DESCRIPTION OF PLATES. xiii 



porting every where a weight proportional to the distance from the extremity ; the 

 outline being a cubic parabola. P. 116. 



Fig. 147. The strongest form for a square or turned beam, supporting every 

 where a weight proportional to the distance from the extremity, and represented by 

 the section of the same figure, which is a pyramid or a.cone. P. 116. 





PLATE XL 



Fig. 148. A machine for examining the strength of materials. The force is 

 applied by means of the winch A, which winds up the rope B C, passing over the 

 first pulley, and under the second, which is directly under the point D, at which the 

 force acts on the piece E F to be broken ; the pullies slide on two parallel bars, 

 fixed in a frame, which is held down by a point projecting at G, from the lever G H, 

 which is graduated like a steelyard, and measures the force. The piece to be broken 

 is held by a double vice, I, K, with four screws, two of them hiding the other two 

 in the figure : if a wire is to be torn, it may be fixed to the cross bar L M ; and 

 a substance to be crushed must be placed under the lever N O, the end N receiving 

 the rope, and the end O being held down by the click, which acts on the double 

 ratchet O P. The lever is double from O to Q, and acts on the substance by a loop, 

 fixed to it by a pin. P. 116. 



Fig. 149. The outline of a column diminished one fifth of its diameter, in two 

 different ways : the side A being an arc of an ellipsis, of which the semidiameter 

 A B is the lesser semiaxis, joined at A to a right line A C, of one third of the length 

 of the column, the part A D being cylindrical ; the side D E is a cubic parabola, 

 and may be drawn mechanically by fixing a straight ruler E F, in such a position 

 that D F may be twice the diminution at E, and then bending it to D : the dimi- 

 nution being every where as the cube of the distance from D. These two methods 

 are compared in a contracted scale at G : the outer line represents the first method, 

 and the next line the second ; the third, which is nearest to G, the conchoid of 

 Nicomedes, recommended by Chambers, said to be found in the columns of the 

 Pantheon ; the curve beginning at the base. Palladio fixes the rule at A, and bends 

 it to H, which makes the curvature abruptly greater at H. P. 122. 



Fig. 150. A section of Mr. Smeaton's light house at the Eddystone. P. 122. 



Fig. 151. Mr. Smeaton's mode of uniting tiers of stones by wooden pins and 

 wedges. P. 123. 



Fig. 152. A string of beads, suspended in equilibrium from two points, and re- 

 maining in equilibrium in an inverted position. The ends are supported by two 

 pieces, which slide backwards and forwards, and are fixed by screws : the string is 

 also tightened by turning a pin. P. 154. 



Fig. 153. A system of bars, hanging in equilibrium, and supporting each other 

 in the same form when inverted. P. 154. 



Fig. 154. A, a chain loaded, at equal distances, with other chains of such a 

 length, as to represent the depth of the materials pressing on an arch of the form 

 shown by the first chain, and holding it in equilibrium. B, an arch of a similar 

 form. P. 154. 



Fig. 155. A comparison of the curves which have various advantages for the 

 construction of an arch supporting a horizontal road. The full line is an elliptic 

 arc, somewhat less than half the ellipsis. The outside curve, which is also con- 

 tinued furthest down, is that which is calculated for resisting the pressure of materials 

 acting like a fluid, or in the manner of wedges; the second dotted curve, for sup- 

 porting the pressure of the materials above each part, supposed to act in a vertical 

 direction only ; the third is a circular arc, making one third of a whole circle ; the 

 fourth is part of a logarithmic curve, which is nearly of equal strength with re- 

 spect to the tendency of the materials to give way for want of lateral adhesion ; and 

 the fifth is composed of parabolic curves, showing the outline which would be 

 strongest for supporting any additional weight placed on the middle of the arch. 

 If the height were greater in proportion to the span, as usually happens in practice, 

 there would be less difference between the curves. The radius of curvature at the 

 summit being A B, the horizontal thrust is equal to the weight of the portion 

 A B C D of the materials. P. 125. 



