A GROIN, is the excavation nr hollow formed by one simple vault piercing another at the same height, such, that two geometrical solids being transversely applied one after the other ; a portion of the groin may love been in contact with the first solid, and the remaining part in contact with the second solid, when the first is removed. The most usual kind of groining is one cylinder piercing another, or a cylinder or cylindroid piercing each other, having their axes at right angles.
A multangular groin, is that which is formed by three or more simple vaults piercing ach other at the same height, so that if the several 'nlids which form each simple vault be respectively applied, only one at a time, to succeeding portions of groined surface, every portion of the groined surface will have formed successive contact with certain corresponding portions of each of the solids A rectangular groin, is that which has the axes of the simple vaults in two vertical planes, at right angles to each other.
An cqui-angular groin, is that in which the several axes of the simple vaults form equal angles, around the same point, in the same horizontal plane.
The axis of each simple vault forming the intrados of a groin, is the same with the axis of the geometrical solids, of which the intrados of the groin is composed.
When the breadths of the cross passages, or open ings of a groined vault, are equal, the groin is said to be equilateral.
AneuEs are also formed by one simple vault piercing another, after the same manner as groins.
Arches have various names, according to the sur faces of the two geometrical bodies, which form the simple vault.
A cylindric arch, is that which is formed by the inter section of one portion of a cylinder with another.
A cylindroidic arch, is that which is formed by the intersection of one portion of a cylinder with another.
A spheric arch, is that which is formed by the inter section of one portion of the spherC with another.
A conic arch, is that which is formed by the intersection of one portion of a cone with another.
The species of every arch, formed by the intersection of two vaults of notqual heights, is denoted by two preceding words, the former of which ending in o, indi cates the simple vault, which has the greater height, and the latter, ending in ic, indicates the simple vault of the less height.
Find the curve line n o ji q, which corresponds to the semicircumference of the semicircle, as in the last prob lem, the straight line aiklin being a tangent, and paral lel to the chord on the concave side ; make all the dis tances b f, cg, d h, &c. respectively equal to in, ko, &c.; draw the curve efg h and it will be the edge of the envelope, which will have enop q, &c. for its seat ; and if f s be made equal to n -o, g t equal to o h u equal to q y, and the curve r s t u, &c. being drawn, will give the other edge of the envelope, which will have the arc v w x y, &e. for its seat.
These two last problems arc exceedingly useful in all kinds of arched work that is circular on the plan, the in tradoses of the arches splaying on the sides and level at the crown, particularly in sash work : but it is to be re gretted, that no accurate method for finding the envelope has yet been discovered; every attempt to greater accu racy than the above has been foiled. There is one me thod, however, that will give the envelope, or veneer, exactly true, by the use of a centre, and describing the lines on its surface the same manner as in plans, then ap plying the equal distances from the seats from a gra duated pole, which is the vertex of the cunioid, that is, by making the distances equal to p q, v 2u, &c. Fig. 11. or by drawing the equal ordinates on the ends of the cen tre, and joining the level lines, and taking all the dis tances from their seats.
Constructive Carpentry.
When an arch is formed by the intersection of two unequal cylindric vaults, it is called a cylindro-cylindric arch.