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 sider the sizes given in this table somewhat too small and would in general recommend about one pipe size larger.

With vacuum systems which have a vacuum only on the air-valve connection, such as the Paul system, it is impracticable to reduce much the sizes of the steam pipes below those given in Table II, as the only feature of this system is that it keeps pipe and radiators perfectly free from air, and does not greatly affect the flow of steam and water of condensation.

Radiator connections.—The connections from the risers to the radiators are always made somewhat larger in proportion than the mains and risers, and Table IV gives sizes which represent good practice for low-pressure systems.

Carpenter and Sickles' rule for steam pipe sizes.—In designing piping for large systems it must be borne in mind that there are many things which affect the flow of steam in a piping system, and special cases must have special consideration. Elbows, bends and valves greatly increase friction in the pipes. According to the recent investigation of Professor Carpenter and Mr. E. C. Sickles, as given in a paper before the American Society of Mechanical Engineers, Volume XX, a single 90-degree elbow is equal in frictional resistance to a length of pipe equal to about 520 times the diameter, while the resistance of a globe valve is equal to a length of 706 times the diameter, and a good gate valve