Special experiments were made to determine the work done against resistances outside the vessel of water, which amounted to about 006 of the whole, and corrections were made for the loss of heat by radiation, the buoyancy of the air affecting the descending weights, and the energy dissipated when the weights struck the floor with a finite velocity.
In the British Postal Telegraph system five sizes of iron wire are in general use, weighing respectively 200, 400, 450, 600 and 800 lb per statute mile, and having electrical resistances (at 60° F.) of 26.64, 13.32, II.
The sizes of copper wire employed have weights of too, 150, 200 and 400 lb per statute mile, and have electrical resistances (at 60° F.) of 8.782, 5.8 55, 4.39 1 and 2.195 standard ohms respectively.
In practice the resistances r, r' are 9 Earth FIG.
The deflection observed on the galvanometer when the lines are leaky is d, while D is the deflection obtained through one coil of the galvanometer with all the other resistances in circuit; and assuming that no leakage exists on the lines, this deflection is calculated from the " constant " of the instrument, i.e., from the known deflection obtained with a definite current.
These tests are in some cases repeated at another temperature, say 50° F., for the purpose of obtaining at the same time greater certainty of the soundness of the core and the rate of variation of the conductor and dielectric resistances with temperature.
The currents thus divide at instrument as in Frischen's method, two resistances the point D, and it is clear that if the difference of potential between P and Q is unaffected by closing the sending key, then no change of current will take place in the instrument circuit.
The leakage through the insulator of the cable is compensated for by connecting high resistances between different points of the strip conductor and the earth coating.
Faults or any other irregularity in the cable may be represented by putting resistances of the proper kind into the artificial line.
The apparatus consists of a sending battery B, a reversing transmitting key K, a slide of small resistance 5, three condensers C1, C2, C3, an artificial cable AC, the receiving instruments I and G, and one or more resistances R for adjusting the leakage current.
The explanation of the action of the shunt is that all slowly varying currents affect the coil of the receiving instrument and its shunt in inverse proportion to their respective resistances; whereas with the comparatively rapid variations of current used in signalling the coil is forced at the beginning of each element of A v
Ann., 1890, 40, p. 56) employed an arrangement as follows: Four fine platinum or iron wires were joined in lozenge shape, and two sets of these R and S were connected up with two resistances P and Q to form a bridge with a galvanometer G and battery B.
If the attack of a parasite is met by the formation of some substance in the protoplasm which is chemo- tactically repulsive to the invader, it may be totally incapable of penetrating the cell, even though equipped with a whole armoury of cytases, diastatic and other enzymes, and poisons which would easily overcome the more passive resistances offered by mere cell-walls and cell-contents of other plants, the protoplasm of which forms bodies chemotactically attractive to the Fungus.
The problems arising out of the special consideration of the power required to propel a railway train against the resistances opposing its motion, the way the power is applied to trains, the agent by means of which the power is exerted, are conveniently grouped together under the general heading of Locomotive Power.
The relation between the b.h.p. and the torque on the driving-axle is 55 o B.H.P. =Tu., (9) It is usual with steam locomotives to regard the resistance R as including the frictional resistances between the cylinders and the driving-axle, so that the rate at which energy is expended in moving the train is expressed either by the product RV, or by the value of the indicated horse-power, the relation between them being 55 0 I.H.P. =RV (Io) or in terms of the torque 55 0 I.H.P.X€=RVe=TW (II) The individual factors of the product RV may have any value consistent with equation (to) and with certain practical conditions, so that for a given value of the I.H.P. R must decrease if V increases.
The pull recorded on the diagram includes the resistances due to acceleration and to the gradient on which the train is moving.
It is usual to subtract these resistances from the observed pull, so as to obtain the draw-bar pull reduced to what it would be at a uniform speed on the level.
A side wind causes excessive flange friction on the leeward side of the train, and increases the tractive resistances therefore very considerably, even though its velocity be relatively moderate.
Rate at which work is done against the resistances given by the curves fig.
Per hour on a level straight road with the values of the resistances assumed.
H.P. - (Were ?-W v r v)V ?2240WV ?2240WVa (22) 55 0 550 550G 550g where W e is weight of engine and tender in tons, Wv the weight of vehicles in tons, W the weight of train in tons =W e r e and r z, the respective engine and vehicle resistances taken from the curves fig.
These considerations also indicate what a difficult matter it is to find the exact rate of working against the resistances, because of the difficulty of securing conditions which eliminate the effect both of the gradient and of acceleration.
Secondly, it must be able to maintain the train at a given speed against the total resistances of the level or up a gradient of given inclination.
Per hour, the tractive force falls to 7400 lb, and this cannot be increased except by increasing the rate of combustion (neglecting any small changes due to a change in the efficiency 7 Knowing the magnitude of R, the draw-bar pull, and hence the weight of vehicle the engine can haul at this speed, can be estimated if the resistances are known.
The calibration of ammeters is best conducted by means of a series of standard low resistances and of a potentio meter.
These headings are: "Geometry and Kinematics of Particles and Solid Bodies"; "Principles of Rational Mechanics"; "Statics of Particles, Rigid Bodies, &c."; "Kinetics of Particles, Rigid Bodies, &c."; "General Analytical Mechanics"; "Statics and Dynamics of Fluids"; "Hydraulics and Fluid Resistances"; "Elasticity."
The strength of the current may also be regulated by introducing lengths of German silver or iron wire, carbon rod, or other inferior conductors in the path of the current, and a series of such resistances should always be provided close to the tanks.
Several pieces of apparatus have been invented for comparing the magnetic quality of a sample with that of a standard iron rod by a zero method, such as is employed in the comparison of electrical resistances by the Wheatstone bridge.
The effective number of turns in the coil surrounding the test rod can be varied by means of three dial switches (for hundreds, tens and units), which also introduce compensating resistances as the number of effective turns in the coil is reduced, thus keeping the total resistance of the circuit constant.
Dubuat, therefore, assumed it as a proposition of fundamental importance that, when water flows in any channel or bed, the accelerating force which obliges it to move is equal to the sum of all the resistances which it meets with, whether they arise from its own viscosity or from the friction of its bed.
For the purpose of measuring resistances up to a few thousand ohms, the most convenient appliance is a Wheatstone's Bridge (q.v), but when the resistance of the conductor to be measured is several hundred thousand ohms, or if it is the resistance of a so-called insulator, such as the insulating covering of the copper wires employed for distributing electric current in houses and buildings for electric lighting, then the ohmmeter is more convenient.
An essential accompaniment therefore of the potentiometer is a series of standard low resistances, say of o 1, o oi, o ooi ohm, and also a series of higher resistances divided into known fractions.
In practical work, the low resistances take the form of certain strips of metal which have on them two pairs of terminals, one termed " current terminals," and the other " potential terminals."
It appears then that this sum is a measure of the total capacity for doing work against extraneous resistances which the particle possesses in virtue of its motion and its position; this is in fact the origin of the term energy.
The terms due to F in (33) are such as would arise from frictional resistances proportional to the absolute velocities of the particles, or to mutual forces of resistance proportional to the relative velocities; they are therefore classed as frictional or dissipative forces.
Principle of Least Resistance.Where more than one system of resistances are alike capable of balancing the same system of loads applied to a given structure, the smallest of those alternative systems, as waS demonstrated by the Rev. Henry Moseley in his Mechanics of Engineering and Architecture, is that which will actually be exerted but are distinguished by an asterisk.
Because the resistances to displacement are the effect of a strained state of the pieces, which strained state is the effect of the load, and when the load is applied the strained state and the resistances produced by it increase until the resistances acquire just those magnitudes which are sufficient to balance the load, after which they increase no further.
Relations between Polygons of Loads and of Resistances.In a structure in which each piece is supported at two joints only, the well-known laws of statics show that the directions of the gross load on each piece and of the two resistances by which it is supported must lie in one plane, must either be parallel or meet in one point, and must bear to each other, if not parallel, the proportions of the sides of a triangle respectively parallel to their directions, and, if parallel, such proportions that each of the three forces shall be proportional to the distance between the other two,all the three distances being measured along one direction.
Considering, in the first place, the case in which the load and the two resistances by which each piece is balanced meet in one point, which may be called the centre of load, there will be as many such points of intersection, or centres of load, as there are pieces in the structure; and the directions and positions of the resistances or mutual pressures exerted between the pieces will be represented by the sides of a polygon joining Pi h2 ~, ~ those points, as in fig.
P4 represent the centres of load in a structure of four pieces, and the sides of the ~ polygon of resistances P1 P2 P2 P4 represent respectively the direc~ I~~ tions and positions FIG.
Of the resistances ex erted at the joints.
Further, at any one of the centres of load let PL represent the magnitude and direction of the gross load, and Pa, Pb the two resistances by which the piece to which that load is applied is supported; then wifl those three lines be respectively the diagonal and sides of a parallelogram; or, what is the same thing, they will be equal to the three sides of a triangleS and they must be in the same plane, although the sides of the polygon of resistances may be in different planes.
Then from the proportionality and parallelism sides of a triangle, there results the following of the load and the two resistances applied to each piece of the structure to the three theorem (originally due to Rankine): If from the angles of the polygon of loads there be drawn lines (Ri, R2, &c.), each of which is parallel to the resistance (as Pi F2, &c.) exerted FIG.
At the joint between the pieces to which the two loads reprfsented by the contiguous sides of the polygon of loads (such as L1, L2, &c.) are applied; then will all those lines meet in one point (0), and their lengths, measured from that point to the angles of Ike polygon, will represent the magnitudes of the resistances to which they are respectively parallel.
When the load on one of the pieces is parallel to the resistances which balance it, the polygon of resistances ceases to be closed, two of the sides becoming parallel to each other and to the load in question, and extending indefinitely.
In the polygon of loads the direction of a load sustained by parallel resistances traverses the point O-i i Since the relation discussed in 7 was enunciated by Rankine, an enormous development has taken place in the subject of Graphic Statics, the first comprehensive textbook on the subject being Die Graphische Statik by K.
In considering its properties, the load at each centre of load is to be held to include the resistances of those joints which are not comprehended in the partial polygon of resistances, to which the theorem of 7 will then apply in every respect.
By constructing several partial polygons, and computing the relations between the loads and resistances which are determined by the application of that theorem to each of them, with the aid, if necessary, of Moseleys principle of the least resistance, the whole of the relations amongst the loads and resistances may be found.
Line of PressuresCentres and Line of Resistance.The line of pressures is a line to which the directions of all the resistances in one polygon are tangents.
Stability of Position, and Stability of Frictio-n.The resistances at the several joints having been determined by the principles set forth in 6, 7, 8, 9 and 10, not only under the ordinary load of the structure, but under all the variations to which the load is subject as to amount and distribution, the joints are now to be placed and shaped so that the pieces shall not suffer relative displacement under any of those loads.