Degrees. Versed sine. Motion for 10° Acceleration during 1°. 0° .0000000 _Aa_ .0003046 10° _AB_ .0151922 _AB_ .0151922 _Bb_ .0003001 20° _AC_ .0603074 _BC_ .0451152 _Cc_ .0002862 30° _AD_ .1339746 _CD_ .0736672 _Dd_ .0002638 40° _AE_ .2339556 _DE_ .0999810 _Ee_ .0002332 50° _AF_ .3572124 _EF_ .1232568 _Ff_ .0001958 60° _AG_ .5000000 _FG_ .1427876 _Gg_ .0001523 70° _AH_ .6579799 _GH_ .1579799 _Hh_ .0001041 80° _AI_ .8263518 _HI_ .1683719 _Ii_ .0000529 90° _AJ_ 1.0000000 _IJ_ .1736482 _Jj_ .0000000
The method of obtaining the decimals representing the acceleration for 1°, at any point, was fully explained in the paper, and compared with the similar method of showing the uniform acceleration of a body acted on by a constant force. The ordinary tables in the hand-books, going only to five places of decimals, are of no use for these computations.
I would suggest a practical experiment. Let any one having an engine running at a good speed, loosen the crank pin brasses a little, so that, at starting, it will thump heavily. Let the engine be lightly loaded, so that only a small portion of the boiler pressure will need to be admitted to the cylinder. As its speed increases, the thump will die away; and, if at its full speed, the pressure of the steam admitted is not so great as to overcome the centrifugal strain of the reciprocating parts on the crank, as it passes the centers, the engine will revolve in silence. Any one can ascertain, by the rule given in the note to the paper, just what pressure can be admitted without causing a thump, or this can be found by a little experimenting. I am running an engine which does not thump with loose crank pin brasses, under eighty pounds pressure, admitted sharply on the centers.
MESSRS. EDITORS;--I submit the following solution of "Practical Problem" on page 147:
Given AB, arm, C, arm, D, chord of half angle of oscillation of arm, D, and angles of arms, with line AB.
To find angles, BAc', ABb, and length of link, E.
1. As the length of arm, D, is to the chord of arc, ab, divided by 2, so is the radius to the sine angle oscillation of arm, D, divided by 4.
2. 360° is to the whole circumference as the angle bBa is to the length of arc ab.
4. The whole circumference is to 360° as the length of arc a'e' is to the angle oscillation of C divided by 2.