76 LECTURE III. 



But if it be requisite to have drawings whicli are not merely 

 comparable but measurable,* then the geometrical method 

 recommended by Dr. Lucae, of Frankfurt, must be appKed. 

 This consists simply in this, that the object is not drawn from 

 a fixed point of view, so that the rays of light emanating 

 from it meet in the eye as in the summit of a cone, but that, 

 on the contrary, the eye constantly changes its position, and 

 forms the representation of the object by means of the parallel, 

 horizontal, or vertical rays emanating from it. In per- 

 spective delineation, which is also that of the photographic 

 instrument, the individual parts of the body to be depicted 

 are greatly foreshortened, according as they form projections 

 or depressions ; in the geometrical delineation everything is in 

 the place which it occupies in the original, with regard to the 

 plane upon which the image is projected. The various cranial 

 measures reducible to a plane, may certainly be measvired on 

 such geometrical drawings with compass and meter-scale ; but 

 only these — and when Lucae asserts that these measurements 

 can supply the place of actual measurements on the skull itself, 

 we can only ascribe such an assertion to his exaggerated 

 predilection for a method which certainly is not without its 



advantages, t 



It must also be admitted that geometrical drawing offers 

 very great difficulties to any one who is accustomed to ordinary 

 drawing, and that in practising it one must abandon all the 

 rules one has hitherto followed, and consent to become a mere 

 machine, which does nothing but mark with pencil or pen the 

 point which indicates the perpendicular ray. Lucae has re- 

 commended two instruments, one constructed by himself, the 

 other by a Herr Wirsing. In both the fundamental principle is 

 the same : a diopter fastened to a perpendicular arm is placed 

 upon a horizontal glass plate, beneath which is the object. 



* Compare Crull., De Cranio ejusque ad faciem ratione, 8vo, Groningen, 

 1810. — Editor. 



f Lucae does not propose to substitute measurements from geometrical 

 drawings for measurements taken on the skull itself j he merely says, speak- 

 ing of the difficulty and uncertainty in obtaining several necessary cranial 

 dimensions, " that they can be taken on such di-awings with greater rapidity 

 and certainty than in very many cases from nature itself." See Morphologie 

 der Rassenschadel, Frankftirt, a. M., 1864, part ii, p. 3. — Editok. 



