. Haswell's engineers' and mechanics' pocket-book ... ength. LENGTH OF AN ELLIPTIC ARC. 77 Note.— When great accuracy is required, if, in the division of a height by thebase, there should de a remainder. Find the lengths of the cuives from the two nearest tabular heights, and sub-tract the one length from the other. Then, as the base of the arc of which thelength is required is to the remainder in the operation of division, so is the differ-ence of the lengths of the curves to the complement required, to be added to thelength. Example.—What is the length of an arc of a circle, the base of whic


. Haswell's engineers' and mechanics' pocket-book ... ength. LENGTH OF AN ELLIPTIC ARC. 77 Note.— When great accuracy is required, if, in the division of a height by thebase, there should de a remainder. Find the lengths of the cuives from the two nearest tabular heights, and sub-tract the one length from the other. Then, as the base of the arc of which thelength is required is to the remainder in the operation of division, so is the differ-ence of the lengths of the curves to the complement required, to be added to thelength. Example.—What is the length of an arc of a circle, the base of which is 35 feetand the height or versed sine 8 feet 1 * 8-^35 =.228|5, .228 = , .229 = , = , , — = .0385, difference of lengths. Hence, as 35 : 20 : : .0385 : .0220, the length for the remainder, and . = , and .6875X12, for inches = 8^ making the length of the arc 39feet 84: inches. To find the length of an Elliptic Curve which is less than halfof the entire Figure,. Geometrically.—Let the curve of which the length is required he the versed sine hd to meet the centre of the curve in the line ce, and from e, with the distance eb, describe bh; bisect cA in e,and from e, with the radius e i, describe k i, and it is equal half the arc a be. To find the length when the Curve is greater than half the entireFigure* Rule.—Find by the above problem the curve of the less portion of the figure,and subtract it from the circumference of the ellipse, and the remainder will be thelength of the curve required. G2 78 LENGTHS OF SEMI-ELLIPTIC ARCS. Height. Table of the Lengths of Semi-elliptic Arcs. Lenstli. Height. ) Length. Height. Length. Height. Length. .100 .101 .102 .103 .104 .105 .110 .115 .120 .125 .130 .135 .140 .145 .150 .155 .160 .165 .170 .175 .180 .185 .190 .195 .200 .205 .210 .215 .220 .225 .230 .235 .240 .245 .250 .255 .260 .265 .270 .275 .280 .285 .290 .295 .300 .305 .310 1.


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