The large number of mathematical operations which have to be performed successfully in order that the law may be demonstrated will now be shown by taking No. 1 as an example.

(A) From the two approximate experimental data of S.G. discover the correct value (4.78) at 15° C.

(B) Divide the at. wt. by 4.78, obtaining the orig. rel. vol. of As (15.68) at 15° C.

(C) Discover the combining relative volume or volumes of As. This can only be done by a systematic study of all the thousands of substances of which the S.G. is recorded. (The volume of each atom in the molecule As,O, is given at the top of Table II.)

(D) Discover the H.F. of each atom in this molecule. (The results in the case of As2O, are given at the top of Table III.)

(H) Subtract the combining vol. of oxygen (7.53) from 10.07, obtaining 2.54.

(I) Multiply 2.54 by 16 and by the constant for sub-sodium elements (795), obtaining 32341.

(K) Subtract the other combining volume of oxygen from 10.07, obtaining 7.56. (L) Multiply 7.56 by 16 and 795, obtaining

96155.

(M) Add the results (F), (I), and (L) as in No. 1, Table III., obtaining 154451, which is considered to be correct if it is within 2000 of the experimental result, 154670, because experimental results frequently differ by more than 2000.

This example demonstrates the exact manner in which the 90 experimental results of H.F. correspond with the experimental results of S.G.

Only 43 elements are available for the demonstration of this law, since the others are not included in the experimental determinations of H.F. 32 of the 43 are here employed. The remaining eleven, viz., Pt, Au, Ce, Nd, Pr, Th, Sr, Be, Br, Cs and Rb, do not come into the demonstration at present, because one of the necessary experimental facts in each case is wanting.

It should be noticed that when an element has several combining volumes, these do not denote a weakening of the proof, but a very great strengthening, because each change of volume is shown to have a corresponding change of heat of formation.

Re Hydrogen, see the Chemical News, 1925, CXXXI, 33.

TESTS OF HOLLOW TILE AND
CONCRETE SLABS REINFORCED
IN ONE DIRECTION.

By DOUGLAS E. PARSONS AND
AMBROSE H. STANG.

(U.S.A. Bureau of Standards.)

Beams which represented sections of typical combination hollow tile and concrete floor slabs reinforced in one direction were made and tested in the laboratory for the purpose of obtaining information on the value of hollow tiles in resisting bending and shearing stresses. The test pieces consisted of 42 beams from 8 feet 10 inches to 15 feet 3 inches long, all 8 inches in depth and having a maximum width of 30 inches. For the purpose of comparison two concrete beams having the same sectional area as the gross sectional area of the composite beams and three concrete beams having the same sectional area as the concrete ribs in the composite beams were also tested.

Observations were made of the deformation in the concrete, tiles and reinforcement,, deflection of the centre of the beam and development of cracks as the loads were applied.

Tables and curves give a summary of the test data, and comparisons are made between these and the usual design computations for reinforced concrete beams.

The results indicate that the tiles assisted the concrete in resisting both bending and shearing stresses. The assistance of the tiles in resisting bending stresses seemed to be approximately proportional to the modulus of elasticity of the tiles. The elasticity of the tiles in resisting shearing stresses varied somewhat with the kind of tile, but, in general, added about 50 per cent. to the shearing strength of each concrete rib.

SUMMARY.

The results of these tests seem to warrant the following conclusions :

For beams without topping.-1. In resisting bending stresses each hollow tile and concrete rib in the combination beams was equivalent in strength to a rectangular concrete beam having a width at least equal to the width of the concrete rib

E

plus 1.3 (s+w) · Ec

where E is taken as 2,000,000 lbs./in.2 and

s = thickness of one vertical tile shell, inches.

w thickness of one vertical tile web, inches, and

E=modulus of elasticity of the tiles, lbs./in.2

2. The average strength of the beams having mortar in the cross joints between the tiles was only slightly greater than the average strength of the corresponding beams having open joints.

3. The effect of the tiles at loads less than the maximum upon the deformations in the concrete, the position of the neutral axis, and the deflections was apparently equal to or greated than the effect of adding a E.

width of concrete rib equal to 2 (s+)

E.

4.The compressive stresses in the shells. of the hard tiles in contact with the concrete ribs were greater than the compressive stresses in the adjacent concrete.

For beams with a topping. The top shells of the tiles in contact with the concrete seemed to be as effective in resisting compressive stresses as an equal area of concrete in the same location.

For both types of beams.-On the assumption that the shearing resistance of the concrete in the combination beams was equal to its resistance in the concrete beams which failed by diagonal tension, the assistance of the two rows of half tile adjacent to each concrete rib was at least equivalent to the following widths of concrete in resisting shearing stress: Tile of lot 1, 2.2 inches; tile of lot 2 with mortar joints, 1.9 inches; tile of lot 3, 3.4 inches; tile of lot 3 with mortar joints, 2.5 inches; tile of lot 4, 2.4 inches.

2. The combination beams containing bent-up bars for web reinforcement resisted an average shearing stress over the b' jod section of concrete of 541 lbs./in. without visible indications of diagonal tension failures.

3.The strength of the bond between the concrete and tiles even with open joints was sufficient to permit failures of the beams by compression and diagonal tension. There seemed to be no failures caused primarily by the failure of this bond.