PERSPECTIVE. 



485 



three principal dimensions on the same scale, we de- 

 nominate " Isometrical,' 1 will be understood from 

 the following detail : 



Suppose a cube to be the object to be represented. 

 The eye placed in the diagonal of the cube produced. 

 The paper, on which the drawing is to be made to 

 be perpendicular to that diagonal, between the eye 

 and the object, at a due proportional distance from 

 each, according to the scale required. Let the dis- 

 tance of the eye, and consequently that of the paper, 

 be infinitely increased, so that the size of the object 

 may be inconsiderable in respect of it. 



It is manifest, that all the lines drawn from any 

 points of the object to the eye may be considered as 

 perpendicular to the picture, which becomes, there- 

 fore, a species of orthographic projection. It is 

 manifest, the projection will have for its outline an 

 equiangular and equilateral hexagon, with two ver- 

 tical sides, and an angle at the top and bottom. The 

 other three lines will be radii drawn from the centre 

 to the lowest angle, and to the two alternate angles; 

 and all these lines and sides will be equal to each 

 other both in the object and representation: and if 

 any other lines parallel to any of the three radii 

 should exist in the object, and be represented in the 

 picture, their representations will bear to one another, 

 and to the rest of the sides of the cube, the same 

 proportion which the lines represented bear to one 

 another in the object. 



If any one of them, therefore, be so taken as to 

 bear any required proportion to its object, e. g. 1 to 

 8, as in my representations of my models, the others 

 also will bear the same proportion to their objects ; 

 that is, the lines parallel to the three radii will be 

 reduced to a scale. 



We omit the demonstration of this, and some other 

 points, partly for the sake of brevity, and partly 

 because a geometrician will find no difficulty in de- 

 monstrating them himself, from the nature of ortho- 

 graphic projection; and a person, who is not a geo- 

 metrician, would have no interest in reading a de- 

 monstration. 



For the same reason, it is unnecessary to show 

 that the three angles at the centre are equal to one 

 another, and each equal to 120 degrees, twice the 

 angle of an equilateral triangle ; and the angle con- 

 tained between any radius and side is sixty degrees, 

 the supplement of the above, and equal to the angle 

 of an equilateral triangle. 



In models and machines, most of the lines are 

 actually in the three directions parallel to the sides 

 of a cube, properly placed on the object. And the 

 eye of the artist should be supposed to be placed at 

 an indefinite distance, as before explained, in a dia- 

 gonal of the cube produced. 



The last mentioned line may be called the line of 



Let a certain point be assumed in the object, as 

 for example, C, fig. B, and be represented in the pic- 

 ture, to be called the regulating point. Through 

 that point on the picture may be drawn a vertical 

 line, C E, fig. 28, plate LXV., and two others, C B, 

 C G, containing with it, and with one another, angles 

 of 120 degrees, to be called the isometrical lines, to 

 be distinguished from one another by the names of 

 the vertical, the dexter, and the sinister lines. And 

 the two latter may be called by a common name, 

 the horizontal isometrical lines. Any other lines 

 parallel to them may be called respectively by the 

 same names. The plane passing through the dexter 

 and vertical lines, may be called the dexter isometri- 

 cal plane; that passing through the vertical and 

 sinister lines, the sinister plane; and that through 

 the dexter and sinister lines, the horizontal plane. 



The drawing implements are thus described by the 

 inventor. It is unnecessary to describe the drawing- 

 table any further, than by observing that it ought ta 

 be so contrived, as to keep the paper steady on which 

 the drawing is to be made. 



There should be a ruler in the form of the letter 

 T to slide on one side of the drawing-table. The 

 ruler should be kept, by small prominences on the 

 under side, from being in immediate contact with 

 the paper, to prevent its blotting the fresh drawn 

 lines as it slides over them. And a second ruler, by 

 means of a groove near one end on its under side, 

 should be made to slide on the first. The groove 

 should be wider than the breadth of the first ruler, 

 and so fitted, that the second may at pleasure be put 

 into either of the two positions represented in the 

 engraving, so as to contain, with the former ruler, 

 in either position, an angle of sixty degrees. The 

 groove should be of such a size, that when its shoul- 

 ders a and d are in contact with, and rest against 

 the edges of the first ruler, the edge of the second 

 ruler should coincide with d e, the side of an equi- 

 lateral triangle described on d g, a portion of the 

 edge of the first ruler; and when the shoulders b and 

 c rest against the edges of the first' ruler, the edge of 

 the second should lie along g e, the other side of the 

 equilateral triangle. The second ruler should have 

 a little foot at k for the same purpose as the promi- 

 nences on the first ruler, and both of them should 

 have their edges divided into inches, and tenths, or 

 eighths of inches. 



It would be convenient if the second ruler had also 

 another groove r s, so formed, that when the shoul- 

 ders r and s are in contact with the edges of the first 

 ruler, the second should be at right angles to it. 

 For representing circles in their proper positions, the 

 writer made use of the inner edges of rims cut out 

 from cards, into isometrical ellipses as represented 

 in the figure ; of these he had a series of different 

 sizes, corresponding to his wheels. Such a series 

 might be cut by help of the concentric ellipses, but 

 he thinks that it would be an easier way to make 

 use of that set of concentric ellipses as they stand, 

 by putting them in the proper place under the pic- 

 ture, if the paper on which the drawing is made be 

 thin enough for the lines to be traced through, as by 

 the help of them the several concentric circles will 

 go to the representation of one which might be drawn 

 at once. It is difficult to execute them separately 

 with sufficient accuracy to make them correspond. 

 For this purpose a separate plate of ellipses should 

 be had, and one edge of the paper on the drawing- 

 table should be loose to admit of the concentric 

 ellipses being slid under it to the proper place. 



By the use of the simple apparatus described 

 above, the representation of these lines in the objects 

 may be drawn on the picture, and measured to a 



