. The Civil engineer and architect's journal, scientific and railway gazette. Architecture; Civil engineering; Science. Let AB and CD be two straight lines, whicli are required to be united by a curve; say for convenience of a mile and a quarter ra- dius, or 100 chains ; by producing the two lines the angle AFD must be ascertained with great exactness ; (tlic angle of its supplement being much less, may be taken with less liability to error). With EC for the radius, the angle CEF may be ascertained, for supposing AFD is 148' â 20', EFC is 74° 10', and therefore CEF is lo° JO'. By this means
. The Civil engineer and architect's journal, scientific and railway gazette. Architecture; Civil engineering; Science. Let AB and CD be two straight lines, whicli are required to be united by a curve; say for convenience of a mile and a quarter ra- dius, or 100 chains ; by producing the two lines the angle AFD must be ascertained with great exactness ; (tlic angle of its supplement being much less, may be taken with less liability to error). With EC for the radius, the angle CEF may be ascertained, for supposing AFD is 148' â 20', EFC is 74° 10', and therefore CEF is lo° JO'. By this means CF & BF will be found '28 ;J6 links, B & C being the commencement of the curve. These points having been measured oH' from F, com- mencing with the odd links, viz. ;3(i, and leaving pegs at every chain, the ordinates may be set off at i ight-anglcs according to a table to be calculated in the following manner, and which will do for any curve of a similar radhis. In the accompanying diagram, EG is the radius. GH is the sine. EH is the co-sine, and HB the versed sine, of the arc BG. Now HB = GF and BF -= GH, therefore the ordinates will be versed lines, where tlie length on the tangent is equal to the sine. Again, HB = EB â HE, and HE=v/EG^âGH-, therefore FG^ EBâv^^G' GH^ ; or, with o for ordinate, /⢠for radius, *â for sine, and V for versed sine; o= râv'r-s-, the table is then calculated thus at every chain. The ordinate at 100 links = 100-00-â»^ â L00= and witii the assistance of " Barlow's Tables of Factors' Roots, &c," a table may be made to any usehd length in a few hours, thusâ again 100 00- â ââ 2 00^ = 100 00' â 10000 0000 _ 1 00" = 1 0000 10000 0000 4 0000 0!)9() 0000 999'J 0000 sq. root of which = 999n-490>S sq. root of wliich = 9997-9998 deducted from 100-=: -oOO'iof a hnk. deductedfroml00-= '2-000-2 To obtain the square root of the above immbers it is convenient to drop the last four figures of o, and alter
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