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The Maximum Parcel To the Editor of the SCIENTIFIC AMERICAN : Under Section 15 of the Parcel Post Regulations, if a parcel exceeds seventy-two inches in length and girth combined, it must be refused, no matter how small the excess may be. In another paragraph of this same Section 15 the measuring of combined girth and length is explained by saying that in measuring the length the greatest distance in a straight line between the two ends of the parcel shall be taken, while the girth is the actual measurement by a tape encircling the parcel at its thickest part. Under these provisions strictly interpreted a rod 72 inches long would have to be infinitely thin to be accepted; and a perfect cube would have to be not more than fourteen and four tenths inches high, because the girth of such a cube is 4 times 14.4 or 57.6 inches, and ts length 14.4 added to the girth 57.6 makes 72.0 inches exactly. The 14.4-inch cube contains 14.4 X 14.4 X 14.4 or 2,985.984 cubic inches; and the 72-inch rod contains zero or no cubic inches; and a question that naturally arises is, have we any form between the thin rod and the cube that will enable the shipper to send a still greater number of cubic inches under the rule? In a rectangular package the square cross section is the most advantageous, so that the problem may be stated in the following form: Whai should be the dimensions of a square bar whose combined girth and length is 72 inches, in order that such bar shall contain the greatest number of cubic inches, and how many cubic inches will it contain? Let ? inches be the width and thickness of this bar, so that its girth will be 4x inches. Its length under the rule will be (72 -- 4x) inches. The cross sectional area is x2 square inches and the volume V is x2 (72---4x) cubic inches. We may, therefore, write: 72x2 -- 4x = V and note that V should be as large as possible or a maximum. Differentiating for the maximum we have: 144 --122 = dV/dx = 0 whence = 12. We, therefore, have: girth, or 4.x, equals 48 inches; length, or (72 -- 4x), equals 24 inches; cross section, or x2, equals 144 square inches; volume, or 242, equals 3,456 cubic inches. This represents a gain of approximately 3,456 --2,986, or 470 cubic inches, which amounts to very nearly 16 per cent, and the package has the advantage of being of a form that is much more conveniently handled than the cube. The dimensions of this package to recapitulate are 12 inches by 12 inches by 24 inches. It is represented in the annexed rapid perspective, where the combined girth and length is the full length of the string A, B, O, D, E, F, Q, and H. A cylinder of the same length, 24 inches, and, therefore, of the same girth, 48 inches, would have a diameter of 48/?, or 15.28 inches, and a volume of almost exactly 4,400 cubic inches. The sphere of all solids is known to be the one that incloses the greatest volume within a given superficial area; but the largest sphere that could be sent through the mails has a diameter d equal to 72/ (ir-fl), or 17.38 inches, with a volume V equal to 1/6 of wd', or 2,749 cubic inches. Under Parcel Post Regulations, therefore, the spherical form of package, which can only be considered as a matter of curiosity, is even less advantageous than the cubical. A point not to be overlooked is that in any case the weight limit of eleven pounds must not be exceeded. Arlington, Va. JOSEPH BECKER. The Levee Question To the Editor of the SCIENTIFIC AMERICAN: About twenty years ago, on the occasion of examinations of old Mississippi River pilots on the question of whether a piece of land was an accretion or island, I took advantage of the opportunities to discuss with them the question whether the levees raised or lowered the bottom of the river. It was their opinion that they raised the bottom and would eventually cause the bottom to be higher than the land at the sides. It seems to me that if the levees increased the current to the extent that the water carried with it the silt, it would be a mass of mud before reaching New Orleans. The theory of opening up through headlands and allowing a straight course to the sea as a panacea has an objection in that it would cause such a current that the river in its course would pick up much more silt on account of its force. Should such a course be pursued, the river would probably be unnavigable on account of the current; then, also, the effect of such a current against a bank would be disastrous. Should not the river be allowed to follow its natural course, spreading out over and enriching and raising the level of the land along its borders on certain occasions? Would it not be better to learn to use the land according to the laws of nature and not to struggle ineffectually against them? The question of leveeing, when near me the years I lived in the Mississippi Valley, raised the legal question in my mind as to whether the levees could be legally built, in view of the fact that they changed the natural course of the flow and raised the water of other land, and at the time the question of whether or not the building of levees on the Arkansas side of the river, raising the flood level in Tennessee, would not be stopped by injunction issued in the Federal Court. Mobile, Ala. GEORGE B. CLEVELAND, JR. Forth and Clyde Battleship Canal To the Editor of the SCIENTIFIC AMERICAN: With reference to the notice of the above project in your issue of March 29th last, permit me to point out through your correspondence columns, that the British government has promised state aid to the project on certain conditions. (See page 1 of the accompanying reprint of the engineer's lecture to the Royal Scottish Society of Arts on January 31st, 1910.) The altered strategical conditions under which the home battle squadrons of the British fleet are now placed have rendered the construction of the ship canal an imperative necessity, and the question is now mainly one of terms between the treasury and the canal promoters. I would further point out that the ship canal would be of the utmost commercial importance to the maritime traffic passing between the New World and north central Europe. MAJOR CHILTON L. ADDISON SMITH. Edinburgh, Scotland.
