ON RAISING AND REMOVING WEIGHTS. 165 



city, but undergo a permanent change of form proportional to the loss of 

 force. Hence, in a soft sand, although the axles of the wheels may move 

 in a direction perfectly horizontal, the draught becomes extremely heavy. 

 The more the wheel sinks, the greater is the resistance, and if we suppose 

 the degree of elasticity of the materials and their immediate resistance at 

 different depths to be known, we may calculate the effect of their reaction 

 in retarding the motion of the carriage. Thus, if the materials were 

 perfectly inelastic, acting only on the preceding half of the immersed por- 

 tion of the wheel, and their immediate pressure or resistance were simply 

 proportional to the depth, like that of fluids or of elastic substances, the 

 horizontal resistance would be to the weight nearly as the depth of the 

 part immersed to two thirds of its length ; but if the pressure increased 

 as the square of the depth, which is a more probable supposition, the re- 

 sistance would be to the weight as the depth to about four fifths of the 

 length ; the pressure may even vary still more rapidly, and we may con- 

 sider the proportion of the resistance to the weight as no greater than that 

 of the depth of the part immersed to its length, or of half this length to 

 the diameter of the wheel ; and if the materials are in any degree elastic, 

 the resistance will be lessened accordingly. But on any of these sup- 

 positions, it may be shown that the resistance may be reduced to one half, 

 either by making a wheel a little less than three times as high, or about 

 eight times as broad as the given wheel. This consideration is of parti- 

 cular consequence in soft and boggy soils, as well as in sandy countries ; 

 thus, in moving timber in a moist situation, it becomes extremely advan- 

 tageous to employ very high wheels, and they have the additional con- 

 venience that the timber may be suspended from the axles by chains, 

 without the labour of raising it so high as would be necessary for placing 

 it upon a carriage of any kind. (Plate XVIII. Fig. 227.) 



But the magnitude of wheels is practically limited, by the strength or 

 the weight of the materials of which they are made, by the danger of 

 overturning when the centre of gravity is raised too high, and in the case 

 of the first pair of wheels of a four wheeled carriage, by the inconvenience 

 that would arise, in turning a corner, with a wheel which might interfere 

 with the body of the carriage. It is also of advantage that the draught of 

 a horse should be in a direction somewhat ascending, partly on account of 

 the shape of the horse's shoulder, and partly because the principal force 

 that he exerts is in the direction of a line passing through the point of 

 contact of his hind feet with the ground. But a reason equally strong 

 for having the draught in this direction is, that a part of the force may 

 always be advantageously employed in lessening the pressure on the 

 ground ; and to answer this purpose the most effectually, the inclination 

 of the traces or shafts ought to be the same with that of a road on which 

 the carriage would begin or continue to descend by its own weight only.* 

 In order to apply the force in this manner to both pairs of wheels, where 

 there are four, the line of draught ought to be directed to a point half way 



* Couplet, Reflexions sur le Tirage des Charrettes, Hist, et Mem. de Paris, 

 1733, p. 49, H. 82. Deparcieux sur le Tirage des Chevaux, ib. 1760, p. 263, 

 H. 151. 



