FrankM

There is a 2014 paper out of LLNL http://www.scirp.org/Journal/PaperDownload.aspx?paperID=50035 The Introduction cites a 2005 Russian study and they note a conclusion from that study. "In 2004 Adushkin and Soloviev studied the generation of electric and magnetic fields from above ground, surface and underground explosions [5]; Academician Adushkin concluded that the actual mechanism of RF generation was not known." I want to see the EM power levels at various spectral ranges, but the LLNL study does not provide this information.

The researchers haven't reached a consensus as to the mechanism that creates the broadband EMP. The researchers know that it is the motion of charged particles that create an EM wave; this is the way it is done in a wire antenna. The LANL paper referenced in my paper presents several theories as to what is causing the charged particle motion. The process is complicated by the double EMP noted by several researchers. Even though there is an abundance of ions produced by a chemical explosion, I see no mention of their motion and contribution to the EMP. A researcher published a paper in an IEEE publication in 2010 that identified the spectral characteristics of airborne explosive EMPs, this to assist in designing EMP protection for aerospace electronics. Measurement of electromagnetic pulses produced in a chemical explosion Unfortunately, the bulk of IEEE publications require a fee to read.

There is a difference between the massive current flow produced by a lightning strike and that produced by am EMP. The current produced by a lightning strike is non-selective, it damages many different structures. I am sure there are pathology reports you can read to see the type of damage a lightning strike causes. Think electrocution. The damage produced by an EMP is frequency selective and there will be no obvious entry and exit points.

Now that you mention it, I have never watched fireworks reasonably close where I had an AM radio turned on and it was not tuned to a station. For those that can get fireworks anytime, you can determine if there is a sharp static response when a fireworks goes off; the sound of the fireworks will be delayed depending upon distance. It would be desirable to have enough distance between the fireworks explosion and the radio to be able to note the static in the radio before before hearing the fireworks sound. The LANL report cited in my report discussed the mechanism that creates an EMP. It is the motion of charges particles, electrons and ions, that create EM waves. Oddly, the LANL report did not mention the role of ions, and a chemical explosion has an abundance of both charged particles. The Russian report cited the range of EM emissions detected from an explosion. I was unaware that Andrei Sakharov worked on producing a chemical explosion EMP; his contribution is not noted in the Russian report. The Russian report cited a 1940 paper by a Russian seismologist that detected EM emissions from an explosion; the first citation in the Russian paper. The actual brain damage caused by an explosion is identified in the 3rd reference in my vixra paper. The John Hopkins pathologists did not identify how the explosion caused the unique honeycomb pattern; that is the focus of my paper.

I know what the SAR regulations pertain to. I also know that a brief exposure to a very high intensity EM source will do the same damage that a lower power source would do in a longer time period. Just what part of physics makes my idea impossible?

The FCC Specific Absorption Rate (SAR) regulations are there to limit the human body to EM radiation. The damage to mammalian brains noted in ref.(11) of my vixra.org paper indicates it doesn't take much EM power to cause damage. I would like to know how much of the 20 billion watts per centimeters noted in the LLNL report is within the spectral range of the GSM phones. What is known in specific technical circles may not be known outside these groups. I suspect those involved in nuclear non-proliferation detection know a lot about the EM spectral characteristics of chemical explosions, but their info is not publicly available.

You do not have to have ionizing radiation to damage body tissue.

Every chemical explosion produces a broadband electromagnetic (EM) pulse (EMP). A Los Alamos National Laboratory (LANL) report states, "The emission of electromagnetic radiation from a chemical explosion is well established." However, it is difficult to find reports that identify the intensities in the various spectral ranges. A Lawrence Livermore National Laboratories (LLNL) report states, "In the brief instant of a high-exlosive detonaton, some remarkable events take place: the shock wave produces pressure up to 500,000 times that of Earth's atmosphere, the detonation wave travels as fast as 10 kilometers per second, temperatures can sore to 5,500 kelvins, and power approaches 20 billion watts per square centimeter." I haven't been able to find a report that discusses the effect a chemical explosion EMP has on the human body. To remedy this deficiency, I have prepared a paper titled, "The Electromagnetic Cause of Shell Shock." http://vixra.org/pdf/1502.0196v2.pdf

In 1975, an article was published titled, "Chirality". Many more examples have been found since then. Chirality The article stated there was a left-hand bias. The final paragraph contained the following: "Thus there are indications that the role of chirality in the universe, or at least on this Earth, may be greater than has yet been understood. This accords with the view often put forward that greater attention should be paid to asymmetries as the necessary initiators of processes."

I don't know the actual current across the worms body. I did find that there are two types of worms, those that burrow vertically and those that burrow horizontally, and I do not know which type(s) I have. I did observe some worms exiting vertically but I don't know if that has anything to do with the manner in which they burrow. I don't have a video camera, which would have allowed me to record and replay the worm exits to get counts and their exit points relative to the positive and negative terminals, there seems to be a slight difference. One really needs something like a variac or a variable resistance to adjust the current to a consistent value when the electrodes are moved to fresh areas. I tried to be consistent in the depth I inserted the electrodes but slight variations are inevitable. The actual in-ground current vectors created by seismic action will be different than what one gets from two rather close space electrodes, but I know that earthworms will respond to relatively low seismic generated currents. At the near surface I would expect the current vectors to be mainly horizontal. One would think the worms original orientation to the current vector would be a factor in how much potential would be across their bodies. I do not have any instruments that would be suitable for measuring the electrical resistance of a worms body, just in case anyone is curious about that. What we really need to know is the range of currents that can be expected from seismic events. I have already concluded worms will respond to relatively low current levels, and it requires a period of applied current to stimulate worms to exit from the ground. Now, how can this knowledge be used to detect seismic generated currents?

On the amateur science experiments thread I posted a few of my observations where I subjected earthworms to AC and DC electric currents. http://www.scienceforums.net/forum/showthread.php?t=26312 An image of an earthworm responding to an earthquake is available at a USGS site. http://folkworm.ceri.memphis.edu/ew-doc/

I read an article that discussed a Japanese physicists observations about earthworms exiting the ground before one of their big earthquakes. http://animalsandearthquakes.com/ikeya.htm Electric currents have been used for earthworm extraction going back many decades (worm getters), but I could not find any studies where their sensitivity to specific currents levels was measured. I have raised garden beds which are prolific with earthworms so I decided to see if I could get them to respond with fairly low electric currents. I used #12 solid copper wire as electrodes, starting out with 6" length and then later making some 12". I started out with a 38.6 VDC source, an old HP printer transformer, the 6" electrodes vertically in the ground and 10" spacing, this giving me approximately 60 ma no matter where I inserted the electrodes in the garden bed. I had multiple worms exiting the ground within 60 seconds (worms move slow). I changed the spacing to 16" (to a fresh area) and the current was just a few milliamps lower, and the same worm extraction experience was noted. The next day I used two different transformers, a 12 VDC and a 9 VAC and experimented with the spacing. The current at 12 VDC was about 20 ma and that for the 9 VAC, approx. 15 ma current. There was a slight difference between worm exit counts and size AC vs DC, but the current was slightly different. The following day I prepared the longer electrodes, 12", and experimented with various spacings, AC and DC (both 12 and 38 V). I also prepared a 13" insulated electrode where only 1" was exposed and inserted that into the ground so that the current had a somewhat vertical component. The number of worms exiting varied somewhat with the applied current, which depended upon electrode size and insertion depth. In the maximum current area I suspect worms were immobilized, but this is conjecture only because of where I observed worms exiting relative to the electrodes. I did not determine the minimum current at which worms would exit the ground but I could get exiting with a little as 3 ma between electrodes, which means the actual current differential experienced by the worms has to be in the sub-milliamp range. I can conclude the earthworms will exit the ground if there is a sustained current. Worms don't move fast, thus they probably started toward the surface as soon as they experienced a current level that was uncomfortable to them. I also had small garden centipedes (beneficials) exiting from the ground in the same area as the worms, thus they were being irritated by the same in-ground currents as the worms. There were a number of peculiarities noted in where the worms exited relative to the electrodes but more studies are needed with better controls to see if these peculiarities are significant. I also placed some of the worms that had exited and moved away from the current influence directly in between the electrodes and watched their reaction. Size seems to matter, and if they couldn't exit immediately from the area of maximum current influence they had problems. The next day I used multiple electrode configurations and switching the polarity of inner and outer electrodes, this to examine if worms have a polarity sensitivity. From what is known, the earth currents generated before and during earthquakes are more a DC type with variations in magnitude, it is not sinusoidal with plus and minus swings.

The title of the .jpg and the character of the circuit board are clues. That was 20+ year old technology and it was a telephone circuit loop control card. The big gold plated contacts are a giveaway to the era. Either way, the +5 or the +42 volts were relatively high current sources. It is not known which one did the major zapping. I believe the individual identified the victim as a "rat snake". Although video cameras can be used to observe critter reactions, there is a problem of constantly monitoring them visually. The Chinese did not note the use of any kind of motion detector, thus when do you watch? The suggestion to use an electro-sensitive fish has the same problem, how do you determine the difference between normal movement and that which results from an electrical current? Do you have to watch 24/7? Putting a couple of wires in the ground sounds good but there is a problem, the direction of the "current vector" from a seismic induced current. For maximum potential the contacts have to be in line with the current vector, if they were at 90 degrees there would be little or no current differential, even though an event created significant current flow. The current will expand outward from the seismic source. For each small segment of surface area the current vectors will be essentially parallel but another segment that is a quarter circle away from the source will have current vectors that are different by 90 degrees. Unlike the "strike point" for lightning, the seismic induced currents do not come from a point source, they come from an extended stress zone which can be kilometers long. Every monitoring station would have to have a minimum of 2 pairs of contacts at 90 degrees. Seismic events are not the only sources that create ground currents. Sunspot activity is one outside source and the intensity of ground currents generated by those events depends upon the earth-sun orientation. Additionally, not all sunspots are created equal and their effects on the earth are not uniform. If ground currents are the source for snakes agitation preceding earthquakes, it would be nice to know exactly what potentials are necessary to get their attention, we could then use that as a threshold.

The lightning safety article stated that you "should not lie down" as this puts you in continuous surface contact, thus you have a greater change to be in contact with "potential points" that are high enough to break-down your resistance, thus creating a damaging current flow. It is simple Ohm's law, a small current across a high resistance results in a high potential difference. This snake crawled across a circuit board until he extended across a potential that exceeded his biological resistance. The individual that took the picture and replaced the board did not note which board potential zapped the snake. There were two voltage sources to the board, +42 volt and +5 volts.

Yes, we definitely have contradictory positions. The action that is creating the in-earth currents is not caused by piezoelectric action. http://www.scec.org/news/01news/es_abstracts/Freund.pdf An underground snake den is just a small cave and is subject to the same "physics" as being experienced in those large enough for humans to enter. http://www.nols.edu/resources/research/pdfs/lightningsafetycavers.pdf I do not know what snakes do when they are exposed to conditions wherein there could be nearby lightning strikes, but humans caught outside in such a condition are supposed to minimize their contact with the ground to reduce exposure. http://www.torro.org.uk/TORRO/research/lightning.php "If caught out in the open with no shelter nearby, move to a place of lower elevation such as a hollow or dry ditch. Crouch down (to lower your height) with both feet close together. Do not place your feet wide apart or lie flat on the ground as this will increase the difference in voltage across your body, increasing the electrical charge you may receive from radial ground currents, if lightning strikes the ground nearby. Tuck your head in and place your hands on your knees." Snakes don't have the luxury of minimizing their contact with the ground. Has anybody been in the field and had the opportunity to observe snake reactions to nearby lightning strikes?

The observations and studies made on animals that were being shocked indicate they definitely "locomote" after being shocked, this in an attempt to remove themselves from where they are feeling discomfort. One of the problems I have found in the studies on dairy cows is that they know the minimum voltage/current combination that causes discomfort, but they have never directly measured the voltage/current the cows actually experienced in "dairy parlors" or in nearby fields. They have been observed acting much more agitated than when exposed to the "threshold" that triggers a reaction. You are depending upon a coincidence that an "experienced observer" will have all the instruments with him to properly record all the conditions that existed when some type of animal reacts somewhat unusually. I doubt if an accidental observer would constantly record conditions wherein the observer did not get some immediate indicator of a causative action for the unusual behavior. The reports of odd animal behavior has preceded the main seismic event by days. We don't even know what instruments we need to measure the causative action. Let's examine #1. Helmut Tributsch is not the only one that has observed the strange animal activity before earthquakes. One of the reasons Tributsch's observations are discounted is because he espoused an earthquake mechanism that was in the process of being discredited at the time he wrote his book, the so-called creaking theory, the creatures were "hearing" it. His observations were compiled from multiple publications, and these publications covered an extended period of time. Tributsch was covering just animal reactions observed before earthquakes, but decades earlier a man named Charles Fort compiled "odd happenings", which he published in several books, that were recorded in the newspapers from events all over the world. He segregated his phenomena by what he felt were the proper categories for what was known at that time. Lo and behold, many of these same events occurred again in the "modern era", and this prompted the "enlightened scientists" of the 1930s to examine the "conditions" related to the "odd happenings" and they eventually found some of their causative mechanisms. The observations of recurring events made by unqualified observers were correct. We have not properly recorded and diagnosed the conditions that are causing aberrant animal behavior. Since you and your colleagues will not even expose snakes to controlled "electrical conditions" that might cause them to react, I do not see how you can conclude they display no behavioral responses to various types of "electrical conditions". Seismic actions before and during earthquakes create massive "current surges" in the earth and these are being detected by both satellite and earth-based measurement systems. Don't ask a traditional seismologist about this, especially U.S. seismologists, they refuse to accept this is happening, plus it is outside of their area of expertise. The French have a satellite up that was designed specifically to detect the electromagnetic emissions that occur during these in-earth seismic produced current surges. http://smsc.cnes.fr/DEMETER/GP_actualite.htm The in-earth precursor currents are strong enough to effect the ionosphere over the seismically active area, and major seismic events have actually reversed the polarity of the ionosphere over and beyond the immediate seismic event, completely disrupting long range communications that are dependent upon ionospheric skip. The Chinese had instruments in place and on-line before the Taiwan 1999 Chi Chi earthquake that allowed them to learn things about the in-ground currents that had not been known before. The magnetic field produced by the main seismic event current was actually measured, and it indicated a current from 500,000 to 1,000,000 amperes. The mechanism that creates the current in rock under stress has been demonstrated in laboratory tests, and it is not a piezoelectric process. The "current sheet" created by a seismic event spreads outward from the fault area and to the surface, and this helps explain some of the "strange" atmospheric visual effects seen before and during seismic events. The earth is normally negative relative to the atmosphere, but the current sheet produced by seismic action produces a short lived "positive" charged area and an opposite "negative charge" area in the atmosphere/ionosphere above it. During thunderstorms equivalent "charge reversal" events have been measured between the earth and the atmosphere. A localized or regional charge reversal is not uncommon, it was never expected that seismic events produced the same effect, from below, that are even more extensive in area and charge intensity. An earthquake and related processes can kill hundreds of thousands of humans in one event. If snakes can be tested to determine what causes their reactions before the main seismic event occurs, then we will know what instruments that can be used to detect what is causing their reaction. Knowing the "minimum" voltage, current, electric field, polarity and ac or dc combinations that cause snakes to react will allow one to establish monitoring stations with the proper instrument sets. I am not so ethically challenged that I wouldn't sacrifice a few snakes to save a few hundred thousand people. If you know what you are doing it is possible to minimize snake losses, but if one gets zapped you can have a barbecue. The snakes being monitored in China are at a snake farm, snakes being raised for food. I do have some concern about their video monitoring system, it might alter the characteristics of the "electrical environment" wherein the snakes are contained, thus possibly voiding the condition that causes the snakes to react.

>From the same BBC article: "When an earthquake is about to occur' date=' snakes will move out of their nests, even in the cold of winter. If the earthquake is a big one, the snakes will even smash into walls while trying to escape,' he told the newspaper. That's describing coherent, albeit undirected and somewhat frantic locomotion, *not* siezures. There's no possible way to confuse the two.[/quote'] I did not use the term "seizure", I called the reaction a muscle spasm, but perhaps "reaction" would be a better term. I thought snakes hibernated in the cold of winter. What would cause snakes to suddenly come out of hibernation and go into an environment where they will freeze to death? Normally, doesn't it take a period of "warming" before a hibernating snake can move?. You keep using the term "electric fields" wherein I am suggesting that snakes can be electrically shocked when they are exposed to an electrical potential that has significant magnitude to overcome the resistance of the snakes skin. I know they can be electrically shocked and killed, as I have a picture of a dead snake that had crawled across an old style computer type circuit board and got fried. The circuit board had a quite a few points wherein the snake could have been across several different voltage potentials, but the individual(s) that replaced the board and took the picture were not particularly interested which potential level killed the snake. The subsequent short ruined the circuit board and the snake. The particular circuit board did not carry very high potentials, the highest being 42 volts and the lowest 5 volts, both dc. It would be of interest to know exactly at what potential a snake will react. Someone with a snake could lay two bare wires in an area where "their" snake traverses, connect the wires to a variable power supply (with suitable current limiting), and gradually raise the potential to observe when the snake reacts. As biological materials go, keratin has an extremely high resistance, but it is also a material that exhibits proton conduction. None of which are in biology or seismology. Why should I give him creedence? Does he have evidence, photographic or otherwise? Tell you what, why don't you get off your ass and find out yourself? You think we have nothing better to do than jump up and do experiments on command? We've got our own work to do, and lots of it. Furthermore, science is not done just by randomly doing crap; Do we have a reason to suspect snakes may have interesting electrical properties? No. Do we have a reason to suspect they can detect electicity or magnetism? No. Do we have a reason to think such abilities or properties would be ecologically relevant? No. Do we have a reason to think the electrical properties of snakes will tell us anything interesting? No. Since you and and others of your profession (that you consider trained observers) do not have the time to observe snakes and other animals reactions to seismic precursors, you have created a catch-22 situation wherein any observation made by another scientist will have no credence. I do not have a laboratory with the needed equipment and it would take a while to become acquainted with the procedures to perform bio-electric measurements. This is why there are forums, to find people that have the equipment and knowledge, and perhaps the curiosity, to perform measurements on something "new". The experiments should be performed with both ac and dc potentials.

The only report I have read is in the cited BBC article. Please cite the sources for the reports you have heard so that I and other members of this forum can examine the material. The report I cited about snakeskin indicated the fibers contain a wax which reduces moisture loss. Moisture is the primary medium which determines "resistance", other factors being much smaller. Can you provide reference to those reports that "thicker skin" results in a higher electrical resistivity? I am interested in measured values as are the members of the technical forum that have read the same report about snakes in China. I am not a herpetologist, thus I considered "spasm" being an appropriate reaction. You state the snakes reaction is not a muscular spasm. I am not describing the behavior, I am trying to interpret what was stated in the BBC article. I have not seen a video of the snakes reaction. Are you aware of any videos that show the same reaction as that stated in the BBC article? I do think it is important to know what causes a reaction, even a "seizure/spasm". Seismologists use instruments that cover the audio spectrum from near DC to well above the hearing of snakes and man. Seismologists have been "listening" to seismic vibrations for many decades and if this were the medium which causes snakes and other animals to react well before an actual earthquake occurs they would have known this a long time ago. Seismologists have not been monitoring the "electrical nature" of seismic action, this being done by many agencies outside of the "traditional" seismology organizations. Guess who gets all the funding for earthquake studies? It could be that they do, but who is watching and reporting if they do or do not?" The biology-seismology communities has discounted that animals or any other species react well before an earthquake, so I doubt if we will find any "academic" reports where various species react or do not react to the "currents" created by seismic action. The material in the book by Helmut Tributsch is ignored by traditional biologists and seismologists. It is the same old story, if a "biologist or seismologist" did not observe and record it, it didn't happen. You can get Helmut Tributsch's technical qualification here- http://www.chemie.fu-berlin.de/ag/tributsch/ A Stanford Professor, who is doing "non-traditional" (electric currents) seismology research, has informed Helmut Tributsch about the research related to seismic produced electric currents. I find it somewhat disconcerting that the "biology/herpetology communities" know so little about the bioelectric characteristics of snakes. It seems them are satisifed with "opinions" rather than "measured" or otherwise researched results.

The classic work on animal responses before and during earthquakes is by Helmut Tributsch, "When the Snakes Awake: Animals and Earthquake Prediction" http://mitpress.mit.edu/catalog/author/default.asp?aid=2223 This was mentioned in the third post to this topic.

Mokele One can make the assumption that the snake reaction the Chinese are observing is a "muscle spasm" response. Other than a jab with a sharp object or contact with a hot poker, I can think of only one other type of stimulus that can cause such a reaction in humans and animals, an electric potential. Apparently the snakes are not being damaged by the stimulus that causes their reaction, as they go about their regular snake activities once it has passed. I would agree that internally the impedance/resistivity would be close to that of other animals, the main conductive medium being the water content of the tissue. However, before the electrical current gets to the interior it has to pass through the resistance of the snakes skin. http://micro.magnet.fsu.edu/primer/techniques/phasegallery/snakeskin.html The ventral scales on the snakes belly will not be as conductive as the internal tissue, thus its electrical resistivity will much higher. I would expect a snake to have a much higher "effective" resistance because of their scales. Ideally, one should be able to test snakes to find out exactly when they feel an electric current that causes them to react. I have been unable to find any research reports in this area. Before doing electrical stimulus tests on snakes you need to know their impedance/resistivity. We react differently to dc and ac potentials, and so should animals and snakes.

I don't know anything about snakes, I assumed from your statement they couldn't detect any electrical stimuli, even directly. Can you cite the reports that have confirmed the above inability in snakes? I am making this inquiry to inform members of a forum that deals with earthquake precursors and they are curious "why" snakes are reacting before any conventional seismic instruments detect anything. The only current tests I have been able to find are those that measure a snakes sensitivity to infrared. The last comprehensive tests I could find on snakes hearing/vibration sensitivity were conducted more than 30 years ago. Instrumentation has improved by several magnitudes since that time. Are you implying they can detect things beyond the dynamic range of seismic instruments or things that are well below their sensitivities? The Chinese were observing violent reactions in snakes, what could cause them to react that way? I still need to know the impedance of snakes.

The bbc article stated that snakes are detecting something from earthquakes well before there is any measured seismic activity. The eventual measured seismic action has vibration frequencies well below the measured range of snakes auditory/vibration sensitivity. Unusual snake activity has been observed all over the world preceding earthquakes. From The MIT Press Classics Series: When the Snakes Awake Animals and Earthquake Prediction Helmut Tributsch http://mitpress.mit.edu/catalog/item/default.asp?tid=5093&ttype=2 The above book was mentioned several times in the "earthquakeprediction.pdf" article below. http://www.gps.caltech.edu/~jkirschvink/pdfs/earthquakeprediction.pdf I did not know snakes could not be electrically shocked. Have you actually tested snakes to determine they do not feel an electric current? What is the impedance of a snake?

I think it is a matter of perspective, physicists do not think of EM waves in terms of angular notation and some in other disciplines do. My shortest response to the concept was from a professor of electrical engineering, who responded with one word, "interesting!" The triangle pair is representing the relationship between wavelength and frequency in an angular form, which I think makes it easy to visualize. I know this is not taught but the concept is not new. It also allows the relationships to be expressed using a trigonometric function, the cosecant function, when the vertical leg is held as a constant. When the vertical legs are held as a constant, changing the angle of both equally results in a different value for the hypotenuse of both triangles. The constant of proportionality is calculated the same way, but it will not add up to a value for the "speed of light" that we are familiar with. The mathematical relationships are perfectly valid, one of the parameters of the constant of proportionality has changed with the angle, the duration of the unit of time. If you wanted to have a different "time base" for calculating the speed of light this provides a seamless transition. When rotated to 45 degrees you now have a numeric value for the speed of light that can be calculated to nearly unlimited precision if you do not use centimeters. Just as a meter is a physical length that is given a value of "one" as a base unit of measure, the length of the wavelength of the H1 emission can be given a value of "one" as a scientific base unit of measure. The end result is a set of base units that are mathematically derived using a natural physical length and a natural mathematical constant expressed as an angular frequency value. The Backwards.pdf article illustrates the progression from the 26.2540 degree to 45 degree angle. As I stated, it is backwards from the way it should be developed, but I have found contemporary scientists understand the process easier if I start with SI units. http://vip.ocsnet.net/~ancient/Backwards.pdf

Inadvertent post.

It is easier to present the concept mentioned in the previous post graphically by showing the relationships in a geometric form. The graphic in TrianglePair-SI.pdf illustrates the relationships when in SI units. http://www.vip.ocsnet.net/~ancient/TrianglePair-SI.pdf The constant of proportionality between the triangle pair is the hypotenuse of one multiplied by the vertical leg of the other. When the results of both sets are equal the triangles are mutual, one is the inverse of the other. With the vertical leg of each being kept constant, thus when the angle is changed, one element of the constant of proportionality becomes a function of the angle. SI units are valid for just the one angle illustrated.