Last spring one of my students asked how a toilet works, which set me on a course of research that led to the book in the title above. It was found in the West Hartford library and has also recently returned to print (I ordered a copy from Borders). The title evokes smiles and grimaces and the book was a good summer "read." What follows is a summary.

Crapper was born in Yorkshire, England in 1837 and walked 165 miles to London in 1848 to work as a plumber's helper. In 1861 he set up a business as a sanitary engineer, a boom period for plumbers, as London had just completed two main sewers that were extended to 83 miles in the next four years. His main contribution to sanitation was actually in the area of water conservation, as to that point all toilets ran continuously- there was no shut-off valve to stop the water flowing! Consequently, many people simply let the water run instead of shutting off a valve manually after using the facility. While there were shut-off valves of a sort, all eventually leaked and the London Board of Trade's big worry was that reservoirs would run dry supplying water for these "water closets." He and his co-workers also perfected the siphon principle as it was applied to toilets.

As you might imagine, testing these prototypes was a challenge! What they used for "waste" typically consisted of apples, sponges, and "air vessels" (crumpled pieces of paper). The magazine Health, reporting on the toilet-testing activities at the Health Exhibition in 1884, told of a "super flush" which had completely cleared away:

1. 10 apples averaging 1.75" in diameter

2. 1 flat sponge 4.5" in diameter

3. 3 air vessels

4. Plumber's "Smudge" coated over the bowl

5. 4 pieces of paper adhering to the smudge.

This was a record that stood at least until this book was written!

Crapper is also credited with reducing much of the noise associated with the flushing and refilling, as Londoners were actually worried about the effect if someone happened to flush in a nearby toilet precisely when the Queen was to be crowned (apparently many of the aged peers were not able to hold it...)! A test was run where all the toilets near the coronation chamber in Westminster Abbey were flushed simultaneously, and fortunately nothing could be heard in the chamber.

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A standard problem (see Halliday and Resnick) is one where a "tiny bird" flies back and forth between two trains on a collision course, instantly changing direction and maintaining speed throughout. If the trains are initially 100 km apart and moving at 40 km/h and the bird always flies at 60 km/h (!), how far does it fly before the collision if it begins from one train?

Using the fact that the sum of the distances the bird and a train move equals the separation of the trains, 40t + 60t = 100, t = 1 h, and the first flight is x = (60)(1) = 60 km. After 1 h the trains are 20 km apart, and using the same equation the second time is 0.2 h for a bird distance of 12 km. After this second flight the trains are 4 km apart, yielding a time for the third flight of 0.04 h and a flight distance of 2.4 km. At this point the infinite geometric nature of the distances (60 + 12 + 2.4) is noticed and the total distance is given by d = a/(1 - r), where a is the first term and r the ratio, so d = 60/(1 - 0.2) = 75 km.

I have heard the story that the physicist John Wheeler was asked this problem and came up with the answer immediately. When asked if he solved it the "quick" way (the trains collide in 1.25 h and the bird flies at 60 km/h for that time), he replied that he had summed the geometric series!