A very important economical consideration should be noted in laying out the arrangement of the bathroom fixtures in this connection. The horizontal branch soil-lines and waste-lines must be carried through the floor construction, and they should be so arranged that they can run parallel with the floor-joists; otherwise deep cuts will have to be made in them. In the case of the branch soil-line it is essential to place the water-closet as near to the main soil-stack as possible, for with a 4-inch pipe the joists must be framed around it rather than be cut, since so deep a gouge would weaken too much the strength of them. A similar consideration must be given to the framing in stud partitions which are bearing the loads of the floors above, for too deep cuts in them, to allow for the passage of pipes, will weaken them greatly. In this connection it ought to be noted that an ordinary 4-inch soil-pipe cannot be carried in a stud partition made with 2 by 4 studs, since the outer edges of the joints of the pipe will project beyond the face of the plaster, and for this reason some convenient place should be planned for them in closets, or 2 by 6 studs should be used in the partition through which they are run. _The More Complicated Back-Vent System_ The essential parts of the plumbing system remain the same as described above, but each trap is considered to be siphonable, and must be prevented from losing its water-seal by the use of back-venting pipes. Whenever, then, there is an unusual amount of semi-vacuum created in the pipes by the discharge of some fixture above, the outside air-pressure can relieve it by passing through the back vents rather than by forcing out the water-seal in the traps. The usual type of trap employed is the modified S trap with the small TY connection to give what is known as continuous venting. Formerly the vent was taken off from the crown of the three-quarter-S trap, which was too near the surface of the water-seal, causing excessive evaporation and danger of clogging, but with the continuous system of venting, the waste-pipe is a continuation of the vent-line, and the trap enters into its side through a TY fitting, overcoming the disadvantage of the older system. The size of traps should conform to the size of waste-pipes, and usually the size of the branch vents is about the same size as the waste-lines. However, there are special conditions where this varies. For venting the water-closet trap, it should be noted that the vent is not taken from the trap which is contained within the fixture itself, but is taken from the upper side of the bend (usually of lead) where the fixture is joined with the piping system, and is 2 inches in diameter. [Illustration: PLUMBING SYSTEM USING BACK-VENTING]