anatomical plates profess to be geometrical; and D'Alton appears to have anticipated in its essential point the method adopted by Professor Lucae.

Before I describe Lucae's apparatus, it will be necessary to refer briefly to the respective principles on which perspective and geometrical drawings are constructed. In the former, the object represented is supposed to be viewed from a fixed point; but in the latter, the observer is supposed to stand directly opposite each point represented. Figure 1 is intended to show the way in which objects are viewed in geometrical delineation. The arrow indicates the object, and the vertical lines the mode of vision. The eye, it will be seen, constantly changes its point of view, and thus each particular spot is looked at vertically. Suppose cd to be a plate of glass parallel to the arrow, and that we draw thereon the arrow, as viewed in the manner described, it is evident that the drawing will be of the exact size of the arrow. If the eye be moved further from or nearer to the glass, or the glass to the object, the drawing taken will not vary in any particular. Geometrical drawings, then, represent objects as they exist extended in space, as far as this is possible on a plane surface, and they are not intended (except secondarily) to represent things as they look.

Figure 2 elucidates the principles of perspective drawing. The lines radiating from the point of sight indicate the mode of vision. If a glass plate be introduced, as in the former case, and the object, viewed in the manner now indicated, delineated thereon, only the central portion of the drawing will correspond to the object; all the rest will be foreshortened. A will appear at a and B at b. If in this case we vary the distance between the eye and the glass, or the glass and the object, the proportion of the several parts of the drawings made on the glass plate will vary too. It is evident from this, that perspective drawings are not strictly and minutely comparable the one with the other; as, even supposing that the drawings are all taken at the same distance from the objects, the amount of foreshortening will vary in each case with the form of the objects. Geometrical drawings, however, admit of strict com

parison inter se, as all planes in the object which are parallel to the plane of the drawing are shown without any foreshortening.

It will be at once objected, that we do not view objects from plane, and that, therefore, geometrical drawings cannot afford any idea of objects as they appear to us, and as they alone exist with regard to ourselves. To this objection Lucae replies, that we do see things geometically when we view them from some little distance, as the rays from such objects are practically parallel; and besides this we retain in our minds a geometrical rather than a perspective image of objects. When we examine a skull, we do not view it from a single point; we constantly change our point of view; and, moreover, our judgment is generally materially aided by the sense of touch. Besides this, our eyes present us with stereoscopic not perspective views.

I will now proceed to describe Professor Lucae's apparatus. It consists essentially of a plate of glass, suspended horizontally, under which the object to be drawn is placed, and of an instrument affording a vertical axis of vision, moveable horizontally upon the glass plate. This glass plate, which should be four decimeters square, is let into a heavy oak frame, so that its upper surface is continuous with that of the frame. At the four corners of the frame there are four pegs, by means of which it is fixed in a horizontal position on a small table or stool, the top of which has a piece cut out of it of the size of the glass plate. The height of the stool with its frame should be about three and three-quarters decimeters. I am indebted to Professor Lucae himself for these details, and it is through his kindness that I am able to exhibit to you the instrument for giving the moveable vertical axis of sight. A plan of this instrument is given in figure 3. v is a diopter, and k the intersection of two crossed threads; the vertical axis is vk. When we look through the diopter in the direction of the crossed threads we see the object lying under the glass, J, 9. The instrument is brought successively over each part of the object, and every point we wish to re

produce in the drawing is noted on the glass, by marking with

ink the exact spot covered by the point of intersection of the crossed threads. We have only to connect the points thus laid down, and we have a perfect geometrical drawing. By breathing on the glass plate, laying on it a piece of paper and rubbing the latter with a paper knife, the drawing may be copied and transferred directly to the lithographic stone.

Lucae's apparatus can also be used for reducing the geometrical drawings, by simply laying them under the glass, and tracing the outline as viewed through the diopter alone, the instrument being kept in one position. The amount of the reduction will depend upon the distance of the drawing from the glass, or of the latter from the diopter. If the eye and the drawing are equidistant from the glass plate the reduction will be one-half. If the glass is three times further from the drawing than it is from the eye, we get a drawing a quarter of the size of the original. In a similar way the apparatus may be used for reducing the drawings to a common dimension, e.g., making the length of two skulls correspond, in order more readily to compare the other dimensions.

It may be thought that practically there is considerable difficulty in taking drawings in the way I have endeavoured to describe, and indeed Professor Vogt, in his Lectures on Man, complains that such is the case. He thinks that to anyone accustomed to the ordinary method there is very great difficulty in geometrical drawing. He allows that in a comparatively short time an accurate outline may be drawn, but he complains that the lines are coarse, owing to the unequal extent to which the glass absorbs the ink, and that the light cannot be so managed that all parts of the object may be seen with the requisite distinctness. As regards the former difficulty, it can easily be avoided by transferring the dotted drawing from the glass to the paper before completing the outline; and the latter difficulty is got over by drawing at a table near a window, and using a small mirror for the illumination of dark parts. The glass plates should be very smooth and dry, and fine steel pens and copying ink should be used for drawing. Great attention must be paid to the accuracy of the diopter, and it must frequently be tested by carefully

drawing an outline four times, the instrument being turned round ninety degrees each time. The adjustment is to be made by shifting the eyepiece.

To return to the great objection which will be made to these drawings, namely that they are not correct representations of objects according to the ordinary mode of looking at them. What I am about to relate will, I think, prove conclusively that they, at all events, sufficiently resemble perspective drawings to answer every purpose that they do. Professor Lucae caused a careful geometrical drawing to be made of a well-known bust of Soemmering, and showed it to several artists of eminence. They none of them detected that it was not a perspective drawing, although the bust was quite familiar to them, and even the sculptor himself confessed that he should not have known that the drawing was not perspective if he had not noticed that the base line of the front of the bust was continuous with that of the side, instead of forming an angle with it. This bust is figured by Lucae in the work already cited, and I leave those who are still sceptical to judge for themselves. I claim for geometrical drawings, that they possess every advantage of perspective ones, and besides this are description, measurement, and picture all in one. The eye of the most practised craniologist may easily be deceived by peculiarities of contour and surface; it is therefore no small advantage that geometrical drawings can be compared by simple superposition, and thus minute differences of form detected, which must escape every other method of observation. It is another advantage of the highest practical importance that these drawings can be prepared with all necessary accuracy by persons totally ignorant of drawing. Of course this applies to outline drawings only, which are, perhaps, after all, of the greatest value. A slight amount of shading may be necessary, but this may be learnt with very little practice.

The writer in the Natural History Review, already alluded to, states that "no drawing can really represent more than a single plane so as to admit of distances being measured on it." This is manifestly incorrect. Geometrical drawings admit of accurate measurement in EVERY visible plane of the object parallel to

the drawing. It therefore does not follow, as argued by this writer, that all the objects proposed by geometrical drawing will be answered by having figures of each plane, in which it may be desired to take the measurements. Besides the objections to perspective drawings already pointed out, if we take figures nearly the size of nature by the aid of the camera lucida, the skull has to be placed so near as to produce a foreshortening amounting to actual distortion.

Let it not be supposed that I am advocating a system which has not been tried. The plates of the Atlas der Cranioscopie of Carus, the Crania selecta of Von Baer, the Crania Germania of Ecker, Morphologie der Rassenschädel, and Zur Architectur des Menschenschädel of Lucae, and the magnificent work of His and Rütimeyer, the Crania Helvetica, consisting of one hundred and sixty-four figures of skulls the size of nature, are all drawn on the geometrical, not the perspective, principle, and are, as a matter of fact, setting aside the question of projection, almost the only published figures of skulls sufficiently accurate for scientific purposes, although there are certainly many extremely beautifully executed and artistic drawings, the value of which, especially when supplemented by geometrical outlines, I should be the last to deny.