On ajixed Unit of Measure. 267 



Lineal measures in former times were often taken from very 

 uncertain materials : — a hair's breadth, a barleycorn, a thumb's 

 breadth, a hand's breadth, a span, a foot, a cubit, a fathom, 

 &c., were all liable to much dissimilarity and variation. 



In traversing natui'e and art, every species of matter tends 

 to alteration and decay. The heights of mountains and peaks 

 are lessened, as well by the gradual disintegration and disrup- 

 tion of their parts, as by the filling up of their conterminous 

 valleys. The pyramids of Egypt are in the same situation. 

 Stone, wood, earth, glass, are liable to change and destruction. 

 Metals oxidize, wear, expand, contract, and are subject to a 

 thousand accidents and uncertainties. In a word, every thing 

 on the earth is in a state of continual mutation and decompo- 

 sition. 



Time, for aught we know to the contrary, is unerring. The 

 planets like the earth are in continual circulation at various 

 vast velocities round tlie centre of their orbits, the sun. We 

 can measure their periodical times ; we can measure our own ; 

 we liuow with almost perfect accuracy the number of seconds 

 the earth takes to perform her annual journey round the sun. 

 It is upon this principle that pendulums, beating true sidereal 

 seconds at a certain latitude, measure 39 inches and a fraction : 

 but does this proposed standard of lineal measure leave nothing 

 further to be desired? 



The French, reasoning on the earth itself being subject to 

 no increase or decrease ol bulk, attempted to measure one of 

 its degrees, and therefrom deduce an unchangeable unit of 

 measure ; but their scheme being on such an extensive scale, 

 performed at so many operations, different times, and by so 

 many persons, was liable to errors in nearly a corresponding 

 proportion. 



The scheme by which I propose, with much deference, to 

 find a fixed unit of measure, is founded on the unchangeable 

 and uniform convexity of the earth, the result of the general 

 law of gravitation. 



In order to make myself completely understood, I shall here 

 quote a passage from some MS. miscellaneous essays written 

 by me a number of years ago. — " Level. That curve or con- 

 vexity which the surl'ace of water at rest assumes, amounting 

 to very nearly 8 inches under the apparent level or straight 

 line, in 1 mile; 32 inches in 2 miles; 72 in 3 miles: 128 in 

 4 miles; 199 in 5 miles; 796 in ten miles; and so on increas- 

 ing in the ratio of 1, 4, 9, 16, 25, &c. ; that is, as the square 

 of the distance. See the Earth." — Here follow various tables 

 and rules for finding the dip necessary in cuttu)g any number 

 of yards or miles of canals, &c. 



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