. The Civil engineer and architect's journal, scientific and railway gazette. Architecture; Civil engineering; Science. 103 THE CIVIL ENGINEER AND ARCHITECTS JOURNAL. [April, parts attnehed. Then, using thfi other letters as before, the moment of impressed forces about A will be P rs'ind — N; P r sin e estimates tlie moment of P correctly, because sin e is nega- tive when the rod descends ; a; the vertical height the rod has risen from its lowest position at time ^—excluding the consideration of its lateral motion by the idea of its lengtli being indp6nitely great. Hence by D'Alembert's princi
. The Civil engineer and architect's journal, scientific and railway gazette. Architecture; Civil engineering; Science. 103 THE CIVIL ENGINEER AND ARCHITECTS JOURNAL. [April, parts attnehed. Then, using thfi other letters as before, the moment of impressed forces about A will be P rs'ind — N; P r sin e estimates tlie moment of P correctly, because sin e is nega- tive when the rod descends ; a; the vertical height the rod has risen from its lowest position at time ^—excluding the consideration of its lateral motion by the idea of its lengtli being indp6nitely great. Hence by D'Alembert's principle, the equation of moment is d- x . , .,,, d- e ,, > P rsin e —N = J»-;^;^rsin e + MA- ^- (1.) But by the geometry dP x-==. r versin ( dl' dx _ dt' de (ft Hence multiplying (1) by ^ we get Integrating C —Prcosfl—Ne=:vJ,«^ + ^MZ:='^ ^" rf«2 rfi And if when 6=0 — = w, dt P versin e — N e = J (m >-2 sin =a + M /;-2) CK-) (2.) Which determines the velocity of the crank for every position. If R denote the reaction at B, R = P-M— (3.) rfi^ But -rT= r Sin 0:77 dt dt : r sm 9 jP r versin e —Na 'm f- sin ^e + M A \ +"=}i from (2.) DifFerentiating with respect to /. , P r versin e — N e , „ \ • • TZ. T cos 9 < •^ 5—-. r . ,, ,., dl- \ mr- sin =9 + M k'- P)-sin9(mrversin29+MF)—N{MF+»ir=(sin=9—9sin2fl)} -j-^rsin9- (mr2 sin 29+MAT Substituing this value of -^ in (3), we have the value of R in terras of 0, &c.; and it will be seen from the exceedingly complicated nature of this expression, even in the simplified form of the problem which we have taken, how remote from the truth is Mr. Pole's as- sumption. We have dealt with this first error thus particularly because, being the basis of every one of the calculations which follow, it totally vitiates them all, and, even if no other error occurred, must condemn the whole paper. But even if this first objection were not fatal, there would be found many others entirely invalidating th
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