THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



[Januabv, 



Ex. — Suppose the diameter of a locomotive wheel is 6 feet ; re- 

 quired the transverse and conjugate diameters of its isometrical 

 projection. 



Here 6 X 1 "408 = 8-448 = the transverse diameter, F B 

 G X -365 = 2-190 = the conjugate diameter, C G. 

 When the angle H B C is 30°, then the rule in last article applies. 

 It appears, therefore, that the ellipse in last article is the isometri- 

 cal projection, both of a vertical and a liorizontal circle, when the 

 angles C F (i and C B G are each 30°. But when the angle H B C 

 =: 60°, then the elliipse, as alluded to in this article, is the isome- 

 trical projection of a vertical circle. 



E 



Fig. 2. Fig. .1. 



Sometimes it is necessary to find the isometrical representation 

 of an ellipse, in the case of an elliptical form of buildings. In 

 such case, when the transverse and conjugate diameters of the 

 ellipse are given, the given ellipse must be circumscribed with the 

 rectangle A B D C (fig. 2), and then its isometrical representation 

 dra%vn as in fig. 3. Bisect aft in c, and erf in/; draw c/ parallel 

 to C A, and then the curve along the oblique axes can be drawn 

 with a trammel. It will be also proper to remark that the curve 

 has two pair of foci. 



As many buildings are often requii-ed to be erected in the form 

 of regular pentagons and hexagons, it would be desirable to ex- 

 hibit some ways of drawing the isometrical representation of the 

 two polygons. 



I. First, with respect to the Pentagon : it is a form usually re- 

 quired in permanent fortification, especially in citadels. In this 

 case, I shall give some numbers to enable any one to draw its iso- 

 metrical representation in the most commodious form. Let 

 A B C D E (fig. 4) be the isometrical representation of a pentagon ; 

 let A B be considered as unity : then will the whole height D F = 

 -889 ; F H = -398 ; E H or H C = -810; the semi-conjugate dia- 

 meter of circumscribing ellipse = -49, and the semi-transverse = 

 -89. By means of these numbers, we can easily draw the isome- 

 trical representation of the polygon when its side is given. The 

 circumscribing ellipse is not required, but only the semi-conjugate 

 DO, to determine the centre O, where all the corresponding ra- 

 diating lines in the original figure must be drawn thereto. With 

 regard to tlie making an isometrical representation of a fortifica- 

 tion, as Vauban's First System, or of Cormontaigne's Modern Bas- 

 tion system, in the form of a regular pentagon, it is only necessary 

 to multiply the above numbers by 180, and then will be given the 

 number of times in lengtb of the constructive lines of the isome- 

 trical representation. 



Fig. 4. > Fig. 5. 



II. Tlie Hexagon is commonly required, as being of a most con- 

 venient form for prisons, workhouses, &c., and can be easily drawn 

 by a common-set square of 45°, as in fig. 4. First of all draw the 

 front side A B, and construct a square ABEF, and then complete 

 the remainder of the figure with the square, as before mentioned. 

 The method of construction is clearly elucidated by fig. 5. Al- 

 though the ellipse is exbibited, yet its representation is not neces- 

 sary. Any other isometrical projection, as making it an angle of 

 30°, would be extremely tinsigbtly. This method of projecting 

 would, in many cases, be very convenient in drawing the nuts and 

 liolts of machinery, when exhibited isometrically. Tlie above 

 metliod could be easily proved geometrically, but it was deemed 

 quite unnecessary to enter on so simple a matter. 



THE GIANTS' STAIRCASE, VENICE. 



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The celebrated Giants' Stairs, Ducal Palace, Venice (named from 

 the two colossal statues, by Sansovino, of jMars and Neptune on its 

 summit), is formed out of the beautiful wliite marble of Carrara, 

 and deservedly admired on account of the splendid effect of the 

 material, as also the art tliat has been displayed in its decoration. 

 Witli great taste, jjurple (or roswo) marble is intermixed with the 

 white in the s(iuare panellings into wldch its flanks are divided. 

 From tlie exterior surfaces, beneath its perforated parapets, the 

 annexed engraving is a sketch of one single slip of the sculpture, 

 as an example of the Imstii-rt'/ievi of this interesting structure. It 

 appears that when originally planned, and when the sculptor 

 worked upon it, no pains were spared, and no expense grudged, 

 in making this ascent a fit, appropriate, and worthy approach to 



