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to terminate and unite in the real point of distance, as those on the left terminate and unite in the fictitious point of distance 3 on the line of the horizon. Without requiring another example, suppose we had, say, an extensive view, and we desired to ascertain the perspective proportions of objects extremely remote; and further, that instead of allowing ten real parts (call them feet if you will) for the space embraced by the foreground or base line, we make it one hundred— thus by multiplying all our numerical points, real and fictitious, by ten, we have all that we desire. ' If we have an accurately laid down horizontal line, to get the perpendicular height of objects, no matter what they may be, at the distance of this line, is an operation already too familiar to need repetition.

69. It will be found that in many of the examples given we have been forced to the use of a shorter distance of view than has been recommended. This the limits of our page have in a great measure compelled, in the first place; and in the next, by exaggerating or making the perspective more violent than would be proper in a picture, the principles it was desired to illustrate may have been made more evident.

It is earnestly desired to impress upon the mind of the student the importance of resting satisfied with nothing short of a thorough comprehension of all as it is placed before him, testing and verifying each and every operation for himself. If less has been said and exemplified on the subject of the elementary principles of the art, with a more strictly mathematical analysis of these principles, it has been from the fear, based upon experience, that the learner might either wear out his patience in groping through geometrical labyrinths to little useful purpose, for want of consciousness of the ends for which he labored, or else break down in the very outset, as many a one has done before him, in terror of the long and cheerless way that presented itself— through mysterious-looking diagrams and geometrical problems, which not every head, if it has the capacity, possesses the resolution to encounter. Indeed, it may be fairly doubted if ever yet any ponderous volume of perspective complicities, however full of geometrical learning and research, was gone through in downright earnestness by the student; and if it. may have been, it has been to comparatively little practical utility. The study of perspective, like that of all others connected with design, is not to be gone through by the book alone, page by page, to its accomplishment ; but its knowledge must be attained by an eye rendered susceptible to the evidences of the truth of its principles, as they are developed in nature, and a mind gradually strengthened to their investigation and application in design, to which it holds the place of an accessory, not that of a primary motive. It comes to the aid of the artist in the development and expression of his art, as do many other branches of knowledge — any one, or all of which, acquired to the utmost extent of learning, would tend but little to constitute an artist, independent of the primary and mere leading qualifications requisite for the imitative and inventive art. As the poetry of thought precedes the measured line and its rules of harmonious expression, and as no rules of prosody can make a poet, or gift the mind with power of expansion to the bright and privileged world of fancy, yet is their assistance indispensable to reduce to order the pictures of its gathering or creation.

70. Here the artist-student of perspective might perhaps be safely left to pursue his course alone, and to rely upon his own judgment in following out the elementary principles of the art in their various and endless applications, as all that remains is chiefly based upon merely geometrical operations. To meet every case that may occur by an example, would swell our work to more volumes than there are pages at our disposal 5 and, after all, if such could be done, it would be scarcely worth the pains, and its place upon the book-shelf might be far better and more usefully occupied. Besides, the artist and draughtsman should hold the art in his mind, and eye, and hand—ready, quick as the thought or the impression, to give it utterance and expression. To be thus learned it is not necessary to be for ever bending over dull diagrams and untangling knotty problems. The field of art is too wide, its privileges too free for this. The artist's best school is abroad, in the bright, beautiful world of nature, for ever developing subjects for admiration, and tempting his imitation. There is nothing on which his eye can rest that does not teach him lessons of his art, when once his perceptions are awakened and trained to their comprehension. Endless as may be his work of knowledge, so are his resources 5 while others plod on a duller way through life, he reaps while he sows, and bright blossoms mingle their perfume with the ripened fruit, which repays his labors and makes glad his toil.

71. In resuming the consideration of the geometrical operations of perspective, we are naturally led back to the beginning, but to that beginning with a degree of preparation that leaves little more to be required than mere hints to assist the student in the application of the princi pies of the art, with which he must be already familiar. It is scarcely necessary to remark that we must have a distinct and definite idea of the forms and objects we desire to place in our picture under the influence of the laws of perspective. We must consider them as real and tangible, and upon the basis of this knowledge we are enabled perspectively to define their positions, proportions, parts, and details. In many cases we may be compelled to have recourse to imaginary data in the course of our operations, but still these data, governed by harmonious

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