In operating large tubes, that is to say, tubes six or eight inches in diameter, there is an advantage in using compressed, rather than exhausted air, in the construction of the sending and receiving apparatus, especially when the tubes are very long. With an ample supply of compressed air always at hand, the air-cushions can be made shorter and more effective in bringing the carriers quickly to rest. With exhausted air the cushions are ineffective, and consequently must be made very long in order to stop the carrier before it strikes the closed end of the tube. This does not apply to small tubes where the carriers are so light that they can be stopped without injury by allowing them to strike solid buffers. Again, when compressed air is used, we have a larger difference in pressure between the pressure in the tube and the atmosphere to operate our mechanism by cylinders and pistons. With an exhaust system carriers are not so easily ejected from the tubes of the receiving apparatus; we could not use the simple form of open receiver. Again, if the tubes are laid in wet ground, and a leak occurs in any of the joints, water will be drawn in if air is being exhausted from the tube, while it will be kept out if compressed air is used. In regard to the question of relative economy of the two systems, we will say that when long tubes are used, requiring high pressures, or, more strictly speaking, a large difference of pressure, to maintain the desired velocity of air-current, there seems to be some advantage in using an exhaust system. The reason is this: the friction of the air in the tube, which absorbs most of the power, increases as the air becomes heavier and more dense. When the air is exhausted from the tube, we are using a current of rarefied air, and this moves through the tube with less friction and, consequently, a higher velocity, for the same difference of pressure, than the more dense compressed air. But for short tubes that require only a small difference of pressure, this advantage becomes very small, and is overbalanced by other advantages of a compressed air system. So, taking everything into consideration, there is not so much to be said in favor of an exhaust system. =Laws Expressed in Mathematical Formulæ.=—While we have heretofore purposely avoided all complicated mathematical formulæ, it may not be out of place here to give a few of the more simple relations that exist between the pressure, velocity, length and diameter of the tubes, etc. In two tubes having the same diameter, with the same pressures maintained at each end, but of different lengths, the mean velocities of the air in the tubes will bear the inverse ratio to the square roots of the lengths of the tubes. This is expressed by the following proportion: _u_ : U :: √L : √_l_ _u_ and U represent the mean velocities of the air in the two tubes and _l_ and L the respective lengths of tubes.