CATALOGUE. PHILOSOPHY AND ARTS, PRACTICAL MECHANICS, 173 



P. Nichoko7i's principles of architecture. 3 v. 



8. 1795. R.I. 



The plates by Lowry. Chiefly on architectural drawing. 

 Labauuie, Lamblardie, and Ballard on ar- 



cbitecture. Journ. Polyt. I. i. 15. ii. 124. 



iv. 577. 

 Prony on the declination of the columns of 



the Pantheon. B. Soc. Phil. n. 57- 

 Sammlung die baukunst betreffcnd. Berlin. 

 Hall on Gothic architecture. Ed. tr. IV. ii.3. 

 B'dsch Practische darstellung der bauwissea- 



schafi. 2 V. 8. Hamb. 1800. R. I. 

 Rees's cyclopaedia. I. II. 



Beautiful plates. 



Columns and Walls ; their strongest 

 forms. 



See Hydraulic Pressure. 



Blondel on the diminution of columns. A. P. 

 . V. ii. 7. 

 Couplet on the thrust of earth against walls. 



A. P. 172Q. 

 Euler on the strength of columns. A. 



Berl. 1757. 252. A. Petr. II. i. lai. 14(3. 



163. 

 Lambert on the fluidity of sand and eartli. 



A. Berl. 1772. 33. 

 Lorgna on the resistance of walls to the 



pressure of earth. A. Sien. II. 155. 

 Emerson's mechanics. 



Does not sufficiently consider the compressibility. 



Belidor on the thickness of walls. Arch. 



hydr. IT. i. 420. 

 *Coulomb. S. E. VII. 

 Lagrange on the figure of columns. M. Tur. 



V. ii. 123. 



Refers the resistance to flexure ; makes a cone stronger 

 than any conoid ; but a cylinder the strongest form of all. 



Account of a memoir on the pressure of 

 earth. N. A. Petr. 175)3. XI. H. 3. 



Girard Traite de la resistance des solides, 

 et des solides d'egale lesistance. 



Contains a general determination of the strongest forms. 



Lambton on the theory of walls. As. res. VI. 



93. 

 Prony on the lateral pressure of earth. B. 



Soc. Phil. n. 24. 

 Front/ surla poussee des terres. 4. Par. 1802. 



R. S. 

 Prony sur les murs de revctement. 4. Par. 



1802. R. S."- 



The strongest form of a substance included by horizon- 

 tal surfaces, or cut out of a horizontal plank, for supporting 

 a weight at its extremity, is that of a triangle. The same 

 form is also the stiffest. For supporting a weight distribut- 

 ed uniformly throughout its length, the form must be that 

 of a parabola, with its convexity turned inwards. 



For a vertical plank, bearing a weight at its extremity, 

 the strongest and stiffest form- is thatof a common parabola, 

 with its convexity outwards. If the weiglit is equally di- 

 vided, it must be a triangfe. To support its own weight, 

 it must have for its outline a common parabola, with its 

 convexity inwards. If such a plank were supported by its 

 lateral adhesion only, its outline must be a logarithmic 

 curve, to sustain its own weight. 



A horizontal column turned in a lathe, or having all its 

 transverse sections similar, must have its outline a cubical 

 parabola, convex outwards, in order to support the greatest 

 weight at its extremity. The same form is also the stiffest. 

 To support a weight equally distributed through the length, 

 the curve must be a semicubical parabola. To support its 

 own weight, the outline must be a common parabola, con- 

 vex towards the axis, having its vertex at the extremity. 



A triangular prism fixed at one end, with its edge upper- 

 most, is weaker than if its depth were reduced to ei-'lit 

 ninths, by cutting away the edge. With, a certain force, 

 such a beam would crack at its edge, and not break off. 



If a beam, cut out of a vertical plank, be supported at 

 both ends, and bear a weight at any one given point, its 

 portions must be bounded by two common parabolas. If 

 the weight be equally applied throughout the length, or If 

 it be applied at a point variable at pleasure, the outline must 

 be an ellipsis. 



If a beam, supported at both ends, have all its transverse 



