767 



PLATE X. 



Fig. 121. The mannci- in which a prismatic column 

 h crushed by pressure, supposing tlic hiteral adhesion 

 to be simply proportional to the surface concerned. 

 P. 1-1(3. 



I'ig. 125. The manner in nhicli a. column is crush- 

 ed, supposing the lateral adhesion to be increased by 

 pressure. P. llti. 



rig. I'i6. The circle is as strong as the circumscrib- 

 ing square, supposing the adiiesion proportional to 

 the surface, tlie relative force of all its chords being 

 equal. P. 116. 



Fig. 127. The three circles are as strong as the cir- 

 cumscribing parallelogram. P. 146. 



Fig. 128. A, the strongest form for a beam, cut out 

 ofa plank of uniform depth, for resisting a longitu- 

 dinal force; U, the form mto which it is bent; both 

 curves being circular. P. 150. 



Fig. 129. A, the strongest form for a beam cut out 

 of a plank of ecpiablo breadth, for resisting a longitu- 

 dinal force which beads it into llie cycloidal cun'e 

 seen at B. P, 150. 



Fig. 130. A, the strongest form for a square or turn- 

 ed beam or column, slightly bent by a longitudinal 

 force:, U, the form into which it is bent by such a 

 force. P. 150. 



Fig. 131. The strongest form of a beam cut out of 

 ft horizontal plank, fixed at one end, and supporting a 

 weight at die other. P. 1 50. 



Fig. 132. The strongest form of a beam cut out of 

 a vertical plank, fixed at one end, and supporting a 

 weight at the other; the outline being parabolic. In 

 practice the best method in such a case would be 

 simply to reduce the depth at the end to one half of 

 the whole, keeping the outline straight; in this 

 manner one fourth of the timber would he saved. P. 

 150. 



Fig. 133. Tlie strongest form of a square or turned 

 beam, fixed at one end, and supporting a weight at 

 the other; the outline being a cubic parabola. P. 

 150. 



Fig. 134. The sU'ongest form for the outline of a 

 compound spring, supporting a weight at the end. 

 P. 150. 



Fig. 135. The strongest form for a beam cut out of 

 a horizontal plank, fixed at one end, and supporting 

 a weight equally distributed throughout its length ; 

 the outline being a parabola. P. 150. 



Fig. 136. The strongest form for a beam cut out of 

 * ycrtical plank, fixed at one end, and supporting a 



weight equally distributed throughout its length. P. 

 150. 



Fig. 137. The strongest form for a square or turned 

 beam, fixed at one end, and supporting a weight equally 

 distributed throughout its length; the outline being 

 a seniicubic parabola, in which the cube of the thick- 

 ness is as the square of the distance from the end. 

 P. 150. 



Fig. 133. The strongest form for a beam cut out 

 of a vertical plank, for supporting its own weight; the 

 outline being a parabola. P. 150. 



Fig. 139. The strongest form for a turned beam, 

 for supporting its own weight; the outline being para- 

 bolic. P. 15<1. 



Fig. 140. The strongest form of a beam calculated 

 to resist the pressure of its own weight by lateral ad- 

 hesion only. The outline is a logarithmic curve, 

 which iKjver comes into contact with the axis, and ia 

 order that the condition of equal strength may be 

 possible, the beam must be loaded with a weight, at 

 Its extremity, qqual to that of the portion which is 

 wanting to complete the figure. P. 150. 



Fig. 141. The strongest form for a beam cut out of 

 a horizontal plank, supported at both ends, and bear- 

 ing a weight at the middle. P. 150. 



Fig. 142. The strongest form for a beam cut out of 

 a horizontal plank, supported at both ends, and bear- 

 ing a weight equally distributed throughout its length; 

 the outhoe being p.vabolic. P. 150. 



Fig. 143. The strongest form for a beam cut out 

 of a vertical plank, supported at both ends, and bear- 

 ing a weight equally distributed throughout, the ouC- 

 liiie being elliptic. P. 150. 



Fig. 144. The strongest form for a beam cut out of 

 a horizontal plank, firmly fixed at both ends,'and sup- 

 porting a weight at the middle. P. 150. 



I'ig. 145. ihc strongest form for a beam cut out of 

 a vertical plank, firmly fixed at both ends, and sup- 

 porting a weight at the middle, the curves being pai- 

 rabolic. P. l.iO. 



Fig. 146. The strongest form for abeam cutout of 

 a vertical plank, and supporting every where a weight 

 proportional to tlie distance from the extremity : the 

 outline being a cubic parabola. P. 150. 



Fig. 14T. 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. 150. 



