774 



The National Geographic Magazine 



Figure 4 



water of the lake. In sighting (C to A 

 on map) at the horizontal line of the 

 standard placed at A, the bar appeared 

 in the field of view projected on the 

 board. The bar did not coincide with 

 the horizontal line, but appeared at the 

 top of the black surface of the board. 

 The view through the telescope is 

 sketched in figure 4. This upheld the 

 expectation with which the experimenter 

 went into the field. The explanation is 

 so obvious as not to need a long disserta- 

 tion. Reference to figure 5, which rep- 

 resents a cross-section of a portion of the 

 earth, may be helpful. The points A', 

 B', and C', which were equally distant 

 above the water surface, may be consid- 

 ered as equal extensions of three radii ; 

 the circumference through A', B', and 

 C is concentric to the earth's circumfer- 

 ence. The chord A'-C must intersect 

 the extended radius BB'. The chord 

 A'— B', extended, will pass out of the 

 circle and cut a still farther extension of 

 CC at C". 



In order to check the experiment an- 

 other standard similar to the one pictured 

 in figure 2 was erected at C. The hori- 

 zontal line was placed at four feet two 

 and one-half inches above the water sur- 

 face. A return was then made to A. 

 The bar at B was inspected and its 

 height measured again, and no change 

 had taken place in its position. At A 

 the height of the horizontal line was 

 measured again, and showed no disturb- 

 ance. From A, a sighting was made on 

 the board at C. The bar again appeared 

 in the field of vision, and again it was 

 projected against the top of the black 

 paper on the board. In returning to A, 

 I had reached the conclusion that inas- 

 much as the distance B-C, 5,660 feet, was 

 greater than the distance A— B, 3,740 feet, 

 the displacement of the bar as seen from 

 A projected on the board at C would be 

 greater than the displacement on the 

 board at A as seen from C. To find the 

 bar projected against relatively the same 

 positions suggested an error in my meas- 

 urements. Each piece of apparatus was 

 measured again, and found to have been 

 at the desired distance above the water. 

 My difficulty was removed on measuring 

 the boards. The black surface of the 

 board placed at C was twelve inches 

 high, while that at A was ten and one- 

 half inches. 



No attempt was made at quantitative 

 work. It is the plan to obtain data for 

 finding the size of the earth. New sta- 

 tions will be selected, and the position of 

 the bar will be located more nearly half 

 way between the terminal points. 



The writer commends a trial of this 

 experiment, wherever conditions permit, 

 to a teacher for a class exercise or to any 

 individual for his own enjoyment. It is 

 simple and it is convincing. 



:j:r: 



Figure 5 



