A Treatise on a Vox of Instruments and the Slide-Rule; For the Use of Gaugers, Engineers, Seamen and Students (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1854 Excerpt: ...will be I da (putting I length andddiameter) and/353.0353 = 18.78, the gauge point for cylinders. In the same way as the pyramid was determined by taking 3 times the prismatic divisor, so the content of the cone will be found by taking 3 times the cylindrical divisor; and 3 X 353.0353 Id--1059.106; consequently, content = loMTUB' an l/1059.106 = 32.54 the conical gauge point. The globe, being f of the cylinder, will be twice the cone; hence the divisor will be the half of 1059,106, namely, 529,553; therefore, putting d the diameter, the content of the globe dd will be 529 553 an V 529.553--23, the gauge point for globes. By having divisors and gauge points thus prepared, round solids are reduced to square ones, by which means their contents are determined with the greatest ease, as they all come under the general formula Is in which I represents the length, s the side or diameter, as the case may be, and G the prepared divisor, or, for the purposes of the Slide-rule, its square root, the gauge point. For finding the solidities of frustums the followiBg is an invaluable rule, and of general applicability: --Find the area of the top, the area of the bottom, and four times the middle area; their sum is six times a mean area, which, being multiplied by one-sixth of the depth, gives the content. Now, since by the above-mentioned divisors we have reduced round solids to square ones, the rule becomes: Add together the square of the top, the square of the bottom, and four times the square of the middle, and multiply the sum by one-sixth of the depth. But four times the square of a number is equal to the square of twice that number; therefore the rule becomes still easier. Add together the square of the top, the square of the bottom, and the square of twice the middl..