824 Transactions of the American Institute. 



Now, instead of a heavy mass revolving at the extremity of an arm 

 A B, and acting through a connecting rod upon another equal arm 

 C D, let us suppose an equal mass to have a reciprocating motion along 

 the line OBG, but still to be connected with the arm C D, by a rod, 

 which, as well as the arm, is without gravity. This is the case pre- 

 sented in the engine under consideration ; and if, for the sake of sim- 

 plicity, we suppose that the distance of the reciprocating body from 

 C D is so great that the connecting rod may be regarded as remain- 

 ing sensibly parallel to itself throughout the revolution, it will also be, 

 to all intents and purposes, the case we have just been considering ; 

 except that the force acting in the direction O G, will be to that exerted, 

 radially at C, as radius to cosine 9 simply, and not to cosV- Supposing, 

 therefore, once more, that the angular motion of C D is uniform, the 

 radial strain upon C D (which we may call the crank), as the heavy 

 body or piston approaches the limit of its course, will be, as before, 

 equal to the centrifugal force which the same heavy body would exert 

 if revolving at the extremity, C, of the crank. 



But it does not appear that this circumstance has anything to do 

 with the facility with which the crank of the Allen engine passes 

 the line of the centers. The heavy body has no tendency in itself 

 to return upon its path, no matter what may be the law determining 

 its final strain upon the crank. If, indeed, C D should offer no 

 resistance at all, and if its angular movement should not be controlled 

 by a fly-wheel or other regulator, the heavy body being in the mean- 

 time acted on by a constant force (say pressure of steam), this body 

 would be regularly accelerated up to the end of its course, and would 

 expend its whole living force upon C D, with a violent concussion 

 in the line of the centers ; motion being at the same time totally 

 •arrested. The strain of the heavy piston upon the crank at the 

 close of the stroke has, therefore, no influence in facilitating the pass- 

 age of the centers ; and this is not the circumstance which, in the 

 heavy piston engine, to use the words of Mr. Porter, " strips the dead 

 center of its terrors." The Allen engine really owes the advantage 

 which it enjoys in this respect to the introduction, on the side of the 

 shaft opposite to the crank, of what the constructors call a " counter- 

 poise," equal in weight to the piston and the moving parts connected 

 with it, which counterpoise not only exerts a centrifugal force equal 

 to the opposing strain of the piston on the crank, but also, by its 

 powerful movement of rotation, compels the crank to pass the center 

 with an unchecked velocity of angular movement. To this must be 

 added, in further explanation of the important peculiarity of this 



