In all cases where asphalt is used, that with the least proportion of bitumen should be preferred. Seyssell asphalt, which comes from France, is undoubtedly the best, and next to this comes the Swiss or Neuchatel asphalt.

Trinidad asphalt, which is much used in this country, is much inferior, being softer and containing a larger proportion of bitumen or tar - a great disadvantage in many cases.

In all walls try to get all openings immediately over each other. A rule of every architect should be to make an elevation of every interior wall, as well as of the exterior walls, to see that openings come over each other.

It is foolish to make chimneys or tower-walls unnecessarily thick (and heavy), as they brace and tie themselves together at each corner, and, consequently, are much stronger than ordinary walls. Tower-walls, however, often require thickening all the way down, to allow for deep splays and jambs at the belfry openings. The chief danger in towers is at the piers on main floor, which are frequently whittled down to dangerous proportions, to make large door openings. In tall towers and chimneys the leverage from wind must be carefully considered.

Considering the importance of ascertaining the exact strength of walls, it is remarkable that so little attention has been paid to the subject by writers and experimenters. The only known rule to the writer is Rondelet's graphical rule, which is as follows:

If A B (Figure 83) be the height of a wall, B C the length of wall without buttress or cross-wall (AB C being a right angle), then draw A C; make A D = to either 1/8 or 1/10 or 1/12 of A B, according to the nature of wall and building it is intended for (1/12 for dwellings,1/10 for churches and fireproof buildings, and 1/8 for warehouses); then make A E = A D, and draw E F parallel to A B; then is B F the required thickness of wall. The rule, however, in many cases, gives an absurd result. Gwilt's "Encyclopedia of Architecture" gives this rule, and many additional rules, for its modification. There arc so many of them, and they arc so complex, however, as to be utterly useless in practice. Most cities have the thickness of walls regulated by law, but, as a rule, these thicknesses give the minimum strength that will do, and where they do not regulate the amount and size of flues and openings, frequently allow dangerously-weak spots in the wall.

The writer prefers to use a formula, which he has constructed and based on Rankine's formula for long pillars, see Formula (3), and which allows for every condition of height, load, and shape and quality of masonry. in the case of piers, columns, towers or chimneys, whether square, round, rectangular, solid or hollow, the Formula (3) can be used, just as there given, inserting for ρ2 its value, as given in the last column of Table I, using, of course, the numbered section corresponding to the cross-section of the pier, column or tower. By taking cross-sections at different points of the height, and using for l the height in inches from each such cross-section to the top, we will readily find how much to offset the wall. Care must be taken, where there are openings, to be sure to get the piers heavy enough to carry the additional load; the extra allowance for piers should be gotten by calculating the pier first as an isolated pier of the height of opening, and then by taking one of our cross-sections of the whole tower or chimney at the level where the openings are, and using whichever result required the greater strength.

Rondelet's rule.

Formula for masonry.

Formula for masonry

Fig. 83

As it would be awkward to use the height l in inches, we can modify the formula to use the height L in feet. Further, we know the value of n for brickwork, from Table H, and can insert this, too; we should then have: For brick or rubble piers, chimneys and towers, of whatever shape:

Strength of piers,chimneys and towers.

w = a.(c/f)/1+0,475.(L2)

Walls And Piers 100156

(59)

Where w = the safe total load on pier, chimney or tower in pounds. Where a = the area of cross-section of pier, etc., in square inches, at any point of height.

Where L = the height, in feet, from said point to top of masonry.

Where (c/f) = the safe resistance to crushing, per square inch, as given in Table V. (See page 135.)

WhereWalls And Piers 100157 = the square of the radius of gyration, of the cross-section, in inches, as given in Table I.

If it is preferred to use feet and tons (2000 lbs. each) we should have w= A.(c/f)/14+0,046.(l2/P2)

(60)

Where W = the safe total load on masonry, in tons, of 2000 lbs each.

Where A = the area of cross-section of masonry, at any point of height, in square feet.

Where L = the height, in feet, from said point to top.

Where ( c/f) = the safe resistance to crushing, in lbs., per square inch, as given in Table V. (See page 135.)

Where P2=the square of the radius of gyration, as given in last column of Table I, - but all dimensions to be taken in feet.

To obtain the load on masonry, include weight of all masonry, floors, roofs, etc., above the point and (if wind is not figured separately) add for wind 15 lbs. for each square foot of outside superficial area of all walls above the point.

Where towers, chimneys, or walls, etc., are isolated, that is not braced, and liable to be blown over by wind, the wind-pressure, must be looked into separately,

In regard to the use of (c/f ) the safe resistance, per square inch, of the material to crushing, it should be taken from Table V. So that for rubble-work we should use:

(c/f) = 100

And the same for poor quality brick, laid in lime mortar.