It has been observed, that after the centres of semicircular arches are struck, they settle at the crown and rise up at the haunches ; now, as this shrinking of the arches must be attended with ill consequences, by breaking the texture of the cement after it has been partly dried, and also by open ing the joints of the voussoirs at one end, Dr. Hutton pro posed to remedy this inconvenience, with, regard to bridges, by the arch of equilibration ; and as the ill effect is much greater in powder magazines, he also proposed to find an arch of equilibration for them also ; and to construct it when the span is twenty feet, the pitch or height ten, which are the same dimensions as those of the semicircle, the inclined exterior walls, at top, forming an angle of 113°, and the height of their angular point above the top of the arch equal to seven feet ; this curious question was answered, in 1775, by the Rev. Mr. \Vildbore, and the solution of it may be tound in Ilutton's Miscellanea Mathematic-a.
the beautiful reddish-brown coloured wood, of which household furniture is now chiefly made. It is a native of the warmest parts of America and the West Indies. It thrives in most soils in the tropical climates, but i varies in texture and grain according to the nature of the soil. On rocks it is of a smaller size, but very hard and weighty, of a close grain, and beautifully shaded ; while the produce of the low and richer lands is observed to be more light and porous, of a paler colour, and open grain; and that of mixed soils, to hold a medium of both.
The mahogany-tree is stated to be of very rapid growth, and makes a very line appearance. Its trunk often exceeds 40 feet in length, and 6 feet in diameter. The mahogany is cut down at two periods in the year ; that is, at Christmas, and in the autumn ; the trees art" cut off at about 12 feet from the ground, the workmen having a stage to work upon. The trunk furnishes wood of the largest ; but for ornamental purposes, the branches are i.ref•r able, the grain ill them being closer and the veins more variegated. ?Mahogany was first brought to London in the
tear 1724.
In a dry state, mahogany is very durable. and not subject to worms. It does not last long when exposed to the weather. It is a kind of wood that would make excellent timbers for floors, roofs, but on account of its price its use is chiefly confined to furniture and doors for rooms, for which purposes it is the material most in use. It is sometimes used for sonic Darts of window-frames, and for sashes, but from its not standing the weather well, it is not so lit for these purposes. It has also been extensively used in the framing of machinery for •otton-mills. &e.
The variety called Spanish mahogany, is imported from Cuba, Jamaica, Hispaniola, and some other of the \Vest India islands, and in smaller logs than the Honduras. The size of the logs is in general about 20 to 26 inches square, and about 10 feet in length. The Spanish mahogany is close grained and hard, generally of a darker colour than Honduras; free from black specks, and sometimes strongly figured ; and its pores appear as if chalk had been rubbed into them.
The Honduras mahogany is imported in logs of a larger size, that is, from 2 to 4 feet square, and 12 or 14 feet in length ; sometimes planks have been got 6 or 7 feet wide. The grain of the Honduras kind is generally very open, and often irregular, with black or gray spots. The veins and figures are frequently very fine and showy ; the best kind is that which is most free from gray specks, and of a fine golden colour. It holds with glue better than any other wood.
The cohesive force of a square inch of Spanish mahogany is 7560 pounds. and of Honduras mahogany 11475 pounds.
The weight of the modulus of elasticity of mahogany, is 1,255,500 pounds, for a square inch for Spanish ; and 4,593.000 for Honduras. The weight of a cubic foot of mahogany is front 35 to 53 pounds. Representing the— Strength of oak by 100, that of Span. mahog. is 67 ; of Honduras is 96. Stiffness of oak by 100, 73 ; 93.
Toughness of oak by 100 61 ; 99.