G4 report — 1859. 



focus of the concave lens should bear to that of the convex lenses the ratio of about 

 13:8. 



On the Angular Measurement of the Picture in Painting. 

 By H. R. Twining. 



The angle subtended by a picture changes as it is removed further from, or brought 

 nearer to, the observer ; and by this change in its position the relation of the near 

 objects to the distant ones becomes altered ; so that they cannot be equally correct 

 in both positions of the picture. By means of a small instrument, which maybe 

 termed the Hand-goniometer, the student is enabled to fix approximately the di- 

 stances of objects as represented in a picture, especially in subjects where linear 

 perspective is little concerned. The span given to the two arms of the goniometer 

 fixes the proximity of the picture, by assigning a given number of degrees (about 50) 

 to its apparent width, and thus ensures a conformity between the objects there 

 depicted, and the natural subject which they represent. 



The nearest point of the foreground in a level scene averages about 10 yards from 

 the observer, corresponding to an angle of 10° below the horizon ; but when the 

 observer is situated above the general level of the prospect, the picture extends down- 

 wards to a greater angle below the horizon, so as to include a larger area, or receding 

 plane, between it and the ground line. Figures would generally appear too large if 

 introduced on the very ground line ; the size of the nearest usually corresponds with 

 the proportion of human figures at about 15 yards off, corresponding to about 7° 

 from the horizon downwards. The relation of many other points to the horizontal 

 line may be obtained in a similar manner. 



A matter of some interest, for marine painters, is the amount of depression of the 

 visible horizon or sea boundary caused by the convexity of the earth ; for although a 

 subject of minute inquiry in an artistic point of view, yet it is just sufficiently appre- 

 ciable to be worth the artist's consideration ; since erroneous drawing, with respect 

 to it, may be observed in many of the pictures of coast scenery ; a greater amount 

 of dip of the horizon being accounted for by the concealment of objects behind it, 

 than is consistent with truth. 



Sir John Herschel, in his 'Outlines of Astronomy,' observes "that two points, 

 each 10 feet above the surface, cease to be visible from each other over still water, and, 

 in average atmospheric circumstances, at a distance of about eight miles;" which 

 limits the horizon of the sea, to an observer's eye situated 10 feet above its level, to 

 a distance of four miles, and assigns to it, at that distance, a real depression of 

 10 feet only. 



With the aid of a glass, the effects of so small an amount of depression become 

 easily appreciable on the sea-side. From the shore, at Eastbourne, I could discern 

 only the sails of a large vessel, which may have been ten miles distant ; whereas, 

 from an eminence of about 60 feet above low water, I could distinctly see, with the 

 aid of a telescope, the entire hull, which probably rose 15 feet above the water. 

 But a vessel situated at that distance scarcely measures an angle appreciable to the 

 unassisted eye, and therefore becomes too minute an object to be safely represented 

 in a picture, as partially hidden by the sea's boundary line ; in fact, this natural 

 effect could only be introduced in very minute art representations. 



It is true, the extremely foreshortened appearances presented by the sea's surface, 

 to an individual on the beach, causes boats and vessels, stationed at considerable 

 intervals from one another, to appear almost in contact, or to seem on the verge 

 of the horizon, although really not at all remote ; but this is owing entirely to the 

 illusions of perspective, and cannot be increased to any appreciable amount by the 

 convexity of the water's surface, or the earth's rotundity. 



But the case is somewhat different with regard to the amount of depression of 

 the visible horizon, as considered in connexion with the existence of mountains on 

 the coast. The elevation of Beachy Head, amounting I believe to 700 feet above the 

 sea, suffices to cause a depression of the visible horizon, which appeared to me 

 appreciable with the aid of this imperfect instrument ; and although this small 

 amount of the horizon's dip does not affect the pictorial character of the sea-view, 

 (which from such a position is remarkable for its vast expanse both horizontally 



