This section is from the book "Shop Projects Based On Community Problems", by Myron G. Burton. Also available from Amazon: Shop Projects Based on Community Problems.
Paragraph 67. The through mortise and tenon joint is very similar to the pinned mortise and tenon joint, with the exception that the mortise is cut entirely through the material B and the tenon A is allowed to extend so as to be exposed a short distance on the opposite side. This form of mortise and tenon construction is frequently used in cabinet work, where the exposed end of the tenon is treated in a decorative manner. This mortise and tenon joint is a little more difficult than the blind mortise and tenon because the joint is exposed on the opposite side and the mortise must fit the tenon perfectly in order to show good workmanship. This joint is laid out exactly like the blind mortise and tenon except that the mortise is laid out on both sides of the material B. In cutting, the work is done from both sides to avoid splintering out and to be sure that the mortise will be accurately cut and that the tenon will fill it properly. The tenon must also be formed with great care so as to make sure that it will properly fill the mortise.

Figure 52.
 
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