RadioBanter

RadioBanter (https://www.radiobanter.com/)
-   Antenna (https://www.radiobanter.com/antenna/)
-   -   Spherical radiation pattern (https://www.radiobanter.com/antenna/146597-spherical-radiation-pattern.html)

Registered User September 15th 09 03:04 PM

Spherical radiation pattern
 
On Mon, 14 Sep 2009 20:30:16 -0700 (PDT), Art Unwin
wrote:

On Sep 14, 9:35*pm, Registered User wrote:
On Mon, 14 Sep 2009 16:30:50 -0700 (PDT), Art Unwin



wrote:
On Sep 14, 5:45*pm, "Dave" wrote:
"Art Unwin" wrote in message


...


Point to a law that I have violated *of which you learned about in
academia.
As for me I am at peace with my offering and thus can move on until a
violation of law is presented.


then don't you dare go away until you explain how your weak and strong force
can have any effect on conduction band electrons when their range of effect
is confined to the nucleus.


And why not?


If you're going to go away just go away. I don't understand why you
would expect anyone to accept your fancies as fact based upon the
rambling, incoherent explanations you provide. Your only success is
the audience you have gathered while acting as troll.


No. "Success" is showing up the self perceived experts.

So says the only self-proclaimed expert.
- snip -
This is not trolling. I am exposing people for what they are and they
are fraustrated

The only person you're exposing is yourself and not in a good way. It
is extremely difficult to take your arguments seriously or even
understand them given your posts' poor spelling and grammar along with
the abysmal formatting.The spelling variants are understandable, my
schooling started on the banks of the Devon river. Words like
"fraustrated' are something else altogether. That isn't a fat-fingered
error.

Don't blame it one the web interface you post through.Your posts could
be composed and spell-checked in a text editor before the content is
pasted into a web interface. You could
also let
the web interface handle word-wrapping
instead of inserting
seemingly random cr/lf pairs in your
posts.

If you want to be taken seriously you need to present your theories
and arguments in a rational, cohesive manner.

in their inability to show me as wrong or even having a book that
states where and why I am wrong.

This is equaled and exceeded by your inability to clearly state and
detail your theories without the use of circular logic. Many times
when a question is asked rather than answer you choose to start a new
thread.

This is not rambling. Since when is
the truth rambling?

What makes any of your ramblings the truth? Was your post on GB
standing alone (3 Sept 2009) the truth? You conveniently ignored the
fact that GB's declaration of war came about because Germany had
attacked GB's ally Poland. GB stood beside Poland and not alone.

If you are an expert take up the challenge in
terms of academics or consult a professor for an answer Either is
acceptable for the purposes of debate of what is true or not
true.Everything I have stated
stands upon this very point

I have previously suggested that you present your theories directly to
those in the academic community. Why not obtain validation there and
then come back and say 'I told you so'?

So guys, direct yourselves at the root
instead of floundering around in a aimless fashion.
And as far as the size of the audience the bigger the better the
exposure and the more success I have against those who rely on
slander. I want this to be as wide spread as possible instead of
running away. Live with it .

Yet you always run to a new thread.

I am quite sure that many hams around the
World is following this augument looking for that first person you
will take up the challenge
and provide closure with an answer to this very simple question,
without the fear of recrimination from the group all of which say it
is illegal.

Did I mention something about spelling, grammar and formatting?

I'm not certain how "many hams around the World is following this
augument" but that number is insignificantly small relative to the
world-wide amateur community. The size of the amateur community is in
turn insignificantly small relative to the world-wide academic
community. You choice of venue is as questionable as anything else.

selah

Art Unwin September 15th 09 03:31 PM

Spherical radiation pattern
 
On Sep 15, 8:15*am, "christofire" wrote:
"jaroslav lipka" wrote in message

...
On Sep 15, 7:06 pm, "christofire" wrote:



There is very little apparent similarity between Nicola Tesla and that
'Art
Unwin' character. Tesla was an inventor who realised amazing feats of
hardware construction, some of which worked as intended. 'Professor Unwin'
doesn't appear to create anything in hardware - he just talks about his
own,
paraphysical theories and expects others to believe what he says.


Again, don't believe what I write - go to a technical library and read the
stuff that made it into books. You can't rely on what people write on the
internet; there are too many 'Unwins' out there.


Chris


* Hi Chris
* * * * * * * *The question that goes to nub of Arts claim is
why is adding a time varying field to the Gaussian law of statics
illegal? *or to state it another way,
* * *How is it illegal to change a static field into a dynamic field?
can you, will you answer the question or are you just sitting on
Richards shirt tail.

*Jaro

I certainly haven't arrived here by sitting on anyone's shirt tails. *If
you'd care to read some of the history of this NG you'd see where I come
from.

Your question is not put clearly, although I have seen garbled sentences
like this before in this Usenet group. *My first question is: have you
bothered to read any of the respected books on the subject, such as
'Electromagnetics with applications' by Krauss and Fleisch. *I suspect if
you had you wouldn't be asking me such a question - it makes no sense! *Do I
take it you are referring to Gauss's law for electric fields? *Are you aware
that there is a counterpart Gauss's law for magnetic fields? *I don't
believe there is such a thing as a single 'Gaussian law of statics' -
someone has made that up!

Gauss's law for electric fields states: the integral of the electric flux
density over a closed surface equals the charge enclosed. *This is an
important part of the basis of electrostatics, that is the study of
electrical phenomena caused by static charges, but it applicable at a point
in time to any scenario that involves an enclosed charge - which means any
electrical conductor, whether it carries a non-moving charge, DC or AC.
Gauss's law for magnetic fields states: the integral of the magnetic flux
density over a closed surface is equal to zero, and this is an important
part of the basis of magnetics, again whether static or changing.

Both of Gauss's laws are embodied in Maxwell's equations and for the normal
RF case of sinusoidally-alternating variables a number of different
notations can be used, a popular one being phasor notation. *As you will
know, phasors are vectors that rotate at the same angular frequency but have
arbitrary phase relationships and amplitudes - so phasor notation is a
compact way of expressing quite a lot. *But, in this case, every one of the
phasors involved, D the displacement current density, rho the enclosed
charge, and B the magnetic flux density, is a variable that alternates with
the passage of time. *'Dynamic' variables if you want to call them that..

Neither of Gauss's laws applies directly to strength of an electric or
magnetic field but the linkage is the other two of Maxwell's equations based
on Ampere's law and Faraday's law, which are both applicable to time-varying
fields - 'dynamic fields' if you must.

So ... would you like to put your question more clearly? *What do you
actually mean by 'to change a static field into a dynamic field' in respect
of antennas, where all the electrical and magnetic variables are changing
with time, especially the fields? *Is this the result of a misunderstanding
of the meaning of the word 'electrostatic' - used to differentiate between
those phenomena caused by the presence of contained charge and those caused
by its movement?

Chris



Gauss's law of statics is enclosed particles in equilibrium. Add a
time varying field to same it becomes a dynamic field in equilibrium
and thus equates with Maxwell's laws.







JIMMIE September 15th 09 04:21 PM

Spherical radiation pattern
 
On Sep 14, 11:30*pm, Art Unwin wrote:
On Sep 14, 9:35*pm, Registered User wrote:



On Mon, 14 Sep 2009 16:30:50 -0700 (PDT), Art Unwin


wrote:
On Sep 14, 5:45*pm, "Dave" wrote:
"Art Unwin" wrote in message


...


Point to a law that I have violated *of which you learned about in
academia.
As for me I am at peace with my offering and thus can move on until a
violation of law is presented.


then don't you dare go away until you explain how your weak and strong force
can have any effect on conduction band electrons when their range of effect
is confined to the nucleus.


And why not?


If you're going to go away just go away. I don't understand why you
would expect anyone to accept your fancies as fact based upon the
rambling, incoherent explanations you provide. Your only success is
the audience you have gathered while acting as troll.


No. "Success" is showing up the self perceived experts.
The question is why is adding a time varying field to the Gaussian law
of statics illegal ?
Or stated another way, what is it illegal by changing a static field
into a dynamic field?
This is not trolling. I am exposing people for what they are and they
are fraustrated
in their inability to show me as wrong or even having a book that
states where and why I am wrong. This is not rambling. Since when is
the truth rambling? If you are an expert take up the challenge in
terms of academics or consult a professor for an answer Either is
acceptable for the purposes of debate of what is true or not
true.Everything I have stated
stands upon this very point So guys, direct yourselves at the root
instead of floundering around in a aimless fashion.
And as far as the size of the audience the bigger the better the
exposure and the more success I have against those who rely on
slander. I want this to be as wide spread as possible instead of
running away. Live with it . I am quite sure that many hams around the
World is following this augument looking for that first person you
will take up the challenge
and provide closure with an answer to this very simple question,
without the fear of recrimination from the group all of which say it
is illegal. Until then......


The easiest way to support your hypothesis is to show a plot or data
table showing how time effects a static field. Frankly I don't know
how you could show any relevant data since the word STATIC means
"unchanging over time" . Applying a time variable to something that is
static is pointless.
Time is relevant to DYNAMIC fields but someone else has already taken
care of that for us.

Jimmie

JIMMIE September 15th 09 04:24 PM

Spherical radiation pattern
 
On Sep 14, 1:56*pm, "christofire" wrote:
"Szczepan Białek" wrote in message

...



"Richard Fry" wrote
....


- - small snip --



QUOTE
A radio antenna may be defined as the structure associated with the

region of transition between a guided wave and a free-space wave, or
vice-versa. *Antennas convert electrons to photons, or vice-versa.


Regardless of antenna type, all involve the same basic principle that

radiation is produced by accelerated (or decelerated) charge. *The
basic equation of radiation may be expressed simply as:


IL = Qv * (A m s^-1)


where


I = time-changing current, A s^-1
L = length of current element, m
Q = charge, C
v = time change of velocity which equals the acceleration of the
charge, m s^-2


Thus, time-changing current radiates and accelerated charge radiates.


In which parts of antenna the charges acclerate?
S*


In all the parts that carry current, of course. *Isn't that obvious?

Incidentally, who is A* ? ... the person who wrote:

* * Does one wave has many polarizations, or one antenna has many
polarizations?
* * Which one: transmitter or receiver? Could you teach me?
* * A*

Chris


Could mean that Art and S are the same person, one does seem to appear
when the other disappears.

Jimmie

christofire September 15th 09 04:24 PM

Spherical radiation pattern
 

"Art Unwin" wrote in message
...
On Sep 15, 8:15 am, "christofire" wrote:
"jaroslav lipka" wrote in message

...
On Sep 15, 7:06 pm, "christofire" wrote:


- - snip - -

I certainly haven't arrived here by sitting on anyone's shirt tails. If
you'd care to read some of the history of this NG you'd see where I come
from.

Your question is not put clearly, although I have seen garbled sentences
like this before in this Usenet group. My first question is: have you
bothered to read any of the respected books on the subject, such as
'Electromagnetics with applications' by Krauss and Fleisch. I suspect if
you had you wouldn't be asking me such a question - it makes no sense! Do
I
take it you are referring to Gauss's law for electric fields? Are you
aware
that there is a counterpart Gauss's law for magnetic fields? I don't
believe there is such a thing as a single 'Gaussian law of statics' -
someone has made that up!

Gauss's law for electric fields states: the integral of the electric flux
density over a closed surface equals the charge enclosed. This is an
important part of the basis of electrostatics, that is the study of
electrical phenomena caused by static charges, but it applicable at a
point
in time to any scenario that involves an enclosed charge - which means any
electrical conductor, whether it carries a non-moving charge, DC or AC.
Gauss's law for magnetic fields states: the integral of the magnetic flux
density over a closed surface is equal to zero, and this is an important
part of the basis of magnetics, again whether static or changing.

Both of Gauss's laws are embodied in Maxwell's equations and for the
normal
RF case of sinusoidally-alternating variables a number of different
notations can be used, a popular one being phasor notation. As you will
know, phasors are vectors that rotate at the same angular frequency but
have
arbitrary phase relationships and amplitudes - so phasor notation is a
compact way of expressing quite a lot. But, in this case, every one of the
phasors involved, D the displacement current density, rho the enclosed
charge, and B the magnetic flux density, is a variable that alternates
with
the passage of time. 'Dynamic' variables if you want to call them that.

Neither of Gauss's laws applies directly to strength of an electric or
magnetic field but the linkage is the other two of Maxwell's equations
based
on Ampere's law and Faraday's law, which are both applicable to
time-varying
fields - 'dynamic fields' if you must.

So ... would you like to put your question more clearly? What do you
actually mean by 'to change a static field into a dynamic field' in
respect
of antennas, where all the electrical and magnetic variables are changing
with time, especially the fields? Is this the result of a misunderstanding
of the meaning of the word 'electrostatic' - used to differentiate between
those phenomena caused by the presence of contained charge and those
caused
by its movement?

Chris



(written by Unwin)
Gauss's law of statics is enclosed particles in equilibrium. Add a
time varying field to same it becomes a dynamic field in equilibrium
and thus equates with Maxwell's laws.


(written by Chris)
This appears to be paraphysical nonsense, once again.

(a) There are no 'Maxwell's laws' - there are the four Maxwell's equations
based on laws ascribed to the other three authors named above. The term
'eqilibrium' does not feature in, and is not required in, Maxwell's
equations or the laws it is based upon. Radio communication has been based
on Maxwell's equations for more than 100 years without need for
modification.

(b) There is no single 'Gauss's law of statics' as I explained above, and
both of Gauss's laws can be applied to time varying quantities but neither
contains a field.

(c) Both of Gauss's laws are included in Maxwell's equations without
modification - there is no need to 'Add a time varying field to same' - it
is there already in each case.
Once again: Gauss's laws are already applicable to time varying
quantities.

(d) What Maxwell provided was unification of the presentation of the four
equations in differential, integral or phasor form, so the relationships and
linkage between them became clear and they could all be used together to
solve electromagnetic problems.

I think the group is aware by now what I think of the writings of people who
claim to know better than Kraus, Jordan & Balmain, Jasik, et al, on the
basis of no practical evidence.

Chris



christofire September 15th 09 04:36 PM

Spherical radiation pattern
 

"JIMMIE" wrote in message
...
On Sep 14, 11:30 pm, Art Unwin wrote:
On Sep 14, 9:35 pm, Registered User wrote:



On Mon, 14 Sep 2009 16:30:50 -0700 (PDT), Art Unwin


wrote:
On Sep 14, 5:45 pm, "Dave" wrote:
"Art Unwin" wrote in message


...


Point to a law that I have violated of which you learned about in
academia.
As for me I am at peace with my offering and thus can move on until
a
violation of law is presented.


then don't you dare go away until you explain how your weak and
strong force
can have any effect on conduction band electrons when their range of
effect
is confined to the nucleus.


And why not?


If you're going to go away just go away. I don't understand why you
would expect anyone to accept your fancies as fact based upon the
rambling, incoherent explanations you provide. Your only success is
the audience you have gathered while acting as troll.


No. "Success" is showing up the self perceived experts.
The question is why is adding a time varying field to the Gaussian law
of statics illegal ?
Or stated another way, what is it illegal by changing a static field
into a dynamic field?
This is not trolling. I am exposing people for what they are and they
are fraustrated
in their inability to show me as wrong or even having a book that
states where and why I am wrong. This is not rambling. Since when is
the truth rambling? If you are an expert take up the challenge in
terms of academics or consult a professor for an answer Either is
acceptable for the purposes of debate of what is true or not
true.Everything I have stated
stands upon this very point So guys, direct yourselves at the root
instead of floundering around in a aimless fashion.
And as far as the size of the audience the bigger the better the
exposure and the more success I have against those who rely on
slander. I want this to be as wide spread as possible instead of
running away. Live with it . I am quite sure that many hams around the
World is following this augument looking for that first person you
will take up the challenge
and provide closure with an answer to this very simple question,
without the fear of recrimination from the group all of which say it
is illegal. Until then......


The easiest way to support your hypothesis is to show a plot or data
table showing how time effects a static field. Frankly I don't know
how you could show any relevant data since the word STATIC means
"unchanging over time" . Applying a time variable to something that is
static is pointless.
Time is relevant to DYNAMIC fields but someone else has already taken
care of that for us.

Jimmie


I've noted, further down the thread, that the term 'electrostatic' is used
in electromagnetics to distinguish between phenomena that depend on the
presence of a quantity of charge (e.g. electric field strength) and
phenomena that depend on the rate of movement of charge (e.g. magnetic field
strength). Perhaps the 'static' part of the word is a misnomer when the
whole system is alternating at a radio frequency, but it is used widely in
the literature. For example, if you look up the components of electric
field around a dipole you'll find close-in reactive components that are
often referred to as 'electrostatic'.

As always: if in doubt, read Kraus.

Chris



Art Unwin September 15th 09 04:45 PM

Spherical radiation pattern
 
On Sep 15, 10:24*am, "christofire" wrote:
"Art Unwin" wrote in message

...
On Sep 15, 8:15 am, "christofire" wrote:

"jaroslav lipka" wrote in message


....
On Sep 15, 7:06 pm, "christofire" wrote:


- - snip - -



I certainly haven't arrived here by sitting on anyone's shirt tails. If
you'd care to read some of the history of this NG you'd see where I come
from.


Your question is not put clearly, although I have seen garbled sentences
like this before in this Usenet group. My first question is: have you
bothered to read any of the respected books on the subject, such as
'Electromagnetics with applications' by Krauss and Fleisch. I suspect if
you had you wouldn't be asking me such a question - it makes no sense! Do
I
take it you are referring to Gauss's law for electric fields? Are you
aware
that there is a counterpart Gauss's law for magnetic fields? I don't
believe there is such a thing as a single 'Gaussian law of statics' -
someone has made that up!


Gauss's law for electric fields states: the integral of the electric flux
density over a closed surface equals the charge enclosed. This is an
important part of the basis of electrostatics, that is the study of
electrical phenomena caused by static charges, but it applicable at a
point
in time to any scenario that involves an enclosed charge - which means any
electrical conductor, whether it carries a non-moving charge, DC or AC.
Gauss's law for magnetic fields states: the integral of the magnetic flux
density over a closed surface is equal to zero, and this is an important
part of the basis of magnetics, again whether static or changing.


Both of Gauss's laws are embodied in Maxwell's equations and for the
normal
RF case of sinusoidally-alternating variables a number of different
notations can be used, a popular one being phasor notation. As you will
know, phasors are vectors that rotate at the same angular frequency but
have
arbitrary phase relationships and amplitudes - so phasor notation is a
compact way of expressing quite a lot. But, in this case, every one of the
phasors involved, D the displacement current density, rho the enclosed
charge, and B the magnetic flux density, is a variable that alternates
with
the passage of time. 'Dynamic' variables if you want to call them that.


Neither of Gauss's laws applies directly to strength of an electric or
magnetic field but the linkage is the other two of Maxwell's equations
based
on Ampere's law and Faraday's law, which are both applicable to
time-varying
fields - 'dynamic fields' if you must.


So ... would you like to put your question more clearly? What do you
actually mean by 'to change a static field into a dynamic field' in
respect
of antennas, where all the electrical and magnetic variables are changing
with time, especially the fields? Is this the result of a misunderstanding
of the meaning of the word 'electrostatic' - used to differentiate between
those phenomena caused by the presence of contained charge and those
caused
by its movement?


Chris


(written by Unwin)
Gauss's law of statics is enclosed *particles in equilibrium. Add a
time varying field *to same it becomes a dynamic field *in equilibrium
and thus equates with Maxwell's laws.

(written by Chris)
This appears to be paraphysical nonsense, once again.

(a) There are no 'Maxwell's laws' - there are the four Maxwell's equations
based on laws ascribed to the other three authors named above. *The term
'eqilibrium' does not feature in, and is not required in, Maxwell's
equations or the laws it is based upon. *Radio communication has been based
on Maxwell's equations for more than 100 years without need for
modification.

(b) There is no single 'Gauss's law of statics' as I explained above, and
both of Gauss's laws can be applied to time varying quantities but neither
contains a field.

(c) Both of Gauss's laws are included in Maxwell's equations without
modification - there is no need to 'Add a time varying field *to same' - it
is there already in each case.
* * * * Once again: Gauss's laws are already applicable to time varying
quantities.

(d) What Maxwell provided was unification of the presentation of the four
equations in differential, integral or phasor form, so the relationships and
linkage between them became clear and they could all be used together to
solve electromagnetic problems.

I think the group is aware by now what I think of the writings of people who
claim to know better than Kraus, Jordan & Balmain, Jasik, et al, on the
basis of no practical evidence.

Chris


You still did not put a stake in the ground, just walked around the
question and then walked away. One more chance before I place you in
"unsure". Where in Maxwell's equations does it refer to "particles" or
do they have no place in his views on radiation?
What is your call sign or do you prefer to remain as a unknown?

Cecil Moore[_2_] September 15th 09 04:53 PM

Spherical radiation pattern
 
christofire wrote:
It is in the nature of a challenge for him to take up if he wishes, and if
he does then his bet will be in respect of his positive assertion, but, of
course, he hasn't taken it up yet. If he doesn't take up the challenge then
nothing new is proved - whichever way you care to interpret that.


Sorry, Chris, I misread your posting. You were not asking
Art to prove a negative which I falsely assumed.
--
73, Cecil, IEEE, OOTC, http://www.w5dxp.com

christofire September 15th 09 04:58 PM

Spherical radiation pattern
 

"Art Unwin" wrote in message
...
On Sep 15, 10:24 am, "christofire" wrote:
"Art Unwin" wrote in message


- - snip - -



You still did not put a stake in the ground, just walked around the
question and then walked away. One more chance before I place you in
"unsure". Where in Maxwell's equations does it refer to "particles" or
do they have no place in his views on radiation?
What is your call sign or do you prefer to remain as a unknown?


Incorrect; I gave a positive answer to the question. My answer was based on
normal physics and identified what must, therefore, be paraphysical or
nonsense (or both). The equations don't make any reference to particles -
as I'm sure you are aware. As to the views of Maxwell, the person, I
daresay you can make them up to your heart's content without provable
challenge.

I don't much care what category you place me in - you already know how I
categorise people who make up their own versions of physics and expect other
to believe them ... and sadly some appear to!

My call sign, if I have one, is none of your business.

Chris






Art Unwin September 15th 09 05:20 PM

Spherical radiation pattern
 
On Sep 15, 10:21*am, JIMMIE wrote:
On Sep 14, 11:30*pm, Art Unwin wrote:



On Sep 14, 9:35*pm, Registered User wrote:


On Mon, 14 Sep 2009 16:30:50 -0700 (PDT), Art Unwin


wrote:
On Sep 14, 5:45*pm, "Dave" wrote:
"Art Unwin" wrote in message


...


Point to a law that I have violated *of which you learned about in
academia.
As for me I am at peace with my offering and thus can move on until a
violation of law is presented.


then don't you dare go away until you explain how your weak and strong force
can have any effect on conduction band electrons when their range of effect
is confined to the nucleus.


And why not?


If you're going to go away just go away. I don't understand why you
would expect anyone to accept your fancies as fact based upon the
rambling, incoherent explanations you provide. Your only success is
the audience you have gathered while acting as troll.


No. "Success" is showing up the self perceived experts.
The question is why is adding a time varying field to the Gaussian law
of statics illegal ?
Or stated another way, what is it illegal by changing a static field
into a dynamic field?
This is not trolling. I am exposing people for what they are and they
are fraustrated
in their inability to show me as wrong or even having a book that
states where and why I am wrong. This is not rambling. Since when is
the truth rambling? If you are an expert take up the challenge in
terms of academics or consult a professor for an answer Either is
acceptable for the purposes of debate of what is true or not
true.Everything I have stated
stands upon this very point So guys, direct yourselves at the root
instead of floundering around in a aimless fashion.
And as far as the size of the audience the bigger the better the
exposure and the more success I have against those who rely on
slander. I want this to be as wide spread as possible instead of
running away. Live with it . I am quite sure that many hams around the
World is following this augument looking for that first person you
will take up the challenge
and provide closure with an answer to this very simple question,
without the fear of recrimination from the group all of which say it
is illegal. Until then......


The easiest way to support your hypothesis is to show a plot or data
table showing how time effects a static field. Frankly I don't know
how you could show any relevant data since the word STATIC means
"unchanging over time" . Applying a time variable to something that is
static is pointless.
Time is relevant to DYNAMIC fields but someone else has already taken
care of that for us.

Jimmie


No, it is not pointless because it enables particles at rest ON
radiators. to be implied. This has been the problem for decades that
has prevented advancement. This extension thus moves away from the
idea of parts removed from the radiator itself. Referring to books is
like saying "all is known". So the question posed is all important
because, if true, it means that a radiator can be any shape size or
elevation as long as all contained is in a state of equilibrium.
Now all avoid the question because they say they don't understand the
word "equilibrium."
So I posed the question to a antenna optimizer where it responded with
a non planar design in equilibrium. Never mind whether it is useable
or not it confirmed the extension given. We have argued for a long
time on a question that contains the word equilibrium rather than
focussing on that which is now revealed. Now along comes this "chris"
who unlike Dr Davis declares he doesn't understand the question( not
equilibrium), tho he has been prolific in advice and insults. So
there has been absolutely no closure on the question thus giving rise
to insults.which all can supply with ease. The question is still
there and does not have academic closure!


All times are GMT +1. The time now is 05:47 AM.

Powered by vBulletin® Copyright ©2000 - 2025, Jelsoft Enterprises Ltd.
RadioBanter.com