THE ELEMENTS OF PERSPECTIVE ARRANGED FOR THE USE OF SCHOOLS AND INTENDED TO BE READ IN CONNEXION WITH THE FIRST THREE BOOKS OF EUCLID PREFACE FOR some time back I have felt the want, among Students of Drawing, of a written code of accurate Perspectice Law; the modes of construciion in common use being various, and, for some problems, insufficient. It would have been desirable to draw up such a code in popular language so as to do away with the most repulsive difficulties of the subject: but finding this popularization would be impossible, without elaborate figures and long explanations, such as. 1 had no leisure to prepare, I have arranged the necessary rules in a short mathematical to m, which any schoolboy may read through in a few days, atter he has mastered the first three and the sixth boos of Euclid.

Some awkward compromises have been admitted between the first-attempted popular explanat on, and the severer arrangement, involving irregular lettering and redundant phraseology; but I cannot tor the present do more, and leave the book therefore to its trial, hoping that, if it be found by masters of schools to answer its purpose, I may hereafter bring it into better form.1

An account of practical methods, sufficient for gereral purposes of sketching, might indeed have been set down in much less space: but if the student reads the following pages carefully, he will not only find himself able, on occasion, to solve perspective problems of a complexity greater than the ordinary rules will reach, but obtain a clue to many important laws of pictorial effect, no less than of out line. The subject thus examined becomes, at least to my mind, very curious and interesting; but, for students who are unable or unwilling to take it up in this abstract form, I

1 Some irregularities of arrangement have been admitted merely for the sake of convenient reference; the eighth problem, for instance, ought to have been given as a case of the seventh, but is separately enunciated on account of its importance.

Several constructions, which ought to have been given as problems, are on the contrary given as corollaries, in order to keep the more directly connected problems in closer sequence; thus the construction of rectanges and polygons in vertical planes would appear by the Table of Contents to have been omitted, being given in the corollary to Problem IX.

believe good help will be soon furnished, in a series of illustrations of practical perspective now in preparation by Mr. Le Vengeur. I have not seen this essay in an advanced state, but the illustrations shown to me were very clear and good; and, as the author has devoted much thought to their arrangement, I hope that his work will be precisely what is wanted by the general learner.

Students wishing to pursue the subject into its more extended branches will find, I believe, Cloquet's treatise the best hitherto published.1

1 Nouveau Traits Elementaire de Perspective. Bachelier 1823.

When you begin to read this book, sit down very near the window, and shut the window. I hope the view out of it is pretty; but, whatever the view may be. we shall find enough in it for an illustration of the first principles of perspective (or, literally, of looking through).

Every pane of your window may be considered, if you choose, as a glass picture; and what you see through it, as painted on its surface.

And if, holding your head still, you extend your hand to the glass, you may, with a brush full of any thick colour, trace, roughly, the lines of the landscape on the glass.

But, to do this, you must hold your head very still. Not only you must not move it sideways, nor up and down, but it must not even move backwards or forwards; for, if you move your head forwards, you will see more of the landscape through the pane; and, if you move it backwards, you will see less: or considering the pane of glass as a picture, when you hold your head near it, the objects are painted small, and a great many of them go into a little space; but, when you hold your head some distance back, the objects are painted larger upon the pane, and fewer of them go into the field of it.

But, besides holding your head still, you must,, when you try to trace the picture on the glass, shut one of your eyes. If you do not, the point of the brush appears double; and, on farther experiment, you will observe that each of your eyes sees the object in a different place on the glass, so that the tracing which is true to the sight of the'right eye is a couple of inches (or more, according to your distance from the pane,) to the left of that which is true to the sight of the left.

Thus, it is only possible to draw what you see through the window rightly on the surface of the glass, by fixing one eye at a given point, and neither moving it to the right nor left, nor up nor down, nor backwards nor forwards. Every picture drawn in true perspective may be considered as an upright piece of glass1, on which the objects seen through it have been thus drawn. Perspective can, therefore, only be quite right, by being calculated for one fixed position of the eye of the observer; nor will it ever appear decepively right unless seen precisely from the point it is calculated for. Custom, however, enables us to feel the Tightness of the work on using both our eyes, and to be satisfied with it, even when we stand at some distance from the point it is designed for.