Page:Atreatiseonstea00bourgoog.djvu/113

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EQUATIONS[1]

RULE I.— In such a combination of two levers at it represented in Figs. 1 and 2, to find the length of radius bar required for any given length of lever C G, and proportion of parts of the link, G E and F E, so as to make the point E move in a perpendicular line.

Multiply the length of G C by the length of the segment G E, and divide the product by the length of the segment F E. The quotient is the length of the radius bar.

RULE II.—(Fig. 2.) The length of the radius bar and of C G being given, to find the length of the segment (F E) of the link next the radius bar.

Multiply the length of C G by the length of the link G F, and divide the product by the sum of the lengths of the radius bar and of C G. The quotient is the length required.

Rule III.— (Figs. 3 and 4.) To find the length of the radius bar (F B), the length of C G being given.

Square the length of C G, and divide it by the length of D G. The quotient is the length required.

Rule IV.—(Figs. 3 and 4.) To find the length of the radius bar, the horizontal distance of its centre (H) from the main centre being given.

To this given horizontal distance, add half the versed sine (D N), of the arc described by the end of beam (D). Square this sum. Take the same sum, and add it to the length of the beam (C D). Divide the square previously found by this last sum, and the quotient is the length sought.

RULE V. – (Figs. 5. and 6.) To find the length of the radius bar, C G and P Q being given.

Square C G, and multiply the square by the length of the side rod (P D): call this product A. Multiply Q D by the length of the side lever (C D). From this product subtract the product of D P into C G, and divide A by the remainder. The quotient is the length required.

  1. In formulas (E) (E’) and (F) a is to be taken equal to the horizontal distance of H from the main centre, + EQUATION. In formula (F) the value of EQUATION cannot be accurately ascertained till the value of c has been calculated; but it can easily be taken by approximation, with sufficient exactness for the practical application of the formula.