Click here to go to the applet.
This java applet is a simulation that demonstrates
magnetostatics and electromagnetic waves in two dimensions.
When the applet starts up you will see a
white circle (called the "source") emitting red and green circular
waves. The color indicates the electric field;
green areas are positive (towards you) and the red areas are
negative (away from you). (In this applet, the electric field is
always perpendicular to the plane of the screen; that means there
are no free charges, and all
currents have to be perpendicular to the screen as well. It also means
the electrostatic potential is zero everywhere.)
In addition to the red and green color, you will see arrows which
indicate the direction of the magnetic field (which is always in the
plane of the screen).
Also, sources and conductors may show a blue or yellow color,
indicating current. Yellow means that current is flowing towards you
and blue means it is flowing away from you.
Conductors, dielectrics, and other media will show up as gray. There
aren't enough colors or shades of gray to make the different
kinds of media look different. Use the Show Material Type
menu option to tell them apart.
These are electromagnetic waves, so in real life they would
be moving at the speed of light.
This is the TM version of the applet. There is also a
TE version.
The Setup popup can be used to view some interesting
pre-defined experiments. Once an experiment is selected,
you may modify it all you want. The choices are:
- Single Source: this is a single wire with an alternating
current, creating circular waves.
- Two Sources: this is two wires emitting circular waves,
creating an interference pattern between them.
- Plane Wave: this demonstrates a simple plane wave source.
- Intersecting Planes: this demonstrates two plane waves intersecting
at right angles.
The following 28 setups are all static, involving steady currents or
permanent magnets, with no waves (except at the start). When you
select one of them,
just wait a bit for the system to reach a steady state.
- Single Wire: this is a wire with a steady current.
- Wire Pair: this is two wires with current in the same
direction.
- Dipole Wire Pair: this is two wires with current in opposite
directions.
- Magnet Pair: this is two permanent magnets with the north
poles facing up.
- Magnet Pair, Opp: this is two permanent magnets; the left one
has the north pole facing up and the right one has it facing down.
- Magnet Pair Stacked: this is two permanent magnets stacked on
top of each other with the north poles facing up.
- Magnet Pair Stacked Opp: this is two permanent magnets stacked on
top of each other with the north poles facing towards each other.
- Uniform Field: this is a (fairly) uniform field created by
currents on the left and right sides of the screen.
- Field Near Aperture: this shows a uniform magnetic field
leaking through an aperture in a perfect conductor.
- Solenoid: this shows the cross section of a coil of wire with
a current running through it.
- Toroidal Solenoid: this shows the cross section of a torus
(donut) with a coil of wire wrapped around it.
- Sphere: this shows the cross section of a
uniformly magnetized sphere (actually an infinitely long cylinder, since
this is 2-D).
- Thick Wire: this shows a thick wire carrying a current.
- Hole in Wire 1: this shows a thick current-carrying wire with a hole in it,
resulting in no field in the hole.
- Hole in Wire 2: this shows a thick current-carrying wire with an off-center
hole in it, resulting in a uniform field in the hole.
- Ferromagnet: this is a ferromagnet (like soft iron) near
a solenoid. The
ferromagnets in this applet are linear and have no hysteresis.
- Diamagnet: this is a strong diamagnet near a solenoid. The
diamagnets in this applet are far stronger than any known diamagnet,
to illustrate the effect more clearly.
- Meissner Effect: this shows a superconductor near a solenoid. The
superconductor rejects all magnetic fields (except at the surface).
The blue and yellow color in the superconductor indicates the presence
of eddy currents. Since this is a superconductor, the eddy currents
do not die out.
- Horseshoe Magnet: this shows an electromagnet in the shape of
a horseshoe.
- Horseshoe + Load: this shows a horseshoe electromagnet carrying
a ferromagnetic load.
- Magnetic Shielding 1: this shows the magnetic field of solenoid
being shielded by a ferromagnet. Notice that there is very little field
below the ferromagnet. (You will see a somewhat strong magnetic field one
grid square
below the ferromagnet, but that is a bug and
this would not happen in real life.)
- Magnetic Shielding 2: this shows the magnetic field of solenoid
being shielded by a ferromagnetic box. Notice that there is very little field
outside of the ferromagnet. The ferromagnet is conducting and thus will
reflect the wave generated when the current is first switched on in the
solenoid; so you will have to wait a bit for the oscillation to die out.
- Magnetic Shielding 3: this shows the magnetic field of solenoid
being shielded by a ferromagnetic sphere. The field
is weaker outside of the ferromagnet; the brightness is turned up
so that you can see that the field outside looks like the field of a
magnetic dipole
(compare it to Dipole Wire Pair and Sphere). You
will have to wait even longer for the oscillation to die out because
the brightness is turned up and the current is much stronger than
in the previous setup.
- Magnetic Shielding 4: this shows a
ferromagnetic box shielding its interior from a uniform external field.
- Magnetic Circuit 1: this shows a
magnetic circuit; the field generated by the solenoid on the right
is being "conducted" by ferromagnetic material.
- Magnetic Circuit 2: this shows a
magnetic circuit with an air gap on the left.
- Monopole Attempt: This is a simulation
of what would happen if you tried to make a
magnetic monopole (a magnet with only a north pole and no south pole)
by taking a bunch of magnets and forcing them into a square with
their south poles in the center. Instead of getting a monopole,
you would find that the gaps between the magnets would act as south poles,
and the field there would be much stronger than on the faces of the
magnets. If you could force them together perfectly with no gaps,
there would be no field at all anywhere because all the currents would
cancel out.
- Quadrupole Lens: this shows four magnets in the shape of
hyperbolas, forced together. This device is used to focus
particle beams.
- Halbach
Array: this shows five magnets in a linear Halbach array. The
magnetic field is concentrated on the bottom side. To see the
orientations of the individual magnets, select Show
Magnetization from the Show popup.
- Halbach Array (long): this shows a longer Halbach array.
- Halbach Array (dipole): this shows a circular Halbach array
with a uniform magnetic field inside.
- Halbach Array (quadrupole): this shows a circular Halbach array
with a magnetic quadrupole inside.
The rest of the setups are all dynamic, involving changing currents
and waves.
- Dielectric: this shows wave packets being reflected by
a dielectric medium. Waves travel slower in a dielectric, causing the
incoming wave to be partially reflected and partially refracted.
- Fair Conductor Reflection: this shows wave packets being
reflected by
a fairly good conductor. When waves hit a conductor, it causes
eddy currents which cause the wave to be mostly reflected. A small
fraction of the wave is transmitted, and that part is attenuated
almost immediately.
- Poor Conductor Reflection: this shows wave packets being
reflected by
a poor conductor. When waves hit the conductor, it causes
weak eddy currents which cause the wave to be partly reflected. Part
of the wave is transmitted, and that part is quickly attenuated by
eddy currents.
- Skin Effect 1: this shows that waves hitting a conductor
will only penetrate a certain distance, called the
skin
depth. (Actually the strength of the wave falls off exponentially,
but the skin depth is a measure of how fast this happens.)
- Skin Effect 2: this shows that the skin depth is smaller
for higher-frequency waves.
- Resonant Absorption: this creates a medium made up of little
resonators. The resonators have a
characteristic frequency which is the same as the frequency of the incoming
radiation. Since this medium has a resonance frequency, it is dispersive,
which means that waves of different frequencies travel at different
speeds. Here, since the incoming radiation's frequency is close to the
resonance frequency, it is
absorbed by the medium, although much of it
is reflected because of the discontinuity caused by the strong absorption.
- Dispersion 1: this setup illustrates dispersion in the resonant
medium. The incident wave has a frequency which is much lower than the
resonance frequency, so the refractive index is only slightly higher
than 1. So it is transmitted largely without reflection.
- Dispersion 2: Here
the incident wave has a frequency which is slightly lower than the
resonance frequency, so waves travel much more slowly in the medium,
and more of the wave is reflected. Also there is some absorption, so the
farther the wave travels into the medium, the weaker it is.
- Dispersion 3: Here
the incident wave has a frequency which is slightly higher than the
resonance frequency, so waves have a phase velocity that is faster
than in a vacuum. So waves seem to move faster than the speed of light
in a vacuum. Still, the signal velocity in the medium is not faster
than the speed of light; when the source is first switched on, the initial
wave train travels at normal speed.
- Dispersion 4: Here
the incident wave has a frequency which is much higher than the
resonance frequency, so waves have a phase velocity that is only
slightly faster than in a vacuum. So the medium has very little
affect on the incoming wave.
- Magnetic Diffusion: this shows a magnetic field (generated
by a wire) diffusing slowly through a conductor. Wait for the field to
slowly build up, then get rid of the wire (the yellow square)
by clicking on it. The field will slowly die out; the presence of
the conductor causes changes in magnetic field to diffuse slowly
rather than happening at the speed of light.
- Oscillating Ring: this shows the cross section of a ring
with an oscillating current running through it. This is approximated
by two wires with current running in opposite directions. The oscillating
current causes radiation; this is called magnetic dipole radiation.
- Oscillating Ring Pair: this shows the cross section of two
rings with an oscillating current running through them in opposite
directions, resulting in magnetic quadrupole radiation.
- Ring Induction: this shows a ring with an oscillating
current running through it, inducing an opposing current in another ring
right below it.
- Wire Induction: this shows a wire with an oscillating
current running through it, inducing an opposing current in another wire
right below it.
- Ring + Fair Conductor: this shows a ring with a slowly
oscillating current running through it, with a fairly good conductor
underneath it. The changing current generates eddy currents in the conductor,
causing the magnetic field to diffuse slowly through the conductor to
the other side.
- Ring + Poor Conductor: this shows a ring with a slowly
oscillating current running through it, with a poor conductor
underneath it. The eddy currents are much weaker, so the
magnetic field diffuses quickly through the conductor to
the other side.
- Wire + Fair Conductor: this shows a wire with a slowly
oscillating current running through it, with a fairly good conductor
underneath it. The changing current generates eddy currents in the conductor,
causing the magnetic field to diffuse slowly through the conductor to
the other side.
- Wire + Poor Conductor: this shows a wire with a slowly
oscillating current running through it, with a poor conductor
underneath it. The eddy currents are much weaker, so the
magnetic field diffuses quickly through the conductor to
the other side.
- Rings + Ferromagnet: this is an oscillating ring (in the middle)
positioned near two conducting rings. There is a ferromagnetic core
present which cause the induced current to be stronger in the lower ring
than in the upper ring.
- Osc. Solenoid: this is a solenoid with an oscillating
current running through it.
- Transformer: this is two coils wrapped around each other,
with an oscillating current in the inner one. This induces a
current in the outer one. This transformer is rather pointless
since the number of turns is the same in the inner and outer coils. This
applet cannot demonstrate transformers very well
because there is no way to measure voltage, and because the current
is always perpendicular to the screen, and none
of the conducting grid squares are connected to one another. Also the
current in the inner coil is fixed and is not affected by the outer coil.
- Osc. Toroidal Solenoid: this is a toroidal solenoid with
an oscillating
current running through it.
- Coaxial Cable: this is a cross section of a coaxial cable,
with an oscillating current running through it. Note that there is
very little radiation (assuming the wavelength of the oscillation is
small compared to the diameter of the cable). This is part of the
reason that coaxial cable is used to carry high frequencies--it reduces
the amount of power loss from radiation.
- Cond. in Osc. Field: this is a small conducting square in a
uniform field that is oscillating.
- Moving Wire: this is a current-carrying wire which is
moving at a significant fraction of the speed of light. The magnetic
field lines are slightly flattened out. It stops
periodically and then starts again so you can see
the radiation generated when its velocity changes.
- Moving Wire in Tube: this is a current-carrying wire which is
moving through a conducting tube. When the wire moves it causes
a changing magnetic field, which generates eddy currents in the tube. The
presence of the tube causes a force on the wire opposing the direction of
motion, which you can see by selecting Show Force from the
Show menu.
- Moving Magnet in Tube: this is a magnet which is
moving through a conducting tube. When the
magnet moves it causes
a changing magnetic field, which generates eddy currents in the tube. The
presence of the tube causes a force on the magnet opposing the direction of
motion, which you can see by selecting Show Force from the
Show menu. The magnet stops periodically to give the eddy
currents a chance to die out.
- Rotating Magnet 1: this is a rotating magnet, which emits
radiation. Select Show Magnetization to see the direction
the magnet is pointing.
- Rotating Magnet 2: this is a magnet which rotates through
180 degrees and then reverses direction. This causes it to emit
radiation.
- Scattering 1: this shows a plane wave being scattered by
a small resonator. The incoming plane wave gets turned off periodically
so you can see the scattered wave better. The frequency of the incoming
wave is close to the resonant frequency of the resonator, so the scattered
wave is relatively strong.
- Scattering 2: Here the
frequency of the incoming
wave is not as close to the resonant frequency of the resonator, so
the scattered wave is much weaker.
- Big TM11 Mode: this creates a small superconducting cavity
with a standing wave inside it. The electric field is 90 degrees out
of phase with the magnetic field. The field in the cavity is oscillating in
its TM11 mode.
- TM11 Modes: this creates a set of small superconducting cavities
with TM11 standing waves inside them.
- TMn1 Modes: this creates a set of small superconducting cavities
with TM11, TM21, and TM31 standing waves inside them. (If the
resolution is set higher then more cavities are present with higher modes.)
- TMnn Modes: this creates a set of small superconducting cavities
with various TM modes inside them.
- TMn1 Mode Combos: this creates a set of small superconducting
cavities, with various combinations of TMn1 modes inside them.
- TMnn Mode Combos: this creates a set of small superconducting
cavities, with various combinations of TM modes inside them.
- Triangle Modes: this creates a set of small triangular
cavities with standing waves.
- Circular Modes 1: this creates a set of small circular
cavities with standing waves.
- Circular Modes 2: this creates a circular
cavity with two standing waves superimposed 90 degrees out of phase
so that the fields appear to rotate.
- Waveguides 1:
This creates a series of waveguides of different widths.
Narrower waveguides, like at the left end of the screen,
have higher cutoff frequencies.
Notice that the waves seem to be moving faster in thinner
waveguides. They appear to be moving faster than waves normally
move in the applet. This is because the phase velocity is faster in
thinner waveguides; but the signal velocity is actually slower than normal,
as you
can verify by clicking the Clear Waves button and watching the
wave move down the guide for the first time.
Since the waveguides are being driven by a plane wave, only the TE01
mode is present. (See the waveguide applet
for another way to view waveguide modes.)
- Waveguides 2:
This is just the same set of waveguides with a lower frequency. The
waveguide on the left has a
cutoff frequency that is higher than the source, so there is no
wave motion in it. You can fix this by turning the Source
Frequency slider up.
- Waveguides 3:
This is a set of identical waveguides being driven by small holes at
different locations. This causes different sets of modes to be excited
in different proportions. When the guide is being driven near the center,
the TE01 mode is dominant, but when it is driven near the edge, the
TE02 mode is more prevalent. The frequency is low enough so that all
other modes are cut off. You can fix this by turning the frequency up.
By turning the frequency down, you can cut off the TE02 mode as well.
- Waveguides 4:
This is a set of identical waveguides with various modes present.
The first waveguide contains the TE01 mode; the second contains the
TE02 mode; the third contains the TE03 mode;
the fourth contains TE01 and TE02;
the fifth contains TE01 and TE03; the sixth contains TE02 and TE03.
(There will not be room on your screen for all these modes if
your resolution is not set high enough.)
Notice that the higher modes (TE02 and especially TE03) seem to be moving
faster. This is because the phase velocity of TE02 and TE03 is greater
than that of TE01.
Their signal velocities are slower, though, which is why it takes
the TE03 wave so long to make it down to the end of the waveguide.
Also if you turn off the source (by setting the source
popup to "No Sources") it will take quite a while for the TE03 mode
to stop.
- Resonant Cavities 1:
This creates a series of rectangular cavities being driven by
a plane wave from above. As you change the frequency you will
see the response of each cavity change. Each cavity has a different
resonant frequency so it will respond differently. After changing
the frequency you may want to wait a bit for things to settle down
(or turn the simulation speed way up).
- Single Slit: this demonstrates diffraction of waves
travelling through a slit.
- Double Slit: this demonstrates diffraction of waves
travelling through a double slit.
- Triple Slit.
- Obstacle: this demonstrates diffraction of waves
travelling around an obstacle.
- Half Plane: this demonstrates diffraction of waves
around the edge of a plane.
- Lloyd's Mirror:
This shows an interferometer which consists of a point source
close to a mirror (at the bottom of the window).
The waves coming from the source interfere with the waves coming
from its mirror image.
The Source popup controls the wave sources (oscillating
currents). It has the
following settings:
-
No Sources: there will be no sources of wave motion.
-
1 Src, 1 Freq: there will
be a single source of sinusoidal waves at a single frequency
(set using the Source Frequency slider). This source can be
dragged anywhere on the screen with the mouse.
-
1 Src, 2 Freq: the source will be emitting
two waves, at separate frequencies. The first frequency is set
using the Source Frequency slider, and the second frequency
is set using 2nd Frequency.
- 2 Src, 1 Freq: two sources will be created,
both at the same frequency. But you can select the phase difference
using the Phase Difference slider. If the slider is all the
way to the left, the sources will be in phase; if it is all the
way to the right, the sources will be 180 degrees out of phase.
(The top one will be green while the bottom one is red, and vice versa.)
- 2 Src, 2 Freq: the two sources will be at
different frequencies. The Source 2 Frequency slider can be
used to set the second one's frequency.
- 3 Src, 1 Freq or 4 Src, 1 Freq:
3 or 4 sources will be created, all at the same frequency.
- 1 Src, 1 Freq (Packet): the source will emit wave
packets periodically.
- x Plane Src, y Freq: the source(s) will emit plane waves
rather than circular waves. The location and direction of the
plane wave can be modified by dragging one or both of the two
white circles. If the white circles are located at the edge of
the screen, the plane is extended offscreen; otherwise it is not.
Since the waves are not extended infinitely offscreen they are
not true plane waves, strictly speaking.
- 1 Plane 1 Freq (Packet): the source will emit
plane wave packets.
The Mouse popup controls what happens when the mouse is
clicked. The following settings are possible:
- Mouse = Add Perf. Conductor:
Clicking on a
point will create a perfect conductor there. Clicking on
an existing conductor will erase it.
- Mouse = Add Good Conductor:
Clicking on a
point will create a conductor which is not perfect but is still pretty
good.
- Mouse = Add Fair Conductor:
Clicking on a
point will create a fairly good conductor.
- Mouse = Add Current (+):
Clicking on a
point will create a wire with current flowing in the positive
z direction (towards you).
- Mouse = Add Current (-):
Clicking on a
point will create a wire with current flowing in the negative
z direction (away from you).
- Mouse = Add Ferromagnet:
Clicking on a
point will create a ferromagnetic
medium. The
ferromagnets in this applet are linear and have no hysteresis
(except for the permanent magnets).
- Mouse = Add Diamagnet:
Clicking on a
point will create a
diamagnetic
medium. The
diamagnets in this applet are far stronger than any known diamagnet,
to illustrate the effect more clearly.
- Mouse = Add Dielectric:
Clicking on a
point will create a dielectric medium.
- Mouse = Add Magnet (Down/Up/Left/Right):
Clicking on a point will create a permanent magnet with the
north pole pointing in the direction indicated.
- Mouse = Add Resonant Medium:
Clicking on a
point will create a resonant medium.
- Mouse = Clear:
Clicking on a point will remove whatever is there.
- Mouse = Adjust Conductivity:
Clicking on a point and dragging out a rectangular area will allow you to
adjust the conductivity of the conductors in that area using the
Conductivity slider. The
Show Material Type menu option may come in handy here (and in
the following options) to see feedback from the changes you are making
and to compare the conductivity of all conductors on the screen.
- Mouse = Adjust Permeability:
Clicking on a point and dragging out a rectangular area will allow you to
adjust the permeability of the ferromagnets in that area using the
Permeability slider.
- Mouse = Adjust Current:
Clicking on a point and dragging out a rectangular area will allow you to
adjust the current flowing through the wires in that area using the
Current slider.
- Mouse = Adjust Dielectric:
Clicking on a point and dragging out a rectangular area will allow you to
adjust the dielectric constant on the dielectrics in that area using the
Dielectric Constant slider.
- Mouse = Adjust Mag Dir:
Clicking on a point and dragging out a rectangular area will allow you to
adjust the direction of the permanent magnets in that area using the
Direction slider.
- Mouse = Adjust Mag Strength:
Clicking on a point and dragging out a rectangular area will allow you to
adjust the strength of the permanent magnets in that area using the
Strength slider.
The Show popup determines which fields or other quantities to
display, and how to display them.
- Show Electric Field (E): Show the electric field
as green (positive, toward you) or red (negative, away from you).
- Show Magnetic Field (B): Show the magnetic field
as arrows. The arrows go from dark green to light green and
then to white as the field gets stronger.
- Show B Lines: Show the magnetic field as lines. The
color of the lines go from dark green to light green and
then to white as the field gets stronger. The density of the
lines is kept fairly constant, so in order to determine the
field strength you need to look at the color of the lines
rather than how far apart they are.
- Show B Strength: Show the magnetic field strength using
shades of green.
- Show Current (j): Show the current density as
yellow (positive, toward you) or blue (negative, away from you).
- Show E/B: Show both the electric field and the
magnetic field arrows.
- Show E/B lines: Show both electric field and the
magnetic field lines.
- Show E/B/j: Show both the electric field and the
magnetic field arrows;
in conductors, or where the current
is nonzero, show the current density instead of the electric field.
- Show E/B lines/j: Show both the electric field and the
magnetic field lines;
in conductors, or where the current
is nonzero, show the current density instead of the electric field.
- Show Mag. Intensity (H): Show the magnetic intensity
vector, which is equal to the magnetic field minus the
magnetization. In linear media (which, in this applet,
is everywhere except for inside permanent magnets) this is
equal to B divided by the permeability. This will be the same
as B unless ferromagnets, diamagnets, or permanent magnets
are present.
- Show Magnetization (M): Show the magnetization
vector, which indicates the direction and degree of alignment
of magnetic media with an external field. In permanent magnets,
the magnetization is constant, and points to the magnet's north pole.
In ferromagnets, the magnetization is proportional to the
external field and in the same direction; in diamagnets, it is
proportional but in the opposite direction. Everywhere else it is
zero.
- Show Material Type: Since all materials show up as
gray, you need this option to tell them apart:
- Diamagnets: red (
)
- Ferromagnets: green (
) (lighter shades indicate higher
permeability)
- Permanent Magnets: purple (
)
- Dielectrics: orange (
) (lighter shades indicate
stronger dielectrics)
- Resonant: light orange (
)
- Perfect Conductors: white (
)
- Imperfect Conductors: cyan (
) (lighter shades indicate
better conductors)
- Wires with Current: blue (
) or yellow (
)
- Show Vec. Potential: Show the vector potential (A)
as green (positive, toward you) or red (negative, away from you). The
vector potential is always perpendicular to the screen.
- Show Poynting Vector: Show the Poynting vector, which
indicates the direction of energy transfer. For waves, it
is in the direction of wave motion.
- Show Energy Density: Show the energy density as
shades of yellow.
- Show Poynting/Energy: Show both the energy density and
the Poynting vector.
- Show Force: Show magnetic force. The total force
on each object is added up by summing over each grid square (ignoring
speed-of-light delay) and
the total is shown on every grid square taken up by the
object. (Note: due to a bug, this only gives accurate results
for objects that are square or rectangular.)
- Show Effective Current: Show the effective current density in
magnetic media caused by the alignment of magnetic dipoles. This is
equal to the curl of the magnetization. So for example, for
permanent magnets,
this will show you the current distribution which will generate the
same field as the permanent magnet; a square permanent magnet acts
the same as a solenoid.
- Show Magnetic Charge: Show the effective magnetic charge
density for any permanent magnets. For setups involving just
permanent magnets, we can think of the magnetic field as originating
from magnetic charges at the north and south poles of the
magnets. Using those magnetic charges, we can calculate a scalar potential
for every point on the screen (just like the electrostatic potential)
and calculate the magnetic intensity vector (H) from that
potential. So if you look the magnetic charge of a permanent magnet you
see that the two poles are oppositely charged; if you look at the
H it looks
like the electric field of two parallel plates with opposite charges on each
plate (with the plates located at the poles).
- Show Curl E: Show the curl of the electric field,
which is equal to the change in magnetic field (in the absence of
currents), by one of Maxwell's equations.
- Show Bx: Show the x component of the magnetic field;
green indicates positive (to the right) and red indicates negative
(to the left).
- Show By: Show the y component of the magnetic field;
green indicates positive (up) and red indicates negative
(down).
- Show Hx,Hy: Show the x or y component of the magnetic
intensity vector.
The Clear Fields button magically clears out any fields but does not
remove any currents, sources, or materials. The Clear All button
clears out everything.
The Stopped checkbox stops the applet, in case you want to
take a closer look at something, or if you want to work on something
with the mouse without worrying about it changing out from under you.
The Simulation Speed slider controls how far the waves move
between frames. If you slide this to the left, the applet will go
faster but the motion will be choppier.
The Resolution slider allows you to speed up or slow down the
applet by adjusting the resolution; a higher resolution is slower
but looks better.
The Brightness slider controls the brightness, just like on a
TV set. This can be used to view faint waves more easily.
Click here to go to the applet.
java@falstad.com
A far higher place must be assigned to Judaism among the competitors for the allegiance of Europe. The cosmopolitan importance at one time assumed by this religion has been considerably obscured, owing to the subsequent devolution of its part to Christianity. It is, however, by no means impossible that, but for the diversion created by the Gospel, and the disastrous consequences of their revolt against Rome, the Jews might have won the world to a purified form of their own monotheism. A few significant circumstances are recorded showing how much influence they had acquired, even in Rome, before the first preaching of Christianity. The first of these is to be found in Cicero’s defence of Flaccus. The latter was accused of appropriating part of the annual contributions sent to the temple at Jerusalem; and, in dealing with this charge, Cicero speaks of the Jews, who were naturally prejudiced against his client, as a powerful faction the hostility of which he is anxious not to provoke.330 Some twenty years later, a great advance has been made. Not only must the material interests of the Jews be respected, but a certain conformity to their religious prescriptions is considered a mark of good breeding, In one of his most amusing satires, Horace tells us how, being anxious to shake off a bore, he appeals for help to his friend Aristius Fuscus, and reminds him of217 some private business which they had to discuss together. Fuscus sees his object, and being mischievously determined to defeat it, answers: ‘Yes, I remember perfectly, but we must wait for some better opportunity; this is the thirtieth Sabbath, do you wish to insult the circumcised Jews?’ ‘I have no scruples on that point,‘ replies the impatient poet. ‘But I have,’ rejoins Fuscus,—‘a little weak-minded, one of the many, you know—excuse me, another time.‘331 Nor were the Jews content with the countenance thus freely accorded them. The same poet elsewhere intimates that whenever they found themselves in a majority, they took advantage of their superior strength to make proselytes by force.’332 And they pursued the good work to such purpose that a couple of generations later we find Seneca bitterly complaining that the vanquished had given laws to the victors, and that the customs of this abominable race were established over the whole earth.333 Evidence to the same effect is given by Philo Judaeus and Josephus, who inform us that the Jewish laws and customs were admired, imitated, and obeyed over the whole earth.334 Such assertions might be suspected of exaggeration, were they not, to a certain extent, confirmed by the references already quoted, to which others of the same kind may be added from later writers showing that it was a common practice among the Romans to abstain from work on the Sabbath, and even to celebrate it by praying, fasting, and lighting lamps, to visit the synagogues, to study the law of Moses, and to pay the yearly contribution of two drachmas to the temple at Jerusalem.335 Jeff’s hand was quietly coming down. “What happened to you?” begged Sandy. “Something new has come up, sir. I was waiting there by my ship a good while back, and I heard another one cruising and spiraling, shooting the field, I guess, because he came in and set down. My crate, just the way you ordered, was down by the grove, not in plain sight in the middle of the course. But Jeff set his ship down, left the engine running, and went off. I stayed hid to see what would happen, but when he didn’t come back, I thought I’d better go and find you—and see if it meant anything to you.” She stood alone, with the sticky, wet knife in her hand, catching her breath, coming out of the madness. Then she stooped, and pushing the branches aside felt about for her pistol. It lay at the root of a tree, and[Pg 80] when she had picked it up and put it back in the holster, there occurred to her for the first time the thought that the shot in the dead stillness must have roused the camp. And now she was sincerely frightened. If she were found here, it would be more than disagreeable for Landor. They must not find her. She started at a swift, long-limbed run, making a wide detour, to avoid the sentries, bending low, and flying silently among the bushes and across the shadowy sands. The year 1756 opened with menaces to England of the most serious nature. The imbecility of the Ministry was beginning to tell in the neglect of its colonies and its defences. France threatened to invade us, and a navy of fifty thousand men was suddenly voted, and an army of thirty-four thousand two hundred and sixty-three of native troops; but as these were not ready, it was agreed to bring over eight thousand Hessians and Hanoverians. To pay for all this it was necessary to grant excessive supplies, and lay on new duties and taxes. In presenting the money bills in the month of May, Speaker Onslow could not avoid remarking that there were two circumstances which tended to create alarm—foreign subsidies and foreign troops introduced, and nothing but their confidence in his Majesty could allay their fears, or give them confidence that their burdens would be soon reduced. There was, in fact, no chance for any such reduction, for wars, troubles, and disgraces were gathering around from various quarters. The first reverse came from the Mediterranean. MUCH to their amazement, the boys waked up the next morning in Nashville, and found that they had passed through the "dark and bloody ground" of Kentucky absolutely without adventure. After drawing and dividing the rations and cartridges. Si gave the boys the necessary instruction about having their things ready so that they could get them in the dark the next morning, and ordered them to disregard the bonfires and mirth-making, and lie down to get all the sleep they could, in preparation for the hard work of the next day. Then, like the rest of the experienced men, who saw that the campaign was at length really on, and this would be the last opportunity for an indefinite while to write, he sat down to write short letters to his mother and to Annabel. "Bully for the Wild Wanderers of the Wabash," Shorty joined in. "They're the boss regiment in the army o' the Cumberland, and the Army o' the Cumberland's the boss army on earth. Hooray for US Co. Le's have a speech. Where's Monty Scruggs?" "Bring a light, do—I can't abide this dark." Albert suddenly began to look uneasy. After all he was not really drunk, only a little fuddled. He walked straight, and his roll was natural to him, while though he was exceedingly cheerful, and often burst into song, his words were not jumbled, and he generally seemed to have a fair idea of what he was saying. "But I heard what the doctor said to you." "A purty accident—wud them stacks no more dry than a ditch. 'Twas a clear case of 'bustion—fireman said so to me; as wicked and tedious a bit o' wark as ever I met in my life." Calverley stept from the shadow of the cliff, and beheld a meteor in the sky, brightening and expanding, as the clouds opened, until it assumed the appearance of a brilliant star, of astonishing magnitude, encircled by dazzling rays, which, in a singular manner, were all inclined in one direction, and pointing to that part of the horizon where lay the rival of England—France. The foreman's face assumed a deeper hue than usual: he looked fiercely at the galleyman, but there was a determination in the weather-beaten face that made him pause ere he spoke. "Galleyman," he at length said, "you knew the business before you came: if you be so fond of saving old witches' lives, why didn't you say so, that I might not now be in this dilemma?" "No, no, not the boy," replied Merritt, rather impatiently.