Line of Draught of Plows. 173 



of resistance, the resistance of the ploAv would be 390 pounds 

 instead of 407 pounds. 



THE WHEEL. 



It is not difficult to show that, theoretically considered, a wheel 

 placed under the beam can in no case lessen the traction of the 

 plow, as many plowmakers and plowmen have alleged. 



Let us suppose that the line of draught is in the horizontal 

 direction; it will therefore require that a support be placed 

 beneath the beam to prevent its sinking too low, which support, 

 in all modern plows, is given by a wheel. It has been shown 

 that whether the plow be drawn in the ordinary direction of 

 draught, b f, in which one oblique propelling force only is 

 exerted, or with two antagonist forces, b i, in the horizontal direc- 

 tion, and the upholding force, b k^ in the vertical, we find that in 

 the latter the diiference in favor of motive force is only one 

 twenty-fourth of the usual resistance; but the upholding force is 

 equal to two-sevenths, while none of these variations has pro- 

 duced any change in the absolute resistance of the plow. The 

 impelling force is theoretically less in the latter case; but since 

 the wheel has a load of 107 pounds to carry, we have to consider 

 the efiect of this load upon a small wheel, arising from friction 

 and the resistance it will encounter by sinking more or less into 

 the subsoil. 



Mr. Stephens has ascertained from experiment that the differ- 

 ence of force required to draw a wheel twelve inches in diameter, 

 loaded as above described, and again when unloaded, over a tol- 

 erably firm soil, is equal to 22 pounds, a quantity exceeding one 

 and a half times the amount of saving that would accrue by adopt- 

 ing this supposed horizontal draught with a wheel. Having thus 

 found the amount of draught at two extremities of a -scale, the 

 one being the oblique draught, in common use, at an angle of 20 

 deg., the other deduced from this through the medium of the 

 established principles of oblique forces, and the latter producing 

 a saving of one twenty-fourth of the motive force while it is 

 encumbered with an additional resistance arising from the support 

 or wheel. It necessarily follows that at all intermediate angles 

 of draught, or at any angle whatever where the principle of 

 the parallelogram of forces finds place — and it will find place 

 in all cases where wheels yielding any support are applied to the 

 plow under the beam — there must necessarily be an increase in 



