Lengths of the irregular hip rafters............................................... ................................................................................................................................... Backing of hip rafters on trapezoidal and other irregular roofs.............................................................................. Side bevels of jack rafters on the sides of the frame........ 69 70 70 70 71 71 72 73 73 73 74 75 75 76 76 Side bevels of the jack rafters on the slant end of the frame................................................................................................ OCTAGONAL AND HEXAGONAL ROOFS.. Length of the hip rafters......... Bevels of the hip rafters....... CHURCH SPIRES.. 78 78 78 79 79 79 81 81 82 83 89 90 INTRODUCTORY CHAPTER. SUMMARY VIEW. The Science and the Art of Framing. No apology is offered for introducing to the Public a work on the Science and Art of Framing. By the Science of Framing is meant the certain knowledge of it, founded on mathematical principles, and for which the master of it can assign intelligent reasons, which he knows to be correct; while the Art of Framing is the system of rules serving to facilitate the practice of it, but the reasons for which the workman may or may not understand. That Carpentry has its rules of Science as well as its rules of Art, no intelligent mechanic can doubt. The rules of the Art are taught by the master-workman at the bench; or, more commonly, insensibly acquired by habit and imitation. But by whom have the rules of the Science been laid down, and where have its principles been intelligibly demonstrated? Something New. It is believed that this is the very first attempt ever made to bring the Science of Carpentry, properly so called, within Deficiencies of Former Works on Carpentry. Whatever has formerly been published on this subject, that can, with any degree of propriety, be classed under the head of Science, has been only available by professional Architects and Designers, being written in technical language and mathematical signs, accompanied by no adequate definitions or explanations; and are as perfectly unintelligible to working-men of ordinary education as Chinese or Choctaw. On the other hand, the numerous works upon the Art of Carpentry, designed and published for the use of working-men, are sadly deficient in details and practical rules. They seem to take it for granted that the student is already familiar with his business; they furnish him with drafts and plans to work from; they tell him authoritatively that such or such an angle is the proper bevel for such a part of the frame; but they neither tell him why it is so, nor inform him how to begin and go on systematically with framing and erecting a building. These works are, in fine, chiefly valuable for their plates; and even these it is not always possible to work from with confidence and accuracy, because no man can work with confidence and accuracy in the dark: and he certainly is in the dark who does not understand the reasons on which his rules are founded. The Author's Experience. These facts and reflections have been impressing themselves upon the mind of the Author of this work for twenty years past, while he has been serving the Public as a practical car penter. During much of this time it has been his fortune. to have large jobs on hand, employing many journeymen mechanics, who claimed to understand their trade, and demanded full wages. But it has been one of the most serious and oppressive of his cares, that these journeymen knew so little of their business. Few Good Carpenters. They had, by habit, acquired the use of tools, and could perform a job of work after it had been laid out for them; but not more than one man in ten could himself lay out a frame readily and correctly. Why Apprentices do not Learn. Now, it is not commonly because apprentices are unwilling to learn, or incapable of learning, that this is so, but it is because they have not the adequate instruction to enable them to become master-workmen. Their masters are very naturally desirous to appropriate their services to their own best advantage; and that is often apparently gained by keeping the apprentice constantly at one branch of his business, in which he soon becomes a good hand, and is taught but little else; and when his time is his own, and he comes to set up business for himself, then he is made to feel his deficiencies. Should he have assistants and apprentices in his turn, he would be unable to give them proper instruction, even were he well disposed to do so for he can teach them nothing more than what he knows himself. In this condition, the young mechanic applies to books to assist him to conquer the mysteries of his Art; but he has not been able hitherto to find a work adapted to his wants. He anxiously turns the pages of ponderous quarto and folio volumes; he is convinced of the prodigious learning of the 10 authors, but he is not instructed by them. On the one hand, their practical directions and rules are too meagre; and, on the other hand, their mathematical reasoning is too technical to yield our young working-man any real benefit or satisfaction. May not these faults be remedied? Is it not possible for instruction to be given, which shall be at once simple and practical in detail, and comprehensible and demonstrative in mathematical reasoning? Design of this Work. An attempt has been made, in this little work, to answer these questions affirmatively; and thus to supply a positive want, and to occupy a new field in the literature of Architecture. Its design is to give plain and practical rules for attaining a rapid proficiency in the Art of Carpentry; and also to prove the correctness of these rules by mathematical science. Importance of Geometry to Carpenters. No certain and satisfactory knowledge of framing can be gained without a previous acquaintance with the primary elements of Arithmetic and Geometry. It is presumed that a sufficient knowledge of Arithmetic is possessed by most mechanics in this country; but Geometry is not so commonly understood. It is not taught in our District Schools, and is looked upon as beyond the capacity of common minds. But this is a mistake. To mechanical minds, at least, the elements of Plane Geometry are so easily taught, that they seem to them to be almost self-evident at the first careful perusal; and mechanics have deprived themselves of much |