AucusT 24, 1 893 J 



NATURE 



405 



from intellectual aptitude, the intelligent and the dull being 

 equally liable to commit the errors in the forms which will here- 

 after be specified. 



Consideiation will first be given to the existence of general 

 la-ius, of which there appear to be three, so strongly marked as 

 tu stand clearly distinguishable as including in themselves the 

 minor manifestations. These laws are as follows : — 



( 1) There is a general law making us fundamentally incapable 

 of drawing in perspective. It is a radical condition — not of 

 ignorance of the laws of perspective but of active negation of 

 them. It is a natural necessity to show by the arrangement of 

 lines the exact contrary to true perspective. It is persistent, and 

 exists long after correct knowledge of the true arrangement of 

 the lines is acquired, and the error is always liable to appear on 

 any occasion of forgelfulness — that is to say, when drawing is 

 not done with the true principles immediately in remembrance 

 in the mind. It is perceivable in the form of direct divergence 

 of lines (parallel in nature) which in perspective should converge 

 to their vanishing point. 



(2) Another general law is a natural incapacity to erect a 

 proper perpendicular for an object unless the same occurs 

 close on the line of direct sight (forward). If the per- 

 pendicular be situate laterally, and especially if it be 

 short, it is liable to a deflection. This deflection occurs 

 in the following manner : — If the same be on the right hand the 

 line inclmes from its top towards the central line of sight (for- 

 ward) ; its foot is therefore nearer this central line than its top. 

 On the left hand the phenomena are directly reversed. This 

 error occurs whether the perpendicular be the obvious physical 

 corner line of a solid or whether it be the integral (invisible) 

 line of any such solid or of a drawn figure. 



(3) The next general law is less distinct, but still abundantly 

 [irovable on test. It affects those lines which, being in right 

 angles to the observer, lie laterally to him ; that is to say, if a 

 line of the surface (horizontal) of a figure occur on the right or 

 lefi hand, at a little distance, the line is not drawn with per- 

 spective inclination to the vanishing point in front ot the 

 olwerver, but is drawn as a perpendicular, or, as is evident, in 

 such a manner as would be the true fact of its direction, void of 

 the influence of perspective. Thus, if a square lie two or three 

 feet to right or left of the draughtsman, those two sides of it 

 which are the sides rectilinear, not sides parallel to the base of 

 ilie picture-plane, are drawn as two perpendiculars, while they 



[ should be converging lines towards a point which leads them 

 i dia^oaal-wise across the paper. 



I These brief particulars are intended to give an account of the 

 , primary, or general, laws. All other manifestations are de- 

 j ilucible from them — that is, in every case where a special aspect 

 I of a figure draws out its special error, this is seen to have its origin 

 ! in one or other of these three primary laws. From this point I 

 1 now proceed to illustrate with examples selected from three 

 I tfgares — the cube, the pyramid, and the hexagon — instances of 

 , special error. Other geometrical figures may at a future period 

 I lie likewise illustrated, but the intention is in this paper only 

 I 10 brusch the subject. 



: The Cube. 



I It is in all cases assumed the object lies on a table before the 

 ! observer. 



j Position I. — Let the cube be placed on the right or left, and 

 ' with two planes parallel to the picture-plane, two in right 

 ' snqles. 



Rrrcr I, — The perpendiculars will be inclined as radiants 

 vardly. 



lirror 2. — The 3 perspectives visible will diverge. 

 j Error},. — Or these will be neutralised of perspective, and 

 I the true perpendiculars be inclined. 



j Position 2. — Let the cube be situate anglewise on the direct 

 line of sight. 



1 Error i. — All 6 perspectives to right and left diverge. 

 Error 2. — Or the top is drawn as a squctre. 

 Position 3. — Poise the cube on an edge, so that one plane, 

 resting exactly balanced on its corner, is in the direct front, and 

 jparallel to picture-plane. 



I Error i. — The perspectives (3) will diverge. 

 I Errors. — The square of the front plane will be confused as 

 irhomboidal. 



j Position 4. — Still having the cube poised on an edge, let it be 

 Iturned so that three faces are seen at one time, and it presents 

 perspectives in g lines. 



Error I. — AM the perspectives, in groups of 3 each, for each 

 plane, will diverge. 



The Pyramid {Square). 



Position I. — Let the pyramid lie exactly in front, parallel to 

 the picture-plane. 



Error I. — The two parallel edges of the square base, extend- 

 ing in right angles from the eye, will diverge. 



Error 2. — The further side of the pyramid will thus be longer 

 than the nearer side. 



Position 2. — Let the pyramid lie on the same spot, but with 

 an angle presented, so that the sides of the square extend in 

 equal angles. 



Error u — If the view of it should be isometrical, or the 

 pyramid7?a///j//, the perspectives will be shown diverging. 



Position 3. — Place the pyramid point downwards towards the 

 observer, in front, and with one side for a base. 



Error I. — -The two parallel retiring lines of the inclined real 

 base will shjw divergence. 



Error 2. — Consequently, the further line of base will be 

 longer than the nearer and upper of this sloping square. 



Position 4. — Place the pyramid so that it still lies on a ssde for 

 a base, but in front, and the apex and the central point of a side 

 of the real base are on a line parallel to picture-plane. 



Error i. —The apex, which should thus lie horizontally ev.n 

 with the central point of that line of real base, which touches 

 the ground, will be shown below that line. The true relation to 

 central p jint given is never seen. 



Error 2. — Such perspectives as occur will diverge. 



The Hexagon. 



Position I. — Place a solid hexagon upright in the exact front 

 of observer, with two planes parallel to picture-plane. 



Error I. — All perspectives of the parallel sides will diverge. 



Error 2. — Consequently, the two parallel lines (integral) 

 which connect opposite angles of the hexagon will lose their 

 perspective. 



Position 2. — Place the hexagon on a side, so that its lines, then 

 horizontal, are parallel to picture- plane and the object is in a lat- 

 eral situation, or not in front. 



Error 1. The end, which is now a plane in right angles, will 

 show the integral connecting lines between top and bottom 

 angles leaning, because these are essentially perpendicular ; 

 therefore the perpendicularity is distorted. (General law i.) 



Error 2. — The line (integral) connecting the two angles mid- 

 way between top and l)ase line of this plane, and which should 

 be of course parallel to these, and partaking of their perspective, 

 will have a course diagonal to them, always deflected down- 

 wards. 



Error 3.— The lines which indicate the further, or unseen 

 plane of hexagon will show exact conformity to this error ; also 

 diverging perspective. 



Position 4. — Place the hexagon again laterally, with its end as 

 a front plane, and a side on the ground, the direction of the 

 object being in a due rectilinear line. 



Error I. — The perspective bias will be lost (general lai» 3) and 

 the lines traced as perpendiculars. 



Error 2. — Or these will indicate divergence in place of con- 

 vergence. 



Errai' 3. — The plane parallel to picture-plane, and essentially 

 void of distortion, will be nevertheless distorted. 



Position 3. — Place the hexagon, still resting on a side, so that 

 its lines take a diagonal line with regard to a line parallel to the 

 picture plane, and it must be in front. 



Error I. — The displacement of the integral perpendicul.nr> will 

 occur in the end planes, as in Error i of Position 2. 



Error 2. — The Error 2, in Position 2, will be repeated. 



Error 3. — The perspectives will diverge. 



Arthur L. Haduon. 



NO. 1 243, VOL. 48] 



THE DEPARTMENT OF SCIENCE AND ART. 



'X'HE fortieth Report of the Department of Science and Art 

 ■^ has just been issued, and is of a highly satisfactory charac- 

 ter. I'rom it we learn that in 1892 there was a very large in- 

 crease, not only in the number of students and classes, Init also 

 in the number of schools or separate institutions in which science 

 is taught. The number of classes in different branch-s of science 

 in 1892 was 10,352, as against 8,568 in the preceding year, and 



