. Mathematics, compiled from the best authors and intended to be the text-book of the course of private lectures on these sciences in the University at Cambridge [microform]. arentto the true level at the distance of 1 mile is very nearly 8inches ; therefore, as the square of 1 mile : 8 inches ::the square of any other distance : the correction forcurvature. Note 2. A table of corrections for given distancesmay be easily computed by means of logarithms. For thelogarithm of the diameter of the earth 13953280, ex-pressed in yards, is 7*14468, (more figures being unneces-sary) which being constan
. Mathematics, compiled from the best authors and intended to be the text-book of the course of private lectures on these sciences in the University at Cambridge [microform]. arentto the true level at the distance of 1 mile is very nearly 8inches ; therefore, as the square of 1 mile : 8 inches ::the square of any other distance : the correction forcurvature. Note 2. A table of corrections for given distancesmay be easily computed by means of logarithms. For thelogarithm of the diameter of the earth 13953280, ex-pressed in yards, is 7*14468, (more figures being unneces-sary) which being constantly subtracted from double thelogarithms of the distances, the differences will be the log-arithms of the corrections, expressed in decimal parts of ayard ; which, being multiplied by 36, the number of inch-es in a yard, gives the corrections in inches and decimalsof an inch. J 90 MATHEMATICS. PROBLEM II. To find the level of two places ; or the ascent or decent from one to the other. This is best done with a spirit level, having telescopicsights ; which may be set horizontally by screws, that raiseor lower the ends of the tube ; and station staves, withsliding To take a level from A to I :—let one assistant stand atA and another at C, and at a convenient place, as P, be-tween A and C, place the level, and set it horizontally bymeans o£ the screws. Let the assistant at A hold the staffupright in his hand at A, while from P you look throughthe sights toward A, and direct him to slip the vane up ordown till the white line at B be level with the sights ; thennote AB. Direct the other assistant to stand at C, and tohold the staff upright, then turning the instrument roundat P, and looking toward C, direct him to raise or lowerthe vane till, through the sights, you can see the whiteline at D ; then note the height above the ground, the difference of the heights, AB and CD, is the as-cent or decent with respect to the apparent level, if therebe no other station. But
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