Chapter 1 HARD LINES I have been obliged to confide the greater portion of the theoretical part of the present work to some mathematical assistants, whose algebra has, I fear, sometimes risen to a needless luxuriance, and in whose superfine speculations the engineer may perhaps discern the hand of a tyro. Bourne (1846) There are many convincing ways to justify a result. A scientist gathers evidence by undertaking a systematic experiment. One can undertake mathematical experiments, such as a sequence of calculations. Another kind of experiment is to draw a picture, be it on paper or sketched in the sand with a stick. Few, if any,