4S4 



PERSPECTIVE. 



When the line drawn perpendicular tofg, in figs. 

 25 and 2(i. from the point in Uie ground plan, whose 

 perspective is wanted, nearly coincides with the line 

 driwn perpendicular to the same \mefg, from the 

 point in the picture-sheet, where the line drawn to 

 the eye, from the point in the ground plan cuts it, 

 the height of the perspective of the point cannot be 

 so exactly found by the rule, as the line drawn to 

 the point e, in the perspective view, is, in this case, 

 nearly a perpendicular line, and the place where 

 this line cuts the line, let t'.ill perpendicular to / g, 

 in figs, 25 and 26, from the point in the picture-sheet 

 where the line drawn to the eye from the place of 

 the point in the ground plan cuts it, is not so exact- 

 ly marked as when these lines, which mark by their 

 rutting the perspective of the point, cross each other 

 in a direction nearer the perpendicular. When great 

 exactness is wanted in a case of this kind, it will be 

 the better way to find the perspective of a horizontal 

 line, parallel to the picture-sheet, passing through 

 the point whose perspective is wanted, and the place 

 where this perspective line cuts the line drawn per- 

 pendicular to the \hiefg, in figs. 25 and 26, from the 

 point in the picture-sheet, where the line drawn 

 from the place of the point in the ground plan to the 

 eye cuts it, is the perspective of the point. 



The eye should not be nearer to the picture-sheet 

 than the greatest height or breadth of the picture, 

 and it should be placed in the ground plan, so that 

 a line let fall from it perpendicular to the picture- 

 sheet should bisect the angle feg, formed by lines 

 drawn to it from the points which mark out the 

 greatest width of the picture. The line e p, in the 

 ground plan, does not bisect the angle feg; but 

 this was done to save room, and to show some parts 

 of the objects that could not have been so well repre- 

 sented if the position of the eye had been more near- 

 ly opposite to the centre of the picture. If the eye 

 is very distant from the picture-sheet a perpendicu- 

 lar let fall from it to the picture-sheet need not fall 

 exactly on the centre of the picture. 



If, in the ground plan, or the elevation, one part 

 keeps another out of sight, the part hid must be 

 drawn before its perspective can be made. The 

 dotted lines in the ground plan showing the small 

 moulding on the top of the pillar, and the dotted 

 lines in the same plan, which show the round pannels 

 in the cube that is close to the picture-sheet, illus- 

 trate this remark. 



When a figure in the objects to be represented is 

 parallel to the transparent plane the perspective of 

 the figure is similar to the original one, but less in 

 magnitude, according to its distance. 



If a picture is wanted in which the transparent 

 plane does not stand perpendicular, the easiest way 

 to make it is to consider the picture-sheet perpen- 

 dicular, and draw the figures corresponding to the 

 ground plan and elevation as if the objects were put 

 off the perpendicular by elevating one side of the 

 horizontal surface passing through the lowest point 

 in them. 



Sometimes after the ground plan of any object or 

 number of objects is drawn, it may be considered 

 better not to have the picture-sheet in this plan par- 

 allel to the top or bottom edges of the drawing board, 

 but in a direction such as the line A c, in fig, 27, is 

 drawn. When this happens draw, as in fig. 24, lines 

 from all the points in the ground plan to d, the point 

 of sight, then let fall perpendicular lines from the 

 same points to the picture-sheet, A c ; after this 

 draw from a point c, (which is beyond the lines 

 drawn from the place of the points in the ground 

 plan to the picture-sheet.) the line c e, parallel to 

 the top or bottom edge of the drawing board. Then 

 from the point c, where the lines A c and e c, meet, 



with a pair of pencil bows draw circles to e c, from 

 all points in A c, where the perpendicular lines, mid 

 the lines drawn to the eye from the points in the 

 ground plan meet it, also the point where a perpen- 

 dicular let fall from the point d to the picture-sheet, 

 meets it, must be transferred by means of the pencil 

 bows to the line e c ; and perpendicular to e c, from 

 this last point transferred, mark off the point/, at the 

 same distance from e c, that d is from A c. It will 

 now be evident that transferring the points on A e to 

 e c : and settling the point /, in the position men- 

 tioned above, produces the same effect as if A c, with 

 all the points on it, together with d, the point of 

 sight, moved with the same angular motion round 

 the point c, as a centre, till A c came to the position 

 e c. The point d would then coincide with /; and 

 e c would be the picture-sheet with all its points upon 

 it brought into a position parallel to the bottom of 

 the drawing board. When the operation is thus far 

 gone through, the rest of the process is conducted as 

 if the ground plan had been drawn to suit the picture- 

 sheet in the position e c. In order that fig. 27 may be 

 fully understood, I need only add that b is an eleva 

 tion of the object a, in the ground plan, and k is the 

 perspective view of it ; g, in the perspective view, 

 being the vanishing point of the lines running per- 

 pendicular to the picture-sheet. Rather than draw 

 a perspective view with the position of the picture- 

 sheet in the ground plan inclined to the sides of the 

 drawing board, as in fig. 27, it will be better to shift 

 the blade of the drawing square so as to draw the 

 ground plan of the objects at the required angle to 

 the picture-sheet, when it is in apositon as in fig. 1. 



Isometrical Perspective. This is a kind of per- 

 spective invented by professor Parish, of Cambridge. 

 We extract, with some modifications, a portion ol 

 professor Parish's paper on the subject, which ap- 

 peared in the first volume of the Transactions of the 

 Cambridge Philosophical Society. The subject has 

 been but little attended to by mechanical draughts- 

 men, but its importance is becoming daily better 

 known. 



After some general remarks on the inadequacy of 

 the common methods of drawing machinery ; he 

 states that it is preferable to the common perspec- 

 tive on many accounts, for such purposes. It is 

 much easier and simpler in its principles. It is also, 

 by the help of a common draw ing- table, and two 

 rulers, incomparably more easy, and consequently, 

 more accurate in its application ; insomuch, that 

 there is no difficulty in giving an almost perfectly 

 correct representation of any object adapted to this 

 perspective, to which the artist has access, if he has 

 a very simple knowledge of its principles, and a 

 little practice. 



It further represents the straight lines which lie 

 in the three principal directions, all on the same 

 scale. The right angles contained by such lines are 

 always represented either by angles of sixty degrees, 

 or the supplement of sixty degrees. And this, 

 though it might look like an objection, will appear 

 to be none on the first sight of a drawing on these 

 principles, by any person who has ever looked at a 

 picture. Por he cannot for a moment have a doubt, 

 that the angle represented is a right angle, on in- 

 spection 



And we may observe further, that an angle of sixty 

 degrees is the easiest to draw of any angle in nature. 

 It may be instantly found by any person who has a 

 pair of compasses, and understands the first propo- 

 sition of Euclid. The representation, also, of circles 

 and wheels, and of the manner in which they act on 

 one another, is very simple and intelligible. The 

 principles of this perspective which, from the pecu- 

 liar circumstance of its exhibiting the lines in the 





