forces transmitted in the rod, if we suppose these forces to act at the centres of the pins, and introduce two additional forces A+B acting at the wrist pin perpendicular to the centre line of the rod and — (A+B) acting in an opposite direction at the crank pin. The above reasoning may seem to involve a departure from the exact conditions of the problem, in which the forces are really applied in lines tangent to the circles rw sin y and r。 sin y, and it is the object of the paper to demonstrate that two such forces introduced into the solution for frictionless pins will give the correct results when friction is considered. It is shown that Pwf and Per, as well as other forces such as the effort exerted on the crank, may be found with all desirable accuracy by employing the values of A and B found by the following approximate formula: Pr sin and B Pe re sin nR Α DR = For instance in the case of a 10" X 12" horizontal, high speed engine, with the extravagant assumption of 25 % coëfficient of friction, these formulae give A+B within of one per cent. and Pwr and Per will be true within 60 and 1400 of one per. cent respectively. GENERAL SOLUTION OF THE TRANSMISSION OF FORCE IN A STEAM ENGINE, THIS problem has been discussed by various writers at home and abroad but among the numerous contributions to the subject the writer has found none which attempt a general solution, either some limited purpose being kept in view, such as the proper stiffness of the connecting rod, or the forces necessary to accelerate it, or else the problem is restricted in various ways, from fear of making it too complicated, as for instance by unnecessarily simple hypotheses and needless approximations. Further than this some of the solutions are faulty. At the last meeting the writer contributed a special case of this problem for the purpose of giving the correct expressions for the accelerating forces in an ordinary steam engine, and discussing their practical application in various special cases. At that time the general solution, though essentially complete, was not in finished form for publication, the calculations of numerical results in several practical cases are yet to be com pleted which will still further delay the complete publication of the article for a short time. In the general solution of the problem the following conditions must be assumed: (a) that the centre of the crank shaft is not in the line of travel of the wrist pin. (b) that the centre of gravity of the connecting rod is not in its line of centres. (c) that the crank revolves at a uniform speed. (d) that the moving parts have mass. (e) that gravity acts at any angle with the engine. (f) that there is friction between sliding surfaces. Y1 =— m22R { (= = =+ Y2 =—m22R { ( X1 = m22R { (n=1 X2 =m=2R { ( ÷ + X2 託 nyn2-(sin —b)0 cyn2- (sin 0—b)2` n (sin e-b) z) — — sino sino} z)+ sin 0 } K2 ) (cose + "==1Z+ cyn3 — (sin 0—b)2 ) (cos 0+ Ꮓ "=2 2+ sino) — z} [{P2+C—F,—H1+Dsinô—(A+B)sin ß—X ̧ } 8 B] tan ẞ+Y1+D cos ô — (A+B) cos ß 1 Puf = √(Pa + C — F1 —H1 — Gytan ç1)2+G? 1 1 Tƒ= {Pa+C—F1—H1— G ̧tan q1+D sin d—(A+B)sinß—X, secẞsin (0+ß)—Y2 cos 0-X2 sino—(A+B)cos(0+ß)—Ecos (0+8) N=Pa+C-F-H-G'tan ç1+D sin ô—(A+B) sin ẞ—X1} sec ß cos (0+ß)+Y2 sin 0 — X2 cos 0+ (A+B) sin (0+ß)+E sin (0+8) M, W1, and F1 are the mass, weight and accelerating force respectively for the piston, rod, and cross head. m W2, and X1, X2, Y, Y2 are the mass, weight and accelerating forces for connecting rod (1) for wrist pin and (2) for crank pin; also n R its length; c R, the perpendicular from its centre of gravity on its centre line; 1 R, distance of this perpendicular from the wrist pin; KR principal radius of gyration. R is the length of the crank and 7 its angular velocity, and b R a perpendicular from the centre of its shaft upon the path of the wrist pin; being the angle of this path with the horizontal. rw, re are the radii of the wrist and crank pins and tan the coëfficient of friction, tan being that of the cross head. Pa is the total effective pressure of steam; H' friction of the piston and rod; Gf normal guide reaction; Puf and Pef pressures of the wrist and crank pins against the rod; Ny and Tf components of Pef parallel and perpendicular to the crank; Ty' the latter reduced to the centre of the crank pin. THE PANAMA CANAL AS IT IS. By Dr. WOLFRED NELSON, 348 Broadway, New York. [This paper will be published in the author's "Five Years in Panama.”] OFFICERS OF SECTION E. Vice President. GEORGE H. Cook of New Brunswick, N. J. Secretary. JOHN C. BRANNER of Little Rock, Ark. Member of Council. ALEXANDER WINCHELL of Ann Arbor, Mich. Members of Sectional Committee. HENRY S. WILLIAMS of Ithaca, N. Y., C. H. HITCHCOCK of Hanover, N. H., N. H. WINCHELL of Minneapolis, Minn. Member of Nominating Committee. L. E. HICKS of Lincoln, Neb. Members of Sub-committee on Nominations. JOHN J. STEPHENSON of New York, JOHN R. PROCTOR Of Frankfort, Ky., JAMES E. TODD of Tabor, Iowa. |