A terrestrial globe was the text for our next lesson. Assuming its form to be spherical, shift its axis as we might, it was clear that its center remained at rest during rotation in all planes. A hint here as to why the calculations of the astronomer are less difficult than if the planets were of other than globular form, for each orb as affected by gravitation may be practically considered as condensed at its center. Turning from astronomy to navigation, we glanced at the principle of great-circle sailing. On the equator of our terrestrial globe we found the Gillolo Islands and Cape San Francisco. A ship's shortest course plainly lay along the equatorial line which joined them. When I asked which was the shortest route from San Francisco, California, to Figami Island, Japan, the boys concurred in the wrong answer, "Along the thirty-eighth parallel." Taking a brass semicircle equal in diameter to the globe's equator, and applying it so as to touch both places, the lads saw at once that the shortest route would take a ship somewhat toward the north for the first half of her voyage; that if two ports are to be joined by an arc, the largest circle of which that arc can form a part marks out the shortest track; and that this largest or great circle is practically no other than a new equator cutting the earth in a plane inclined to the geographical equator.
By this time about a year had elapsed since our little class in geometry had been formed, and its progress was very satisfactory. The eldest boy was now studying Euclid at a high school and earning high marks for his proficiency. In the lessons I have described, and in others which followed them, all three lads showed their interest by being constantly on the lookout for new illustrations. Let an instance or two of this suffice. One day they walked to an immense sugar-refinery some distance off, paced around it, estimated its height, and brought me their calculations as to its storage capacity in comparison with that of a small warehouse near by; calculations showing how much outer wall and roof were saved in the vast proportions of the refinery. At home an extension of the house was heated in the winter by a small stove; at a neighboring station of the street railway there was a much larger stove of the same pattern. Counting efficiency to depend on surface, one of the boys asked me if it would not be better to have two small stoves instead of that large one. He was perfectly conversant with the reason why steam-fitters make their heating-coils of small pipes, and why their radiators abound in knobs and ridges.
It may be no more than the effect of bias due to an individual preference for the study, but, in the light of its influence on these three young minds, I can not help thinking that geometry affords a most happy means of developing powers of observation and