On a Common Law in Reference to Electric Induction.
By R. CLAUSIUS, Hon. M. Inst. C.E.

(Annalen der Physik und Chemie, new series, vol. i., pp. 493–499.)

There are already manifold laws of reciprocity in reference to mutual induction between two electrical conducting bodies. The Author believes that the following enunciation is new, and that the laws of reciprocity are consequent therefrom.

Let there be given any number of conducting bodies, C1, C2, C3, &c., which influence one another. These become charged with electricity in two distinct ways. By the first charge let there be upon each single body the quantity of electricity represented by Q1, Q2, Q3, &c., and the corresponding potential of the bodies by V1, V2, V3, &c.; and by the second charge let the potentials and quantities of electricity be 91, 92, 93, &c., v1, v2, v3, &c. Then the following equation will hold

V191+V292+ V3 3 + &c. = v1 Q1 + V2 Q2 + V3 Q3 + &c. ;

or substituting the summation sign,

1

v3

ΣVq = Σv Q.

P. H.

The Dynamo- and Magneto-Electric Machines of the Lontin

System.

(Annales du Génie civil, 2nd series, vol. vi., pp. 137–148.)

The Author describes a magneto-electric machine in which upon a central axis is mounted radially a series of electro-magnets. These electro-magnets have the whole of their bobbins connected in one continuous circuit; from each connection between two bobbins a wire is led to a segment of a cylindrical commutator, there being as many segments of the commutator as there are radial electro-magnets. Each electro-magnet is capable of forming a separate inductor, or the whole series may form one powerful inductor, the current of which may be taken from two brushes, or from as many brushes to form separate circuits as there are radial electro-magnets or segments on the commutator. The outer poles of the radial electro-magnets are caused to revolve by rotation of the axis between the positive and negative poles of a powerful horseshoe electro-magnet.

The novelty of the system lies in the production of as many separate current-circuits as there are radial electro-magnets, by which means as many electric lights can be produced from one

machine as there are circuits; or a single electric light of concentrated power may be obtained from the entire circuit of the whole number of radial electro-magnets. Further it is an advantage of this machine that it may be used as a motor actuated by the current produced by another dynamo machine.

P. H.

On the Theory of Screw-Propellers. By C. SZILY.

(Der Civilingenieur, vol. xxiii., p. 177.)

After quoting Redtenbacher to the effect that "A rational method in the construction of screw-propellers is not known, and that it has hitherto been impossible to deduce the best form of the blades from mechanical laws;" and Rühlmann, "As regards the present form of the screw-propellers, theory leaves us entirely in the dark as to their determination and thus it is that nearly every maker of screw-propellers has his own forms, all founded more or less on empirical rules;" the Author makes an attempt to obtain a useful theory in applying the differential calculus to the problem of the screw. His problem is :

A surface, plunged into water, rotates with constant angular velocity round an axis which moves in a straight line at a constant velocity. The water, in consequence of its resistance, exerts a pressure upon each part of the surface of the propeller, the direction of which falls in the perpendicular to the surface, and the magnitude of which is proportional to the surface and the square of the normal velocity. Between given limits find the surface on which the pressure of the water in the direction of the forward movement is a maximum or a minimum. Friction is disregarded. With the aid of a diagram the Author produces a lengthy series of highly complicated algebraic formulæ, from which he draws the following deductions :

1. The task of determining that surface which, rotating in water and moving forward simultaneously, is subject to a maximum of pressure from the water in the direction of its forward movement, leads to a highly complicated differential equation, the solution of which seems at present to be met by insuperable difficulties.

2. Among conoidal surfaces the Archimedian screw only can give the best effect, because it alone fulfils the conditions of the maximum and minimum.

3. The angle of inclination of the most effective conoidal-surfaced screw depends upon the relation between velocities of rotation and forward movement. Other angles of inclination would have to be given to the screw when at sea, or up or down the current.

4. On starting the conoidal screw in still water the angle of inclination should not be less than 22° 39' 27", otherwise its effect is not only not a maximum, but absolutely a minimum.

A. H.

INDEX

TO THE

MINUTES OF PROCEEDINGS,

1877-78.-PART I.

ABBEY, J. H., transferred member, 136.

Abstracts of papers in foreign transactions and periodicals, 277.-Ditto referred
to in the annual report, 169.

Accounts, auditors of, appointed, 162.—Review of the financial position of the
Institution in the annual report, with statement of the trust and other funds
belonging to or under the charge of the corporation, 170.-Abstract of receipts
and expenditure from the 1st of December, 1876, to the 30th of November,
1877, 172.

Acland, A. D., admitted student, 1.

L. M., elected associate, 135.

Acton, W. R., elected associate, 135.

Aitken, R., remarks as to the construction of quay walls and piers without the
use of cofferdams, 154.

Aix-la-Chapelle, waterworks of, 381.

Aldridge, J. G. W., admitted student, 1.

Allen, P. R., Miller scholarship awarded to, 169, 176.

Almguist, P. W., Swedish state railways, 310.

Althans, H., boring by rope in the United States, 339.

Anderson, W., Telford premium awarded to, 169, 176.

Annual general meeting, 161.-Annual report, 163.-Ditto read and ordered to
be printed, 161.

Armstrong, T. W., memoir of, 261.

Aveling, T., transferred member, 136.

Awdry, Lieut. A., R.E., elected associate, 135.

Ayalla, A. K. de B., the Horta harbour of Fayal, Azores, 375.

Bache, A., elected associate, 135.

Bailey, J., C.B., remarks as to the progress of steam shipping, 80.-Ditto as to
the possibility of obviating the heavy cost and delay in renewing the boilers
of marine boilers by the use of the Perkins boiler, 81.-Ditto as to the im-
portance of lessening the consumption of fuel in steamers, 81.-Ditto as to the
absence of danger in case of bursting of the Perkins boiler, 82.—Ditto as to
the small quantity of water used in the Perkins boiler, 82.-Ditto as to its
slight wear, 82.-Ditto as to the superiority of the Perkins piston metal, 82.
Baldry, J. D., appointed one of the scrutineers of the ballot for council, 161.-
Vote of thanks to, 162.

Ballard, R., transferred member, 136.

Bamford, T. V., admitted student, 136.

Bar at entrance to Bilbao harbour, depth of water on the, during the years
1873-5, 257.

Barbenson, R. T. O., elected associate, 135.

Barker, J., transferred member, 136.

Barron, F. C., "The Works of the Bilbao Iron Ore Company, in the Province of
Biscay, Spain," 237.

Barry, W. H., vote of thanks to, 162.

Basin at Birkenhead, Low Water, description of the cofferdams across the
entrance to the, 146. Vide also Cofferdams.

Bateman, J. F., elected President, 162.

Bazalgette, C. N., Manby premium awarded to, 169, 176.

Beams, graphic diagrams for the strength of teak, 286.

Beardmore, W., memoir of, 268.

Beaumont, W. W., Watt medal and Telford premium awarded to, 169, 176.
Beever, B. W., admitted student, 136.

Bell, R. Bruce, remarks as to steam shipping, 33.-Ditto as the disadvantage
of the screw-propeller in the case of pitching, 34.-Ditto as to the objection on
the part of the Board of Trade to spring-loaded safety valves, 34.

Bellingham, A. W. H., admitted student, 136.

Bertin, L. E., compressed air-blast for steam boilers, 324.

Bessemer, H., transferred member, 136..

Bilbao Iron Ore Company, "The Works of the Bilbao Iron Ore Company, in the
Province of Biscay, Spain," 237.-Formation of an English company to work the
iron ore mines of Somorrostro and Galdames, 237.-General description of the
works, 237.-Railway from Galdames to the coast, 238.-Construction of the
Sestão tunnel, 240.-Permanent way, 241.-Stations, 242.-Shipping pier, 243.
-Dredging operations in Sestão harbour, 244.-Analyses of the Galdames and
Somorrostro iron ores, 247, 248.-Rolling stock, 249.-Cost of land and works,
251.-Difficulty of exporting the ore on account of the bar at the entrance of
the river Nervion, 251.-APPENDIX: Table I. Cost of the Sestão tunnel in a
period of one hundred days, 253.—Table II. Cost of one kilomètre of permanent
way laid in position, 254.---Table III. Cost of dredging Sestão harbour during
seven months in 1876, 255.-Table IV. Exportation of iron ore from Biscay,
256.-Table V. Depth of water on the bar at Bilbao, 1873-75, 257.

Bisset, J., transferred member, 1.

Blanck, H., on the coal depôt of the Philadelphia and Reading railway, 309.
Blast, compressed air, for steam boilers, 324.

furnaces, protecting the linings of, 331.

Boileau, P., properties common to pipes, canals, and uniform rivers, 359.

Bold, E. H., elected associate, 135.

Borer, the Turretini rock, 342.

Boring by rope in the United States, 339.

machine, Brandt's rock, 342.

machines in Prussia, 344.

Bouches-du-Rhône, department of the, irrigation in the, 213.

Bourne, R. W., elected associate, 135.

Boussinesq, J., equilibrium of pulverulent bodies, 277.
Bowie, B. J., Jun., hydraulic mining in California, 337.
Boydell, J. E. N., elected associate, 135.

Brandt's rock-boring machine, 342.

Bridge, Douro.

"

Vide Viaduct.

East river suspension, New York, cable making for the, 296.
New York and Long Island, 304.

over the Danube to connect the Buda and Pesth railways, 290.
Prague-Smichow, pneumatic caisson foundations of, 288.

St. Louis over the Mississippi, 293.

Briggs, R. A., admitted student, 1.

Brine, E. A., admitted student, 1.

Brisse, A. and Rotrou, L. de, the drainage of Lake Fucino, 367.

Brock, W., remarks as to the progress of steam shipping, 83.-Ditto as to the
Government interference having been in the main prejudicial and obstructive,
83.-Ditto as to the Board of Trade detail rules for machinery being unreason-
able, 83.- Ditto as to the factor of safety for boilers being excessive, 84.-
Ditto as to the Board of Trade inspection of new and of old boilers, 84.
Broom, G. J. C., elected associate, 135.

Brown, F. B., admitted student, 136.

G. V., elected associate, 135.

T. C., elected associate, 135.

Browning, A., memoir of, 265.

Bruce, G. B., remarks as to the use of balks, instead of 6-inch piles in making
cofferdams, 153.-Ditto as to the kind of timber used for cofferdams, 153.
Brunlees, J., remarks as to the cofferdam at the Avonmouth Dock, 153.-Ditto
as to cofferdams at Lynn and Whitehaven, 153.

Brunton, R. H., Telford premium awarded to, 169, 176.

Cabezas, A. G., elected associate, 135.

Cable-making for suspension bridges, as exemplified at the East River Suspension
Bridge, New York, 296.

Cadett, W. J., memoir of, 270.

Caffin, F. C., admitted student, 1.

Canal, Alpines irrigation, description of the, 219.

Craponne irrigation, description of the, 218.

Lower Ganges, training works of the, 363.
Marseilles, description of the, 220.

Verdon, description of the, 224.

Canals and uniform rivers, properties common to pipes, 359.

Cathels, E. S., transferred member, 1.

Cements, on the limes and, of Casale, Piedmont, and Liguria, 284.

Chain and rope, traction by, in the Von der Heydt coal mine at Saarbruck, 322.

Chalk, W. J., Miller prize awarded to, 169, 177.

Church, J., transferred member, 136.

[1877-78. N.S.]

2 D