xii DESCRIPTION OF PLATES. 



PLATE X. 



Fig. 124. The manner in which a prismatic column is crushed by pressure, sup- 

 posing the lateral adhesion to be simply proportional to the surface concerned. P. 112. 



Fig. 125. The manner in which a column is crushed, supposing the lateral ad- 

 hesion to be increased by pressure. P. 112. 



Fig. 126. The circle is as strong as the circumscribing square, supposing the 

 adhesion proportional to the surface, the relative force of all its chords being equal. 

 P. 113. 



Fig. 127. The three circles are as strong as the circumscribing parallelogram. P. 1 13. 



Fig. 128. A, the strongest form for a beam, cut out of a plank of uniform depth, 

 for resisting a longitudinal force ; B, the form into which it is bent ; both curves 

 being circular. P. 116. 



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

 breadth, for resisting a longitudinal force which bends it into the cycloidal curve 

 seen at B. P. 116. 



Fig. 130. A, the strongest form for a square or turned beam or column, slightly 

 bent by a longitudinal force : B, the form into which it is bent by such a force. P. 116. 



Fig. 131. The strongest form of a beam cut out of a horizontal plank, fixed at 

 one end, and supporting a weight at the other. P. 116. 



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 be saved. P. 116. 



Fig. 133. The 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. 116. 



Fig. 134. The strongest form for the outline of a compound spring, supporting 

 a weight at the end. P. 116. 



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. 116. 



Fig. 136. The strongest form for a beam cut out of a vertical plank, fixed at 

 one end, and supporting a weight equally distributed throughout its length. P. 116. 



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 semicubic parabola, in which the cube of the thickness is as the square of the 

 distance from the end. P. 116. 



Fig. 138. The strongest form for a beam cut out of a vertical plank, for sup- 

 porting its own weight ; the outline being a parabola. P. 116. 



Fig. 139. The strongest form for a turned beam, for supporting its own weight ; 

 the outline being parabolic. P. 116. 



Fig. 140. The strongest form of a beam calculated to resist the pressure of its 

 own weight by lateral adhesion only. The outline is a logarithmic curve, which 

 never comes into contact with the axis, and in order that the condition of equal 

 strength may be possible, the beam must be loaded with a weight at its extremity, 

 equal to that of the portion which is wanting to complete the figure. P. 116. 



Fig. 141. The strongest form for a beam cut out of a horizontal plank, sup- 

 ported at both ends, and bearing a weight at the middle. P. 116. 



Fig. 142. The strongest form for a beam cut out of a horizontal plank, sup- 

 ported at both ends, and bearing a weight equally distributed throughout its length ; 

 the outline being parabolic. P. 116. 



Fig. 143. The strongest form for a beam cut out of a vertical plank, supported 

 at both ends, and bearing a weight equally distributed throughout, the outline being 

 elliptic. P. 116. 



Fig. 144. The strongest form for a beam cut out of a horizontal plank, firmly 

 fixed at both ends, and supporting a weight at the middle. P. 116. 



Fig. 145. The strongest form for a beam cut out of a vertical plank, firmly 

 fixed at both ends, and supporting a weight at the middle, the curves being para- 

 bolic. P. 116. 



Fig. 146. The strongest form for a beam cut out of a vertical plank, and sup- 



