of August, 1874, he was still carrying on with the assistance of his eldest son. Mr. Woodcock took out several patents connected with the subjects of warming and ventilation, including improvements in the original Gurney stove. He was elected an Associate of the Institution of Civil Engineers on the 9th of January, 1855. A Paper of his, entitled On the Means of Avoiding Visible Smoke from Boiler Furnaces," was read before the Institution on the 14th of November, 1854. He also took a prominent part in a discussion on a subsequent Paper on Steam Boilers. Mr. Woodcock was possessed of great energy and sound common sense. His integrity of character and unassuming manners, together with his thorough knowledge, both practical and theoretical, of the subjects to which he devoted a great part of his life, won for him the esteem and regard of all those with whom he had business relations. Of his private life, it is sufficient to say that it was a bright example for his children to follow, and that his memory will always be held in most affectionate regard by many friends. MR. CHARLES FAVELL FORTH WORDSWORTH, Q.C., was born at Harwich in 1803, and was the son of Mr. Robinson Wordsworth, a relative of the Poet-Laureate. He was educated at the Grammar School in his native place, was called to the bar in January 1833, and became Queen's Counsel in June 1857. He died on the 18th of February, 1874, after a short illness, from bronchitis. He was the author of the following works: "The Law of Joint-Stock Companies," which ran through several editions; "The Railways Construction Facilities Act, 1864;" "The Law of Railway, Water, Gas, and other Companies, requiring express authority of Parliament;""The Law of Compensations, by Arbitration and by Jury, under the Lands Clauses Acts;" "A Summary of the Law of Patents for Inventions;" "Practice at Elections of Members of Parliament." And he contributed frequently to legal and other periodicals. In 1857 he unsuccessfully stood for Paisley in the advanced Liberal interest. He was elected an Associate of the Institute on the 21st of January, 1851, and was in 1852 appointed Honorary Counsel, which position he held until his decease. 1 Vide Minutes of Proceedings Inst. C.E., vol. xiv., p. 1. SECT. III. ABSTRACTS OF PAPERS IN FOREIGN TRANSACTIONS AND PERIODICALS. On the Distribution of Loads over the Superstructure of Bridges. By M. LAVOINNE. (Annales des Ponts et Chaussées, Feb. 1874, pp. 166–203.) The superstructure of bridges usually consists of longitudinal beams, united by cross bearers, on which rests the actual roadway. The strain on a beam is generally calculated by supposing it to support the load which rests on the nearest half of each of the spaces between it and the adjacent beams. If, however, the cross bearers are continuous across the bridge, they will to some extent distribute this load over the whole of the beams, instead of leaving it concentrated on one. The object of this paper is to investigate the effect of this distribution, and to determine how far it should be allowed for, in designing the beams or main girders of bridges. The general theory of what may be called "mat-work systems" (that is, composed of two sets of ribs crossing each other at right angles) has been given by the same author in the "Annales des Ponts et Chaussées" for 1867, the subject being a kindred one, viz., the strains upon the vertical planking and horizontal ribs of a lock gate. The problem as there stated is as follows:-Given a number of parallel ribs, supported at their extremities and crossed at right angles by other ribs which are loaded in a given manner, to find the bending moment of any rib of either system at any point of its length. The investigation of this problem leads to numerous and complicated equations. To simplify matters, it is assumed in the present memoir (1) that the cross bearers are close together, and infinitely narrow, so as to cover the whole surface of the bridge; (2) that the beams are either three or four in number; (3) that both the beams and the cross bearers are of constant section throughout; (4) that the load is one of two classes, viz., either distributed over the whole length, and covering a zone of constant width, or else isolated in the middle of the span, and occupying a certain width on each side of the centre line. First, in the case of three beams of equal strength, the final results show that no material advantage is gained by the cross bearers being continuous across the bridge, except when the load is equally distributed on each side of the longitudinal axis. If however, the load be evenly distributed over the whole surface, the strains on the three beams tend to become equal, as they would be if the beams were independent, and each carrying the same load. It follows that the effect of cross bearers in distributing loads is very great where these are permanent and uniform, but small where they are local and accidental. In designing a bridge with three beams, it is usual to make the central one twice the strength of the others. On examining this case, it appears that, with a symmetrical load, no advantage is gained by the continuity of the cross bearers; and on further comparison, it is seen that, for a bridge of three beams, a central one of double strength, with discontinuous cross bearers, is the most economical design, in point of materials, which can be employed. The case of four beams is next examined. The equations are more complicated, but their development leads to the same results as those just given, viz., (1) The continuity of cross bearers is useful only with a symmetrical load covering the whole bridge, and with an unequal load it is a positive disadvantage; (2) The most economical design is one in which the cross bearers are discontinuous, and the middle beams are double the strength of those outside. The problem of a larger number of beams than four is not discussed in detail; but an attempt is made to examine it by adopting the hypothesis that the cross bearers are rigid, or, in other words, infinitely strong, so that under all circumstances of strain their form is that of a straight line. The investigation appears to point to the same result, viz., that the continuity of cross bearers is not to be recommended. This conclusion is the reverse of that arrived at in the former memoir with reference to lock gates, as it is there shown that the effect of continuous vertical planking is to convey a great part of the pressure to the sill, and to distribute the remainder nearly equally over the ribs of the gate. The difference between the two results is due to the fact, that in a bridge there is no solid support corresponding to the sill, and that the loads are more symmetrical. W. R. B. Graphic Method of calculating the Stresses on Roof-trusses. (Civilingenieur, xx., 4, 1874, cols. 206-216.) Only those constructions are dealt with in this essay the members of which are subjected to simple tension and compression. Further, all the arrangements of bracing have at least one pair of members connected together, and reaching from one abutment to the other. Those constructions, the general outline of which is trapezoidal, or which are not bounded by members forming a triangle, but are composed of a series of triangles arranged in succession, will be discussed in a second essay under the head of bridges. Deviating from the customary method, in which the supporting forces at the abutments are first ascertained, and the stresses on the members of the truss derived from these proceeding from the extremities inwards, each separate load is followed, and the supporting forces are obtained as a final result. The forces in the several members are exhibited in the diagrams, as sums, in which the part due to each separate load can be recognised with facility. Accordingly, this graphic method serves not only for the solution of special numerical examples, but also for discovering the fundamental law of the distribution of stress for each construction. The Author investigates first the simplest roof-truss, consisting of two rafters, inclined upwards so as to be in compression, or downwards so as to be in tension. By combining the results he gets the diagram for a roof-truss, consisting of a pair of rafters, a bent tie, and a kingpost. He then replaces the kingpost by a triangle of bracing. Lastly, he shows how the diagrams for the more complicated forms of roof-trusses may be built up out of the simple diagrams previously obtained. The method could not be rendered intelligible without illustrations. W. C. U. Graphical Determination of the Weights, corresponding to a given Span and given Unit Strain, which a double T Iron can support, when resting on two Bearings, and of which the moment of Inertia and Depth are known. By M. DE BLONAY. (Mémoires de la Société des Ingénieurs Civils, May 1874, pp. 278-279.) The relation between the moment of strain and the moment of resistance of a beam or girder, resting on two supports, with a span and load uniformly distributed corresponding to a given unit strain, is expressed by the general equation PC R1 R 1 = In this equation C is equal to the half span, P half the total load uniformly distributed, and the moment of resistance. If 2 C and 2 P, or the span and the load, be considered as variable quantities, and be represented by x and y respectively, then, putting A for the constant quantity 8 R1 the preceding equa tion may be written x y = A, the equation of a hyperbola with respect to its asymptotes. Without altering the value of the ordinate, let the abscissa x and it may be replaced by another x having the value of 1 = then be written y Ax, the equation of a right line passing through the origin of the figure. When x = 0, x1 = When the value of x increases, the corresponding value of x, decreases; and when x = ∞, x1 = 0. Since the value of x, diminishes as the span increases, it is evident that the lengths of the spans should be regarded as starting in a positive direction from right to left. M. de Blonay observes that it is customary, and also more convenient, to start the abscissa from left to right, and therefore changes the sign of the angular coefficient in the last equation, thus putting - A = B, which gives y Bx,. This equation, which is that of a right line symmetrical with the former, represents the relation between the load and the span, with the difference that the positive values of the spans increase from left to right. = As there is no practical use in considering spans whose lengths are below a certain minimum, M. de Blonay takes the origin from the left at a distance a, the minimum span which is considered equal to The new abscissa X has for its value 1 a 21a, and the equation becomes y B (X-a). Whatever value may be given to B, the right line cuts the axis of x at the point where the abscissa is equal to a. It may, therefore, be completely determined by calculating the ordinate of a second point; for instance, of that which corresponds to X = 0. Afterwards the load can be graphically ascertained which corresponds to a span somewhat greater than The diagram pre 1 a pared by M. de Blonay gives the loads not only for iron of the double T form, but for any description of beam of which the depth and the moment of inertia are known. C. T. On the Joining of Inclined Lines by Parabolic Arcs. (Annales des Conducteurs des P. et Ch., March to June 1874, 27 pp., 3 pl.) Three methods of drawing a parabolic curve to join two inclined lines are compared. In the first method one point in each of these lines, being tangential points, and their point of intersection, are the data; a line is drawn between the tangential points, and the centre of that line being joined to the point of intersection already referred to gives a diameter of the parabola. The means of drawing the curve is described, but the method being complicated, it is not one to which the Author further refers. In the second and third methods a vertical line (see Figs. 1 and 2) is drawn from the point of intersection S, and a horizontal line from the tangential point A of one line of inclination of such a length that the vertical line bisects it, and a vertical line is let |