I do not think Mr. Woodward himself would endeavor to lay out a pure Ionic volute, or a beautiful winding stairway, by any such application of circular carves as he recommends to garden artists. That curved lines of every class are strictly mathematical, or may be resolved into strictly mathematical lines, I do not dispute: no line, from a dot upwards, nor combination of lines, exist, but may be analyzed and reduced to their proper mathematical elements and value.

I will give you a few practical illustrations of the effects of the two classes of curves, which will strike the most inexperienced eye. Compare the full-breasted Dutch galliot with semicircular bows, or the old-fashioned, tea-kettle-bottom ships, with the clipper ship of the present day, with her flowing curved lines; the one built for carrying, the other for fast sailing. The one class certainly inclosed the greatest quantity with the smallest circumference; the other class competes with the winds in swiftness. Which is, artistically speaking, the most beautiful in outline? can there be a doubt as to the perfection in beauty of its kind, of the clipper ship? but are her lines not those which study and experience have taught us are the lines produced by a body passing swiftly through the water?

You can not go five hundred feet on the Central Park without meeting with notable instances of the incongruities and deformities produced by the adoption of the system of circular curves. The Park has been managed and laid out by lawyers, brokers, merchants, farmers, engineers, architects, and literati. From its counsels and direction, in any shape or form, all artistic or horticultural skill has been studiously, constantly, and continuously ignored; and not at present to refer to the results in other matters than those of the lines of the roads, there is not a consecutive hundred yards of curved walk or road on which either the pedestrian or the vehicles follow the lines of the roads as laid down. It is a very interesting and instructive study for the landscape artist to note and contrast the natural and therefore beautiful lines formed by the vehicles or pedestrians on the roads, with the lines of the roads themselves; so in opposition are they, that even the water-cart horses have to be forcibly compelled to deviate from the natural and therefore true line, in order to regularly sprinkle the roads.

Iu concluding, I would again call attention to the fact that the circular curve does not exist in nature or among the celestial bodies, as far as we have cognizance of them; that it has never been used by artists of true genius or taste for the production of lines expressive of sublimity, of purity, or of beauty; that its elements being those of a quiescent body, are not, and can not be made properly serviceable in deducing the lines of bodies in motion; and that such lines can not be truthfully laid down by any system or combination of circular curves; that the true lines or curves of beauty are those composed of the various carves of motion harmoniously combined and laid out by their own proper elements, and so brought into accord with those natural surroundings which nature furnishes us for the adornment of rural scenes. The moment we introduce other forms we make discord and produce incongruities. He succeeds best who brightly illuminates his work by the lamps of Truth, Power, and Beauty; if the first is at all dimmed, the others will be more than correspondingly darkened.

The art or science of engineering is a noble one, but when it steps from its own proper sphere into that of art, insisting upon the adoption of its formula and theorems exclusively, it becomes empiricism. Its rules and practices should be subordinate to aesthetics, and should be adopted only in so far as they assist in aiding and carrying out the designs and requirements of artistic taste; beyond this, they are, in such matters, not to be recognized.

The practical and material modes of thought of our day, and the great achieve-ments of engineers in the legitimate line of their profession, have rather led the public mind astray, and made it to ignore the proper claims of the artist, Not all the knowledge of engineering science in the world would ever make an artist; he may be compelled to study engineering to enable him to carry into effect his thoughts and ideas, but there is nothing in engineering to suggest the beautiful; it has to deal with immutability, (so to speak,) compulsion, the intractable; it overcomes, but does not create; the true artist creates and overcomes. Many of the old painters were architects and engineers, but that did not impel them to produce those sublime works which challenge the admiration of the world; others had equal, perhaps better scientific knowledge, but they have left no such monuments behind them.

[Learning, in conversation with Mr. Hogg, that he entertained views, in regard I to the circular curve, quite at variance with those expressed by Mr. Woodward, we requested him, in a note, to put them on paper, and he has done so, for which he has our thanks. Mr. Woodward will respond in our next number. We be-lieve the discussion of this subject will prove highly interesting and instructive to a large class of readers. It remains to be seen whether these gentlemen will leave us any room for remarks. - Ed].