268 Mr. Boaz on ajixcd Unit of Measure 



To take advantage of tliis spherical curvature for my pie- 

 sent purpose, lay level, at the level of the sea, in a straight line, 

 due east and west, say one mile of cast-iron inch pipe ; let each 

 end hate a knee bending upwards, terminating above ground 

 in a fjiucette or locket, into each of which cement a glass tube : 

 these tubes for distinction's sake I call A and B ; fill the whole 

 length of pipe with some homogeneous fluid, say water, until 

 it rises a few inches in the said tubes. Place a straight piece 

 of brass about 36 inches long, truly level, at the same height as 

 the surface of the water in tube A. In looking along this 

 straight edge, or by means of a level micrometered telescope, 

 the line of vision will lead, not to the surface of the water in the 

 distant tube B, hut 8 inches higher up. This experiment will 

 prove, that the amount of the earth's convexity in 1 mile is 

 8 inches; were the pipe to be 2 miles long, the convexity 

 would be 32 inches; Smiles, 72 inches ; 4? miles, 128 inches; 

 5 miles, 199 inches; 10 miU^s, 796 inches, and so on: any of 

 these inch numbers may be adopted as the unit. I would pre- 

 fer the 72. 



In 1 mile, the unit of 8 inches is found 7920 times. 

 In 2 miles, the unit of 32 inches is found 3960 times. 

 In 3 miles, the unit of 72 inches is found 2640 times. 

 In 4^ miles, the unit of 128 inches is found 1980 times. 

 In 5 miles, the unit of 199 inches is found 1592 times. 

 In 10 miles, the unit of 796 inches is found 796 times. 



It is a curious coincidence, that the earth's convexity in 10 

 miles or 633,600 inches is 66^ feet, or 796 inches : were this 

 last number adopted as the unit, there would be just 796 of 

 them in the 10 miles ; in other words, the convexity is a 796th 

 part of that lineal distance. 



Ho'w to reproduce the Unit, if lost. 



Suppose a person were to be deprived of all kinds of mea- 

 sures whatever ; how could he without them find out the exact 

 length of 6 feet, and the exact distance of 3 miles ? Answer : 

 He would first lay his pipe as near to 3 miles as possible. This 

 he could approximate, by making for himself a wooden fathom 

 measiure or rod the length of his outstretched arms. To prove 

 its correctness, he v/ould place it vertically just above the sur- 

 face of the water in B, to see if from A, at the distance of 

 2640 of these approximated fathoms, his straight line of vision 

 led exactly to the upper end or top of the rod under examina- 

 tion. If it led above its top, then he might be certain that what 

 he had considered as 3 miles was actually more: he would 

 therefore shorten his rod, and measure 2640 lengths of it again. 



On 



