chosen as a lever arm between tension and compression. The strain in the upper part of the concrete of the ceiling plate does not move within such narrow limits as this lever arm of Z and D and this strain should be calculated, for which purpose the following more exact course might be adopted. The neutral axis lies within the distance x from the upper part of the plate in the groin, k to be the distance of the reinforcement from the same part, fe means the cross-section of the reinforcement reduced to the unit of the operative width of the plate. The calculation is then easily made, the small compressive forces in the upper part of the girder left out of consideration, one obtains, assuming a constant modulus of elasticity Ec for the compressed concrete, the distance of the neutral axis : 2 x a x k x fe + d2 2 x (a x fe + d) The distance of the centre of the compressive strains or the distance of the point of gravity from the neutral part, forming a trapezium, can be calculated as follows: d d? y=x 6 X (2x - d) If the centre point of the pressure is known, the compressive force D=2 as well as the strain de can be ascertained by means of the following formulæ :-- = X + 2 de x x dc= a (k - x) In the case of plate beams the correct calculation for their cross-sections as regards the shearing forces is just as important as the one regarding the tensile strains, and the construction of the plate beams became only possible when it was recognised that the concrete on the one part could take up a considerable shearing stress in itself, and that on the other part with a suitable reinforcement it could counteract the shearing strains. With the plates the calculation shows such small values for the shearing stress, that they can safely be taken up by the concrete itself. With plate beams, however, special reinforcements for the shearing forces are to be added, and the calculation for the shearing strains of the stirrups and the adhesion strains becomes necessary. The calculation of the shearing strains is done in the following way : :- The shearing forces appearing in the area CC'. Fig. 5 between two neighbouring cross-sections are equal to the difference of the normal forces in AC and A'C'. If we, therefore, draw the line t of the shearing strains, the shearing strains in the upper part will be equal to 0 and will increase up to the value T in the direction of the neutral axis. Under the assumption hitherto observed in connection with all strain calculations, namely, that the concrete should not take up any tensile strains, the shearing strains underneath the neutral axis will remain constant. The value in rectangular cross-section can be calculated as follows : shows also the sum of the adhesion strains acting on the outside of the reinforcement, so that the same can also be calculated in a simple way. With the cross-section of the plate beam the distance of the tensile and compressive centre point is substituted in place of It may also be mentioned that the simultaneous presence of a great bending moment the mentioned value for the shearing strain is not altered even if the tensile strength of the concrete is taken into consideration For in concrete, subjected to great tensions, the difference between neighbouring cross-sections is zero. An increase can therefore not take place for the shearing strains in the part of the cross-section under tension. Out of the adhesion strain the number of iron bars is calculated which must still be present on the bearer, and it is therefore evident that it will not do to assume the dimensions by the line of the maximum moments solely. If sufficient reinforcement is not given to the supports the destruction of the girder occurs through the irons being pulled out of the concrete at the bearer ends. The distance and the thickness of the stirrups are calculated out of the shearing strain; it is a rule that 43 to 72 lbs. per square inch can be taken up by the concrete and the rest falls to the stirrups. If we know that concrete is capable of following the extension of the iron, and we do not take into consideration the tensile strains in the calculations of the dimensions. This is, in my opinion, a method of calculation giving the greatest protection against the occurrence of cracks, quite apart from the absolute safety and strength which is obtained thereby. In reality the tensile strength of the concrete is naturally still present, which fact will show only slight deflections of reinforced concrete constructions under loading tests. Further, it must be considered that in consequence of the strong and close interlocking of all parts of a ferro-concrete structure more factors take part in the bearing of the load than generally appears in the calculations, and any of the other building systems manifest it. The slight deflection can also be easily accounted for and determined beforehand. a I herewith hope I have proved to you that the above-mentioned assumptions may be accepted as really existing facts, and that statical calculations of ferro-concrete structures can be made on a similar basis as laid down here. In conclusion, I wish to make a few general remarks : Everyone familiar with this new building system will admit that there exist a great many reinforced concrete constructions, which give great satisfaction for the purposes they are erected for, and still exercise that resistance, if the limit of the strain is reached or even exceeded, for which the structures are calculated. Considering the splendid qualities which are proved in existing structures, there should be no difficulty in erecting buildings of greater dimensions and with complicated stresses, if the formulæ employed for calculating the dimensions of the proved structures were generalized, and extended to the new contemplated purpose, and if the fundamental materials, concrete and iron were of the same quality and were worked with the same carefulness. While iron, wood, brick buildings, etc., are liable to decay, therefore requiring frequent overhauling, reinforced concrete constructions are gaining in strength in the course of time. Not only do these buildings resist elements as moisture, temperature, etc., but also chemical reactions have no effect on them. The iron embedded in the Portland cement concrete remains perpetually unaltered, and ferro-concrete constructions can be considered as practically indestructible by any causes. If the reinforced concrete principle is to be extensively used in building construction, there is one important fact which must not be overlooked, “ we must have cheap cement." I do not mean cement of an inferior quality, but first quality cement at a lower price. This can only be done by erecting factories in various parts of the country, and if sufficient enterprise is forthcoming, and a factory equipped with the latest modern machinery, cement could be sold in Kimberley at 50 per cent. less than the landed cost to-day. Only quite recently I have tested samples of the raw material which have been submitted to me, and found them equal to any sample I had seen in Europe used for the manufacture of the best Portland cement. These samples were obtained from a place within one hundred miles of Kimberley, and in close proximity to the railway line. Another reason why reinforced concrete should be used on a more extensive scale is that South Africa does not possess a producing iron industry, and every girder has to be imported. In conclusion, I would like to express the wish that reinforced concrete may sooner or later be introduced in constructional engineering throughout this sub-continent, and that the money which is being expended by the Governments and Public Corporations, in the purchase of steel bridges and other structures, may be retained and circulated in South Africa by the adoption of the reinforced concrete system which I have been privileged to put before you. By A. E. PAYNE. Two years ago, in a paper which the writer had the honour of reading before this Association in Johannesburg, * reference was made to the apparently simple object of measuring an angle in an underground traverse by means of a transit theodolite. The writer called attention to the care with which the simple operation should be conducted so as to justify the reliance which must later be placed on the results obtained. Since that date it has been brought home to the writer, as a member of the Commission of Examiners for Mine Surveyors' certificates, appointed by the Transvaal Government, that there is a great diversity of opinion amongst the mine surveyors of these fields as to how this operation should be best conducted. It would seem, therefore, advisable to follow up the outline of the mine surveyors' work, as sketched in the remarks of two years ago, with a few details of some of the methods employed in conducting an underground traverse, and the subsequent calculations connected therewith. To obtain the necessary information from authoritative source, the writer asked the Consulting Engineers of the chief Mining Groups represented on the Witwatersrand fields to furnish him with a copy of the form of calculation, the method of procedure, and any other relative information in general use in that group. The result of this enquiry is tabulated in the following pages : an I. METHOD OF PROCEDURE. First Method.—Self-explanatory. Second Method—(Note to Page 403).—“In the first column the station at which the instrument is set up is noted, the second and fourth columns being for angles observed. In the column marked mean azimuth” the stations observed are noted, under which also appears the mean reading to that station. Always reading the angles from left to right, it is easy to see which is the back sight and which are foresights. The instrument is set just over 360° and set on the back sight, lower limb clamped, upper limb unclamped, and the foresight taken ; upper limb unclamped, and telescope revolved end for end on its axis and set on back sight ; upper limb unclamped and foresight taken, each time reading both verniers." “The reason for setting the instrument just over 360° is to make it necessary to read the angle instead of taking it for granted that the vernier is at zero. The readings are then meaned “B” vernier over “A” vernier, and then again B A and A B, the result of which is the true mean reading. Carrying this process through all the stations sighted, and deducting the mean reading of back sight from the foresights, the true mean horizontal angle is at once obtained. The underground stations are not more than 100 feet apart, partly because of chaining and because they are afterwards useful in stope measuring.” "In levelling the collimation method is used, rail and peg level being taken at each station." The Mine Surveyor and His Work in the Witwatersrand District,” vide report of the South African Association for the Advancement of Science, Johannesburg Meeting, 1904, pp. 393-401. I. METHOD OF PROCEDURE. (I)=First Method -0° = south ; 90° = west ; 180° = north; 270° = east. (501 signifies station 501. (501 to (502 (502 to (520 4 R 89° 52 S. 85° W. S. 85° E. Alright, see vol. 2, p. 30. V= 21.07 112° 14' N. 75o W. N. 85° E. H=114:60 Vertical angle 10° -25' 116-52 Old Copper spad in plug in roof. +25' sides 3R 3L Ist sd. Boxhole 5' R 4 L +67' sides 4R IL +75' Ist sd. Winze 3R 3L + 80' 2nd sd. 3R 3L +95' Drive leaves reef in hanging on Rt. 3' Rt. sides IR 5L (No reef) 3R 3L V= 1.82 96° 55' N. 89° W. S. 73° E. H=25.55 2562 Vertical | angle 4° 05' New copper spad in plug in roof. ...10 sides 4R 2L 100' 110' 116-52 1620 to (621 |