday 13 June 2020

### Imperial Math

I just dug out a copy of Pendlebury's New School Arithmetic [with answers!] 1924. It was first published in 1904 and reprinted 22 times over the next 2 decades. Must have been a desirable commodity. Looks like the planner at the publishers was not really on the ball. It must be cheaper to set up once, or a few times, and then print enough copies to satisfy demand. Then again, 20 years is a generation of new pupils coming through schools and looking to master compound interest, book-keeping, measurements, foreign exchange and graphs. The publisher certainly wouldn't want to plunge the whole warehouse space on this one book. If another book came out in competition with Pendlebury then the publisher would look a bit silly with stacks and stacks of unsellable stock.

Yes, yes, all very interesting about the economics of early 20thC publishing, but worrabout the 'Rithmetic?  You'd think that arithmetic would be the same as it ever was, since the Egyptians used a 3-4-5 triangle to to make their pyramids square but the past is a different country in ways that transcend the fact that pocket calculators only came on the scene in about 1975. Consider the gratituous difficulty of adding in units which are related by different multipliers. In sensible = decimal = "metric" addition "carries" numbers when they exceed ten. In summing weights, as in the top pictured  example:
• 16 oz = 1 lb [ounces ~ 30 g; pound ~ 450 g)
• 14 lb = 1 st [stone]
• 2 st = 1 qr [quarter]
• 4 qr = 1 cwt [hundredweight which thus weighs 112 lb)
• 20 cwt = 1 [long] ton [which thus weighs 2240 lb or as close a dammit to 1 tonne = 1,000 kg]
Everything is chunked differently! When we bought potatoes in Moore Street market in the 1970s, it was typically as a quarter stone = 3.5 lb = 1.5 kg. Now nobody buys loose potatoes, let alone in such bonkers quantities. I've been here before where you can get help to sort out the second illustrative sum, which involves lengths. Exec.Summ: 12 in ; 3 ft; 22 yd; 10 ch; 8 fur; mile; 1760 yd = 1 mile. And don't get me started on the parallel wonkiverse of Troy weights.

That's not the only difference in a 100 year old arithmetic book. The interests and obsessions are quite different too. In the Problems at the end of the book, Pendlebury tries to relate the theory to practice in real life.
• 83. A besieged garrison have sufficient provisions to last them for 23 weeks at the rate of 18 oz per man per diem; but receiving a reinforcement of 40% on their original number, this allowance is reduced to 15 oz per diem. How many days will they be able to hold out?
• 99. A ship 600 miles from shore springs a leak which admits 6 tons of water in 20 minutes. 60 tons of water would suffice to sink her but pumps can throw out 70 tons in 4 hours. Find her average rate of sailing that she may reach shore just as she begins to sink
• 157. The proprietor of a boarding school having already 30 pupils, finds that an addition of 5 increases his gross yearly expenditure by £300, but diminishes the average cost per head by £1. What did his annual expense originally amount to?
• 194. A rectangular fold is to be made of hurdles 6 ft long, to contain at least 1,000 sheep allowing 8sq.ft per sheep. Find the number of hurdles  needed for the cases where one side of the fold consists of 10, 11, . . . 20 hurdles. Draw a graph shewing the relation between the total number of hurdles and the number on one side. Hence find the smallest number that will suffice.
Lots more where they came from.