To find the depth of a beam supported at both ends, to sustain a given weight, the length and thickness or breadth of which is given - The weight multiplied by the square of the length, and this by 'Oil, and the result divided by the thickness, gives a quotient, the cube root of which is the depth for pine.

To find the thickness of a beam, the weight, length, and depth being given - The weight, multiplied by the square of the length, and the result multiplied by .011, gives a quotient, which divided by the cube of the depth in inches, gives the breadth or thickness required. In both these rules, the weight to be supported must be in pounds.

To find the diameter of a round post of red pine, to sustain a given weight - Weight in pounds multiplied by 17, multiplied by .0021; multiply the square root of the result thus obtained by the height in feet, and the square root of the product is the diameter required. The length should not exceed ten times the diameter.

To find the depth of a rectangular post of red pine, the breadth or thickness of which is given - Take the square of the length of the post in feet, multiply this by the weight in pounds which the post has to sustain; multiply the quotient by .0021 and divide by the breadth in inches, the cube root of the quotient will be the depth of the beam.

The following, giving the dimensions of various parts of king-post and queen-post roofs, may be useful for ready reference. "We classify the various parts according to the positions which the timbers assume, such as horizontal, vertical, and inclined, as this may make the references perhaps still more easily available. We shall take the vertical timbers first, these being comprised of two members only; the king posts and queen posts.

 King Posts. Span, or distance fromWall to Wall. Dimensions, or Scantling inInches. 18............ 4 X 3. 20............ ... 5½ X 3. 22............ 4 X 3½. 24............ ... 4½ X 84. 26............ . 5 X 3½. 28........... 5 X 4. 30............ ... 5½ X 4.
 Queen Posts. 30............... 4½ X 4. 32............... 5 X 4. 32............... 5½ + 4. 36............... 5½ X 4½.
 King-Post Roofs. Tie Beams. 18.............. 7½ X 3. 20.............. 8 X 3. 22.............. 8½ X 3½. 24.............. 9 X 3½. 26.............. . 9½ X 4. 28.............. 10 X 4. 30.............. .10½ X 4.
 Pole Plates. Span, or Distance fromWall to Wall. Dimensions, or Scantling inInches. 18............ 4 X 3½. 20............ 4 X 4. 22............ 4 X 4. 24............ 4 X 4. 26............ 4 X 4. 28............ 4 X 4. 30........... 4 X 4.
 Wall Plates. 18............. 4 X 3. 20............. .. 4½ X 3. 22............. .. 4½ X 3. 24............. 5 X 3. 26............. 5 X 3. 28............. 5 X 3. 30............. 5 X 3.
 Purlins. 18............... 6 X 34. 20............... 6½ X 34. 22............... 7 X 3½. 24.............. 7½ X 34. 26............... 8 X 4. 28.............. 8½ X 4. 30............... 8½ X 4½.
 Queen Posts. Tie Beams. 30............... 5 X 3. 32............... 5 X 4. 34............... 5 X 4. 36............... 5 X 4.
 Wall Plates. Span, or Distance fromWall to Wall. Dimensions, or Scantling inInches. 30............ .,, 9 X 4. 32............ .. 9 1/2 X 4. 34............ . 10 X 4 1/2. 36............ ...10 X 5.
 Purlins. 30.............. . 7 X 3½. 32.............. . 74 X 3½. 34.............. 8 X 4. 36.............. 8 X 4.
 Straining Pieces. 30............... 7 X 4. 32............... 74 X 4. 33............... 8 X 4. 36............... 8 X 4.
 Straining Sills. 30............... 4 X 4. 32............... 4½ X 4. 34.............. 5 X 4. 36............... 5 X 4½.
 King Posts. Principal Rafters. 18............... 5 X 3. 20............... 5½ X 3. 22............... 6 X 3. 24.............. 6 X 3½. 26............... 6i X 3½ 28............... 6½ X 4. 30............... 7 X 4.
 Common Rafters. Span, or Distance fromWall to Wall. Dimensions, or Scantling inInches. 18............ ... 3 1/2 X 2. 20............ ... 3 1/2 X 2. 22............ ... 4 X 2. 24............ 4 X 2. 26........... ... 4 1/2 X 2 1/2. 28............ ... 4 1/2 X 2 1/2. 30............ . 5 X 2 3/4.
 Braces or Struts. 18............... 3 X 24. 20............... 34 X 2½. 22............... 3½ X 3. 24............... 4 X 3. 26............... 4½ X 3. 28............... 44 X 34. 30.............. 5 X 3½.
 Queen Posts. Principal Rafters. 30............... 5½ X 4. 32............... 6 X 4. 34............... 6½ X 4½. 36............... 64 X 4½.
 Common Rafters. 30.............. 4 X 2. 33.............. 4 X 2½. 34.............. . 4½ X 2½. 36.............. 5 X 2½.
 Braces or Struts. 30............... 4 X 3. 32............... 4 X 34. 34............. 44 X 3½. 36............... 5 X 3½.

71. As already stated, cast-iron is almost universally used for metal columns, to sustain heavy weights, its greatest strength being shown in its resistance to crushing powers. It is, however, a very uncertain, indeed treacherous material, being liable to break suddenly at and in unexpected times and situations. It is ill calculated to bear sudden shooks or blows, its power to resist tension is comparatively feeble, that of compression being generally estimated at four tons per square inch.

Wrought-iron is seldom used for columns, although its resistance to crushing powers is high; still it is liable, from its flexibility, to be bent or forced out of the perpendicular line, and weakened to a very great extent. Its cohesive powers, however, constitute its most valuable feature, hence for beams, tie rods, etc., which are subjected chiefly to tensile strain, it is most extensively used; seven tons per square inch being generally allowed as the safe tensile load. The following gives the strength of some of the leading qualities of cast-iron to resist the crushing strain, as, for example, that to which iron columns are subjected per square inch of section. Low Moor, 28.809 tons; Clyde, 41.249; Coltness, 44.723; Plaen War, 40.562; Brymha, 33.399; Ystalyfera anthracite, 44.6610. A quality of iron which may be said to be sui generis, and which is not a pure cast-iron, having a portion of wrought-iron in its composition, and which was patented by Mr. Morris Sterling, shows in its best quality the highest strength of the samples experimented upon in Mr. Hodgkinson's series of trials, being as high as 70.824 tons per square inch of section; the lowest quality being 53.329. The mean breaking weight of cast-iron varies of course according to sample, as our readers will all probably know. Cast-iron is now smelted chiefly by the hot-blast plan; that is, by the use of air of a very high temperature, in contradistinction to the old plan, in which cold air was used. Cast-iron prepared on these two plans are known respectively as " hot" and "cold blast iron." The following gives the mean breaking (in pounds) weight of some of the leading qualities, giving the highest first, hot and cold blast will be here classed separately, taking the cold-blast first. Ponkey, 581 lbs., this in colour is whitish-grey, and of hard quality; Cleator, 537 lbs., white colour and hard; Low Moor, 472 lbs., dark-grey and soft; Carron, 444 lbs., grey and soft; Blaina, 448 lbs., bright grey colour and hard; Coed - Tallon, 413 lbs., grey and rather soft in quality. Coming now to the hot-blast irons we take the Devon, which has a mean breaking weight in pounds of 537, and is white in colour and hard in quality; Carron, 527 lbs., whitish-grey and hard; Butterley, 502 lbs., dark-grey and soft; Beaufort, 474 lbs., dull-grey and hard; Gartsherrie, 447 lbs., light-grey and soft; Muirkirk, 418 lbs., bluish-grey and soft. As already stated, beams supported at both ends, and either loaded, or in virtue of their own weight, have a tendency to bend or get depressed below the line of level of their supporting points, this is known as their "deflection." The following gives the rate of the deflection of cast-iron bars 4 feet 6 inches long : - Ponkey, cold-blast (c. b.), 1 .7'47 inch; Cleator (c. b.), 1.001; Low Moor, 1.852; Blaina, 1726; Coed-Talon, 1.470; Devon, hot-blast (h.b.), 1.09; Carron, 1.36; Beaufort, 1.51; Gartsherrie, 1.557. Cast-iron beams placed in the circumstances named in last sentence are sometimes subjected to blows or sudden shocks, their power to resist these is known as their "resistance to impact." The following are examples of the strength of the leading qualities we have named in two previous sentences to resist impact: Ponkey (c. b.), 992, the bars being 4 feet 6 inches long; Cleator, 537; Low Moor, 855; Blaina, 747; Carron, 593; Coed-Tallon, 600. All these are cold-blast iron. The following are hot-blast (h. b.): - Devon, 589; Carron, 710; Butterley, 889; Beaufort, 729; Gartsherrie, 998; Muirkirk, 656. The ratio of power which cast-iron has to resist tension and crushing strain, may be stated in round numbers to vary from 1 to 4½ of the lowest, of 2, 6¾ of the highest qualities named in the above sentences.