. Locomotive engineering : a practical journal of railway motive power and rolling stock . Fig. I. a tapered course or the frustum of a rightcone. Rule.—Divide the circumference of thelarge end by the difference between^ thelong and short circumference and multi-ply the result by the length of the frus-tum; the result will be the length of theperpendicular. For the difference between the long andshort circumference in the foregoingexample we have — 1539384 =, and for the perpendicular we have,by simple proportion: : :: 40 : 2,000. To find the versed sine of the larg
. Locomotive engineering : a practical journal of railway motive power and rolling stock . Fig. I. a tapered course or the frustum of a rightcone. Rule.—Divide the circumference of thelarge end by the difference between^ thelong and short circumference and multi-ply the result by the length of the frus-tum; the result will be the length of theperpendicular. For the difference between the long andshort circumference in the foregoingexample we have — 1539384 =, and for the perpendicular we have,by simple proportion: : :: 40 : 2,000. To find the versed sine of the large end,divide the square of one-half the long. ilttfniccrfitf Fig. 3. circumference by twice the length of theperpendicular. For the versed sine of the small the square of one-half the shortcircumference by twice the length of the November. i8g8. LOCOMOTIVE ENGINEERING. 523 perpendicular, minus tlie length of thefrustum. For convenience let Us put the rules inthe form of formulas, using the lettersmarked on Fig. 3. Let A = one-fourth the long circum-ference. b ^ one-half the short circumference. B ^ one-half the long circumference. C := the long circumference. c = the short circumference. /- ^ length of frustum. P =: perpendicular of large triangle. /> =: perpendicular of small triangle. R = radius of arc of large end. p ^ versed sine of line C. i; r; versed sine of line c. .r:= distance from the line C to thearc on the quarter. p = P - L R = \/B + P i P~- _ b^ = \/ R Then P ■■ L ■ slR - : P+ y B v =. R - P 3,.^ I D F JK \\ \ - > r \ \° V e\ f \. =/ \ \ / / \ ^\~ / 6/ 7< \ \ / / -■J / V^1t\ ^ 7A
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Keywords: ., bookcentury1800, bookdecade1890, bookidlocomotiveen, bookyear1892
