ON RAISING AKD REMOVING WEIGHTS. 215 



Tiie greater part of the resistance to the motion of a carriage very frequently 

 arises from the continual displacement of a portion of the materials of the road, 

 which do not react on the wheels with perfect elasticity, but undergo a per- 

 manent 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 perfect'ly hori- 

 zontal, 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 car- 

 riage. Thus, if the materials were perfectly inelastic, acting only on the pre- 

 ceding half of the immersed portion of the wheel, and their immediate pres- 

 sure or resistance were simply proportional to the depth, like thatof 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 in- 

 creased 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 

 consider 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 arc in any degree elastic, the resist- 

 ance will be lessened accordingly. But on any of these suppositions, it may be 

 shown that the resistance may be reduced to one half, either by making a wheel 

 a little lessi than three times as high, or about eight times as broad as the given 

 wheel. This consideration is of particular consequence in soft and boggy soils, 

 as well as in sandy countries ; thus, in moving timber in a moist situation, it be- 

 comes extremely advantageous to employ very high wheels, and they have the 

 additional convenience 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. Tig. 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 overturn- 

 ing 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 Avheel which might interfere with the body 

 of the carriage. It is also of advantage that the draught of a horse should be in 



