768 



PLATE XI. 



Fig., 148. A machine Cor examining tlie strength of 

 materials. The force is applied by means of the 

 winch A, which winds up the rope BC, passing over 

 the first pulley, and under the second, which is directly 

 under the point D, at which the force acts on the piece 

 EFto be broken; the puUies slide on two parallel 

 bars, fixed in a frame, which is held down by a paint 

 projecting at G, from the lever Gil, which is gra- 

 duated 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 wive is to be torn, it may be fixed to be 

 the cross bar LM; and a substance to be crushed 

 must be placed under the lever N O, the end N re- 

 ceiving the rope, and the end O being held down by 

 thejclick, which acts on the double ratchet O P. The 

 leve.r is double from O to Q, and acts on the substance 

 by a loop, fixed to it by a pin. P. 151. 



Fig. 149. The outline of a column diminished one 

 ^fth of its diameter, in two difierent Avays : the side A 

 being an arc of an ellipsis, of which the semidiameter 

 AB is the lesser semiaxis, joined at A to u right line 

 AC, of one third of the length of the column, the 

 part AD being cylindrical; the side D E is a cubic 

 pjiraboU, and may be drawn mechanically by fixing a 

 straight ruler EFjinsuchaposition that DF may be twice 

 the diminution at E, and then bending it to D : the dinii- 

 Qutiofi being every where as the cube of the distance 

 from D. These two methods are compared in a con- 

 tracted scale at G: the outer line represents the first 

 method, and the next line the second ; thq third, 

 which is nearest to, G the conclioid of Nicomedes, re- 

 commended by Chambers, said to be found in the 

 columns of the Pantiicon; the curve beginning at the 

 base. Palladio fixes the ruler at A, and bends it to H> 

 which makes the curvature abruptly greater at II. P. 

 158. 



Fig. 150. A section of Mr. Smeaton's liglit house 

 at the Eddystone. P. 159. 



Fig. 151. Mr. Smeaton's mode of uniting tiers o*^ 

 stones by wooden pins and wedges. P. 160. 



Fig. 152. A string of beads, suspended in equilibrium 

 from two points, and remaining 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 turn 

 ing a pin. P. 161. 



Fig. 153. A system of bars, hanging in equilibrium, 

 and supporting each other in the same form when in- 

 ,,erted. P. 161. 



Fig. 154. A, a chain loaded, at cqu^ 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. 161. 



Fig. 155. A comparison of the curves which have 

 various advantages for the construction of an arch sup- 

 porting a horizontal road. TVie full line is an elliptic 

 arc, somewhat less than half the ellipsis. The outside 

 curve, which is also continued furthest down, is that 

 which iscalculated for resisting tlie pressure of materials 

 acting like a fluid, or in the manner of wedges : the second 

 dotted curve, for supporting the pressure of the mate- 

 rials above each part, supposed to act in a vertical di- 

 rection only: the third" is a circular arc, making one 

 third of a whole circle : the fourth is part of a logarith- 

 mic curve, whicli 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 prac- 

 tice, there would be less difference between the curves. 

 The radius of curvature at the summit being AB, the 

 horizontal thrust is e'qual to the weight of the por- 

 tion A B C D of the materials. 



