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This java applet demonstrates electromagnetic waves
in a 3-d rectangular waveguide.
At the top of the applet on the left you will see the waveguide
with a wave moving in the positive z direction. The color green means that
an electric field component is present and is pointing in the
positive or negative y direction.
The guide is being driven with a single driving
frequency, but various normal modes may be present. Each one is
operating at the same frequency, but the phase velocity will generally
be different
for different modes.
Below the guide you will see two grids showing each
normal mode's contribution to the wave pattern in the guide.
The TE modes (transverse electric modes; modes with the electric
field vector perpendicular
to the z axis) are shown on top and TM modes (transverse magnetic modes;
modes with the
magnetic field vector perpendicular to the z axis) are shown on the
bottom. Move the mouse over a grid square to see what mode
it represents.
Each element of the grid has a color which indicates the presence or
absence of that mode. Black means the mode is not present;
green means the mode is present with a positive coefficient, and red means
it is present with a negative coefficient.
In addition, each mode may have a phase shift, which indicates that its
oscillatory cycle leads or lags others with the same phase velocity.
This is indicated by
a vertical blue line.
A phase shift is normally hard to detect. If the applet is stopped,
then by altering the phase of a mode you can see the mode oscillate.
If the applet is running it is harder to tell, unless the mode is
combined with some other mode; in that case, the phase will affect
the interference pattern between the two modes.
Also, some modes may be crossed out with a diagonal line. This means
the driving frequency is not high enough to drive that mode. Adjusting
the Driving Frequency slider will allow that mode to be activated.
You can add or remove a mode by clicking on it. If you click and drag
up and down you can fine-tune the magnitude of the mode. If you drag
left and right you can alter the phase shift.
Double-clicking on a mode will clear all other modes and just set that one.
For performance reasons, only 10 modes can be active at a time.
The Show Electric Field popup will let you select which
field is shown: the electric field, the magnetic field, or both.
You can also view the currents or charge in the walls.
The Show Field popup controls how the field is displayed.
The choices are:
- Show Field (tri-color) shows the x component of the field as red,
y as green, and z as blue. The sign of the field component isn't
indicated.
- Show Field X shows the x component of the field as green if it's
positive and red if it's negative. The other components aren't shown.
If the field has no x component then the display is blank.
- Show Field Y shows the y component of the field as green if it's
positive and red if it's negative.
- Show Field Z shows the z component of the field as green if it's
positive and red if it's negative.
- Show Field Magnitude shows the magnitude of the field vector in green.
The direction of the field is not indicated.
- Show Field Vectors shows little field vectors indicating the
magnitude and direction of the field. As the field gets stronger, the
vectors turn from black (weakest) to green to white (strongest).
The number of vectors shown can be controlled with the
Vector Density slider.
- Show Particles on Field Lines shows a bunch of particles moving
in the direction of the field lines. They move faster where the field
is stronger.
Note that the particles are only a educational device
intended to show the shape
of the field lines; in real life, particles would not move in this manner.
The Show Field popup also controls how you can view the current;
in that case, think "current vector" when you see "field" in the above
directions. There is only one way to view the charge, however; green
means positive charge and red means negative.
The Slice popup allows you to look at planar slices of the guide
rather than looking at the contents of the entire guide.
If the popup is set to No Slicing, you view the entire
guide. Otherwise you will see the guide sliced in one of three
directions. The location of the slice can be adjusted by dragging
the line running along the sides of guide near the slice.
The Mouse popup controls what happens when you click on the guide.
If you set it to Adjust Angle or Adjust Zoom, you can
adjust the orientation or size of the 3-d view by clicking and
dragging on the guide.
The Stopped checkbox can be used to stop the applet
for a moment.
The Stop Oscillation checkbox can be used to stop the oscillation
for a moment; this is useful when "Show Particles" is selected.
The particles keep moving, to illustrate the field lines, but the
oscillation of the electric and magnetic fields stops so the field
lines are easier to follow.
The Show Sides checkbox shows the field on the sides of the
guide rather than inside.
The Alternate Rendering checkbox is used to speed up
rendering, but it actually slows things down on some machines.
Also for large windows and low resolutions it is usually slower.
(Internally, it uses the MemoryImageSource class instead of drawing
a bunch of rectangles.)
The Oscillation Speed slider controls the speed of oscillation.
The Particle Speed slider controls the speed of the particles.
The Number of Particles slider controls the number of particles.
The Brightness slider can be used just like the brightness on
a TV, to brighten dim areas of the guide.
The Image Resolution slider can be used to generate a higher
quality image. If you move it to the right, it will increase the
resolution of the image, but it will also slow things down,
so be careful.
The Width and Height sliders will adjust the width or height
of the guide. This changes the phase velocities and
cutoff frequencies of each mode.
The Clear button clears all modes.
The Reset Particles button resets the particle positions to
some random state.
Back 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.