MY CLASS IiV GEOMETRY. 47 



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 con- 

 sidered 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 ware- 

 house 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 



