Speed of Stationary Objects, Stellar data analysis, Stellar clock/time |

Speed of Stationary object If you are standing with both feet on the ground in front of your house, how far did you and your house move in the past 24 hours? Are you going: A - 0 Miles Per Hour B - up to 1,000 Miles Per Hour C - both A and B D - 67,000 plus or minus 1,000 Miles Per Hour F - all of the above. The correct answer is F. Logically, you must think that is absurd. There isn’t any way for a person to be standing still with both feet firmly on the ground, in front of their house and still be moving. Would it help you deal with the question if I said that you and your house are standing on the equator or on the north pole? We all know that the earth is spinning around it's axis. At the equator, the rate of rotation is about 1,000 MPH. At the poles, the rotation is zero. At about 40 degree north or south, the speed is about 750 MPH. Now think about the question with that additional information. If you are standing on the equator, with both feet on the ground, in front of your house, at sea level, holding some test equipment, how fast are you going? It should be easy to understand that C is obviously a correct answer if you include the words describing the relative point of reference. For answer A, relative to the ground, you are moving 0 mph. For answer B, relative to the center of the earth, you are moving about 1,000 mph. That is because the surface of the earth, at sea level, at the equator is moving about 1,000 mph relative to the center of the earth. Note that I said “at sea level”. If you were on the top floor of 10 story building, the distance from the center of the earth to the 10 floor of the building is greater than the distance at sea level. Since the distance is greater, the circumference of the circle is greater which results in a greater distance to go in the same amount of time which results in a greater speed for the person standing on the 10th floor of the building with some test equipment. A person standing at 40 degree north or south is moving at about 750 mph relative to the center of the earth while a person standing at the north or south pole is moving 0 mph relative to the center of the earth as well as 0 mph relative to the surface of the earth. Suppose we have 4 people, with the same type of test equipment, who are standing at the 4 main points I described; one at sea level at the equator, one on the 10 floor of a building at sea level on the equator, one at 40 degree north and one at the north pole. Now suppose the 4 people can see each other and they can see each other’s test equipment. All 4 will say that they are all moving 0 mph relative to each other and to the surface of the earth and to the test equipment. However; we also know that three of the people and their test equipment are moving at three different speeds relative to the center of the earth. In one hour, the person on the north pole will simply rotate. The person at 40 degree north will move about 750 miles while the person at the equator will move about 1,000 miles and the person with test equipment on the 10th floor will move a little more than the person on the ground. Relative to the center of the earth and the surface of the earth, the following table summarizes the relative MPH and distance moved in a day and a year at different points on the earth. Point of reference Location of person MPH Miles moved in a day Miles moved in a year Earth surface north pole 0 0 0 Earth surface 41 degree north 0 0 Earth surface equator 0 0 0 Center of the earth north pole 0 0 0 Center of the earth 41 degree north 783 18,792 6,863,778 Center of the earth equator 1,038 24,912 9,099,108 Now we should return to the original question. We still have answer D to address. It says: 67,000 plus or minus 1,000 Miles Per Hour. Most people know that it takes just over 365 days for the earth to go around the sun. Some people know the earth is moving at a speed of about 67,000 mph as it goes around the sun. With that additional information, it should be easy for most people to understand that they are riding on the earth that is moving at a speed of about 67,000 mph relative to the sun while they are moving 0 mph relative to the surface of the earth. It should also be easy for people to understand that they are also moving up to 1,000 mph relative to the center of the earth. It takes a little more explanation to address the difference between the night time speed vs the day time speed. Since the earth is spinning while it goes around the sun, the speed of a point on the earth surface is going with the direction of the earth’s movement half of the time and it is going against the direction of the earth’s movement the other half of the time. Hence, the speed of a person relative to the sun being 67,000 mph plus or minus up to 1,000 mph. It is important to note that the speed of the point on earth relative to the sun is either accelerating or decelerating as it proceeds from dusk to dawn. The maximum addition or subtraction is at the middle of the day and night. The minimum addition or subtraction is near dusk and dawn. This is basic information that should be easily understood by everybody. In the past it was hard to convenience anyone that the earth is moving. Today the earth’s movement is readily accepted. Now it should be easy for anyone to understand that a person, standing next to some test equipment, someplace on earth, is moving 0 mph relative to the point on the surface of the earth where they are standing, as well as up to about 1,000 mph relative to the center of the earth, and about 67,000 mph plus or minus about 1,000 mph relative to the sun. That means, anyone who is reading this while they are standing or sitting on earth is moving a distance of about 67,000 miles per hour plus about 1,000 miles per hour. In a day, they move a distance of about 1,608,000 miles plus about 24,000 miles for a total of about 1,632,000 miles. If you eat at the same place on Monday and then went back on Tuesday, you will have traveled over one and a half a million miles between lunch on the two days. If the person was standing next to some test equipment, the equipment is also moving the same speed and has covered the same distance in one day. Relative to the sun, the center of the earth and the surface of the earth, the following table summarizes the relative MPH and distance moved in a day and a year at different points on the earth. Point of reference Location of person MPH Miles moved in a day Miles moved in a year Earth surface north pole 0 0 0 Earth surface 41 degree north 0 0 Earth surface equator 0 0 0 Center of the earth north pole 0 0 0 Center of the earth 41 degree north 783 18,792 6,863,778 Center of the earth equator 1,038 24,912 9,099,108 Center of the Sun north pole 67,000 1,608,000 587,322,000 Center of the Sun 41 degree north 67,000 1,626,792 594,185,778 Center of the Sun equator 67,000 1,632,912 596,421,108 Now lets consider sound. Suppose some people are in a box on the equator at sea level and the temperature is 59 degrees Fahrenheit and one person talks to another person. Since the box is at the equator it is going about 239 mph faster than the speed of sound, will the second person be able to hear the first person talking? How can the people in the box hear each other since they are going faster than the speed of sound? The speed of the sound in the box is relative to the box. Hence; relative to the surface of the earth, they are not moving while they are talking. However; relative to the center of the sun, they are moving 67,000 MPH which is about 88 times the speed of sound. From this we see that the speed of sound is relative. So, relative to the surface of the earth, the speed the sound, in the box with people and test equipment inside, is about 761 mph. However; relative to the center of the earth, the speed of sound in the box is between, 1,761 mph and a minus -239 mph. Relative to the sun, the sound is moving at about 67,761, plus or minus up to about 1,000 mph. That shows that the variation in the speed of the test equipment and the speed of sound relative to the sun is greater that the speed of sound relative to the surface of the earth. Now let’s suppose a person, with some test equipment, is riding on a train that is going 100 mph. How fast is that person moving relative to the sun? The answer to that question depends upon the direction of the train and the time of night or day. That person will be going some variable speed between 67,000 mph plus or minus 1,000 mph plus or minus 100 mph. That gives a variable speed of the person riding a train moving 100 mph some where between 65,900 mph and 68,100 mph. That is because the speeds are additive relative to the sun. The 67,000 mph speed of the earth moving around the sun plus or minus the accelerating or decelerating speed of the surface of the earth as it goes between dusk and dawn plus or minus the speed of the train gives us up to 2,200 mph difference in the variable speed. Now let’s suppose there is a bowling alley on the train and the person is about to roll the bowling ball. Suppose the person walks at 5 mph and rolls the ball at 45 mph. How fast is the ball going relative to the sun? The ball is accelerating or decelerating somewhere between 65,850 and 68,150 mph relative to the sun. That is because all the speeds are additive and the speed of a point on the earth’s surface is changing speed as it moves between dusk and dawn. Although the point in space where the person rolled the ball remains constant, the bowling pin are moving with the train and the surface of the earth relative to it’s movement around the sun. The time it takes for the ball to arrive at the pins remains constant although the distance the ball moves is considerable greater than the length of the bowling alley on the train. The distance from the person who rolls the ball to the pins relative to the train remains fixed while that distance relative to the sun is very great and is variable depending upon the time of day and direction of the train. Remember the test equipment I keep mentioning. Now suppose a person is conducting an experiment to determine the speed of light while riding on a train going 1,000 mph. on the surface of the earth that is moving at some accelerating or decelerating speed up to 1,000 mph somewhere between dusk and dawn and the earth is moving 67,000 mph around the sun and those speeds are additive. We have also already determined that the speeds of moving objects on the train are additive to the speed of the train relative to the sun. We know the distance between points A and B on the train are constantly moving at a greater speed or a lesser speed relative to the sun while they remain constant relative to the train. Suppose two virtually identical tables are setup similar to the tables used in the Michelson-Morley experiment. It is an example of measuring the speed of light at 186,300 miles per second using a table that could turn to check the speed going different direction and always gives the same result. In their experiments the table was riding on the surface of the earth that is moving. We simply add the condition of the experiment being on the train that is moving at 1,000 mph on earth that is rotating at while it is going around the sun. We use two tables that are geared to test the speed of light in opposite directions at the same time. How fast is the speed of light on each table on the moving train on the spinning earth that is going around the sun? We have already established that the answer is relative to a point of reference. Relative to the train, both tables are going 0 mph and the light on both tables is going 186,300 mps. Relative to the surface of the earth, the tables are on the train that is moving 1,000 mph so the lights on the tables is going 186,300 mps plus and minus 1,000 mph for the speed of the train. That is because one table will test the speed of light going with the train while the other table will test the speed of light going against the speed of the train. Relative to the center of the earth, the tables are on the train that is moving on the surface of the earth. So, we have 186,300 mps for the speed of light on the tables plus and minus 1,000 mph for the speed of the train plus and minus 1,000 mph for the speed of the earth's rotation. That gives us a speed of light that is accelerating or decelerating between 186,300 mps plus and minus 2,000 mph. Also, relative to the sun, the tables are moving with the train that is moving with the earth as it spins and goes around the sun. That makes the speed of light on each table 186,300 mps plus and minus 67,000 mph for the speed of the earth going around the sun and plus and minus 1,000 mph for the speed of the earth at the equator and plus and minus 1,000 mph for the speed of the train. In the theory of relativity, it says w=c-v which means the speed of light in the frame is additive to the frame to get the speed of light relative to the frame of reference. That formula comes from the train thought experiment using man walking on a moving train. In that example, the speed of the walking man on the train is additive to the speed of the train resulting in a relative ground speed. Then the speed of walking man is replaced with the speed of light to get the speed of light on the train relative to the ground. My example simply takes a known actual experiment and puts it on a train. The outcome is the same for the experiment regardless of the use of addition of the train. Every experiment to measure the speed of light under identical conditions has consistently given the same constant speed of light on earth. The location or orientation or speed of the moving test equipment has not changed the outcome. The speed of light relative to the earth or any moving frame of reference is a constant c. At about 40 degree north, the speed of earth’s rotation is about 750 MPH. At the equator, the speed of rotation is about 1,000 MPH. Relative to the center of the earth, the speed of light at 40 degree north going EAST is 250 MPH slower than the speed of light at the equator. Relative to the center of the earth, WEST bound light at the equator is going 2,000 slower than EAST bound light. That is: WEST light speed = c-1000 MPH, while EAST light speed = c+1000 MPH. Relative to the sun, the relative speed of light on earth is 67,000 MPH faster than the relative speed of light on the sun. That is because the earth is going around the sun at a speed of about 67,000 MPH. That gives us: the relative speed of light on earth of c + 67,000 MPH + or - 0 to 1,000 MPH depending on the location and orientation of the test equipment relative to the earth’s rotation. We see from these examples that the speed of light is relative to the frame of reference. We also see that the speed of light is additive to the frame of reference as shown in the theory of relativity with the formula w=c-v. We also see that the speed of the frame of reference does not change the relative speed of light in the frame. As a result, the speed of light will remain constant within the frame of reference even when the frame of reference is moving at any speed including virtually unlimited speeds. If a box is moving at 186,300 mps, the speed of light inside the box will be 186,300 mps regardless of the orientation of the test device. If a box is accelerated to a speed of 500,000 mps, the speed of light inside the box will be 186,000 mps regardless of the orientation of the measurement device. The relative speed of light in a frame moving 500,000 mps is 686,300 mps. As we all know, the relative speed of light in a vacuum in a moving frame of reference is a constant 186,300 MPS regardless of the motion of the frame of reference. We also all know that the speed of light is relatively additive to the frame of reference. - The fact that the earth spins while it moves around the sun does not alter the requirement for the laws of physics to apply to an internal frame and all it’s contents whether moving or stationary. - In addition to the changing relationship of a point on earth relative to the sun, our solar systems frame is moving in space at a speed of about 450 thousand miles per hour in some direction. That means that you and your test equipment are moving over 517,000 miles per hour. - None of the above mentioned movement of any of the above mentioned objects changes the fact that the laws of physics are the same in any inertial frame, and, in particular, any measurement of the speed of light in any inertial frame will always give 186,300 miles per second. That is just the way it is for the relatively additive speed of light and the requirement for the laws of physics to apply to any and all objects within or external to any frame of reference. We all know speed of light is constant in every inertial frame. The issue is across frames. Even Albert specified in his theory of relativity that the speed of light is additive across frames. He has a formula that specifies the cross frames difference. Since it is additive, and he knew it, he had to eliminate the meaning of time. He gave his train thought experiment as proof. A person on a moving train doesn't know they are on a moving train. The person on the train moves past a However; Albert says the illusion represents fact. Albert specifically states the obvious, that the lightning strikes person on the ground just as lightning strikes two places an equal distance away. The person on the ground observes the lightning strikes as simultaneous. That is because he or she is at the mid point between the light flashes so they arrive at him at the same time. The person on the train moves away from the mid point. Hence the person on the train is moving toward one lightning strike and away from the other. He is racing ahead of one lightning strike so that lightning strikes arrives at him later than the lightning strike he is racing toward. Therefore, the train observer doesn't observe the lightning strikes as simultaneous. Now we all know that the person on the train has moved away from the mid point so they can't observe the lightning strikes as simultaneous. Even Albert stated that he knew that fact. It doesn't matter if the train is moving or stopped on the track. If the person on the train isn't an equal distance between the lightning strikes when the light arrives, one light will have a shorter distance to travel then the other so the observer who isn't at the mid point can’t observe them as simultaneous. Again, even Albert acknowledged that fact. don't seem to be simultaneous in the train frame. He then concludes that simultaneous in one moving frame aren't simultaneous in another moving frame because the person on the train doesn't observe them as simultaneous and doesn't know he is on a moving train and doesn't know he has moved from the mid point. We all know the person in the train is moving. Albert knew he is moving. If the train observer knew he is moving, he could use Albert's cross frame speed of light formula in his theory. He could use his speed and distance traveled to identify exactly how much of a difference will be observed between the different arrival time of the lightning strikes. Then the simultaneous events across frames would remain constant and Albert wouldn't have resolved the problem he knew of and specifically spelled out in detail. The fact is, Albert didn't eliminate the meaning of time because simultaneous events across moving frames of reference remain simultaneous. Everybody knows that the speed of light is constant in an inertial frame. Everybody knows that light traveling two different distances will arrive at different times. Therefore; everybody should agree with Albert when he wrote his formula that specifies the additive cross moving frame speed of light. I agree with Albert on the cross moving frames additive speed of light. I disagree with Albert’s conclusion that a false perception eliminates the meaning of time. I read the theory of relativity. It is all we need to prove it is based on illusion. In the early part of it, Albert states that the truth isn't the truth. It is very clear about the use of false perception to represent fact. See how light changes speed as it moves from a train frame to the earth frame. Light from a flashlight moved from a train to a bicycle rider. Don Edward Sprague Copyright 23 July, 2008 All rights reserved. |

Stellar data analysis, Stellar clock/time Constant time vs variable time data analysis. According to Einstein’s relativity, time varies based on the speed of the observer. Time supposedly slows for the faster moving person. A second for the faster moving person is shorter than a second for the slower moving person. When 2 or more people moving different speeds or velocities observe the same distant events, the duration of those events are 2 fold. First, the duration is the length of time it takes for the event to happen where the event occurs. Second, the duration of the event is the time it takes as determined by the each observer. A faster moving observer would record a shorter event duration. According to any constant time progression and constant space theory, the duration of events is 1 fold. The duration of events will be the same for all observers regardless of their location or velocity. We have considerable data of stellar events. An analysis of the data will prove which is accurate. There are certain givens: - We have many observations points that have recorded stellar events over various times. This gives considerable data to analyze. - Every observation point is moving at different velocities throughout time. – Every stationary observation point is only stationary relative to other common points, – All observation point on earth are relatively fixed from all other observation points on earth. – Observation points in fixed orbit are relatively fixed distance from all ground points, - Various observation locations are known distances from each other so their difference in Einstein variable time can be determined as compared to each other. An observation point that is at a higher altitude and closer to the equator has a higher velocity than lower altitude observation points that are north or south of the equator. - Since Einstein says the velocity of the observer changed the length of their seconds, and - Since the speed of all observation points is different, and - Since Einstein specifies variable time based on speed of the observer, - Then the duration for stellar events to happen is 2 fold. – 1, It is the event duration of the event as it happens – 2, It is the various event durations as observed at each observation point based on the different rate of time progression as compared to the different observation point velocities. Thus, according to Einstein the duration of distant stellar events will vary based on the velocity of the observer. Event durations will also vary based on one observer location since the observer location never has the same velocity over time. According any theory with constant time progression in a constant space, the duration of events is the same regardless of observer location or velocity. It simply takes several data from different or the same locations of observations. If Einstein is correct, the time duration of the stellar events is always variable based on the velocity of the observer, the distant events will never have a predictable duration. That is because the observation point velocity is never the same so their seconds are never the same. Don Edward Sprague Copyright 04 Oct, 2010 All rights reserved. |

There is an old saying about not needing to state the obvious. In this case, it seems that the obvious for some is obscure for others. - An atomic clock moved inches higher than another showed a measured difference in time reading. - A few years ago, the change in earth’s motion was calculated as the result of a of a large earth quake. - The Mercury orbit difference is about 1 turn in 2 centuries. Thus, we see that there is a valid concern about minute differences. The Earth Rotation is 19,700 inches per second Earth around sun 1,180,000 inches per second Sun around galaxy 9.840,000 inches per second Galaxy in cluster 11,800,000 inches per second On point on the equator has a different day/night velocity of 39,400 inches per second. That is because the night rotation goes with it’s movement around the sun. The night rotation goes against it’s movement around the sun. The same point on the equator has an annual difference of 2,399,400 inches per second. That is because the earth movement around the sun is with sun movement half the year and against the sun movement half the year. The day/night difference is also added in. Since a slight movement of an atomic clock of just a few inches gives a measured time difference, the vast difference of the earth rotation and it's movement around the sun and the sun’s movement has a huge Einstein variable time difference for any observation station over just one year. The difference is greater when considered for hundreds or thousands of years. Then considering the locations of different observatories makes the difference even larger. Don Edward Sprague Copyright 13 Oct, 2010 All rights reserved. |

Hubble Law is based on red shift but redshift does not support Hubbles Law.[quote]The galaxies we see in all directions are moving away from the Earth, as evidenced by their red shifts. Hubble's law describes this expansion. http://hyperphysics.phy-astr.gsu.edu/hbase/astro/hubble.html [/quote] Hubble and others observed a correlation between dim stars and red shift. Some redshift shows motion from the observer. So they say; red shift must be showing the expansion of the universe. [quote]Hubble's law is a statement of a direct correlation between the distance to a galaxy and its recessional velocity as determined by the red shift. [/quote] There it is. It is worth repeating: Hubble's law is a statement of a direct correlation between the distance to a galaxy and its recessional velocity as determined by the red shift.[quote]The Hubble constant H is one of the most important numbers in cosmology because it may be used to estimate the size and age of the Universe. It indicates the rate at which the universe is expanding. Although [B]the Hubble "constant" is not really constant [/B]because it changes with time (and therefore should probably more properly be called the "Hubble parameter"). http://csep10.phys.utk.edu/astr162/lect/cosmology/hubble_constant.html [/quote] The Hubble constant H is one of the most important numbers in cosmology: - it is not constant because it changes with time - it is properly be called the "Hubble parameter" The most important CONSTANT numbers in cosmology: - may be used to estimate the size and age of the Universe. - indicates the rate at which the universe is expanding. - is NOT CONSTANT [quote] In 1929, Edwin Hubble announced that almost all galaxies appeared to be moving away from us. This phenomenon was observed as a redshift of a galaxy's spectrum. This redshift appeared to have a larger displacement for faint, presumably further, galaxies. Hence, the farther a galaxy, the faster it is receding from Earth. [/quote] Redshift appeared to have a larger displacement for faint, presumably further, galaxies. Hence, the farther a galaxy, the faster it is (SUPPOSEDLY) receding from Earth. The greater the distance light travels through and is shifted,empty space the greater is the shift.[quote]Vesto Slipher, an astronomer at the Lowell Observatory in Flagstaff, Arizona, was finishing a detailed study of the night sky. He examined several of the faint, fuzzy "nebulae" that he saw in his telescope. He carefully measured the nebulae's spectra - the amount of light they emitted at different wavelengths. He found that the spectra of nearly all of them were "redshifted" - their light was redder than it should have been. Slipher knew that when an object's light was redshifted, it was moving away from Earth, and that the object's speed was proportional to the redshift. He calculated the nebulae's speeds, and found they were all moving away from us incredibly quickly: http://cas.sdss.org/dr5/en/proj/advanced/hubble/ [/quote] It wasn’t really Hubble who came up with the idea. He simply took or was given credit for Slipher’s work. Einstein called it his biggest blunder for not recognizing it. Two main question emerge.- Is there other proof of expanding universe other than Redshift? - NOFirst, is there other proof of the expanding universe. It seem that there is not. In fact, It seems - Could the redshift be from something other the object moving away? - YES that even the use of Hubble constant is not constant and the redshift is not consistent. The analogy of a balloon with dots does not support Expanding universe. It only supports changing universe. A balloon with dots is used as an example of the expanding universe. However; it is not a good analogy. The painted dots get further apart when the balloon is expanded. A balloon has a place where air is added. That gives a reference point for all observers riding on the balloon. Also, an observer in the middle of the balloon is not actually in the middle and there would need to be a layer of balloons with dots painted on to simulate the universe. Aside from the poor analogy, using the dots on a balloon concept in distant study, it seems that the distances between stellar bodies is not increasing proportional to the redshift. Thus, the balloon example does provide a method of showing that Hubble is incorrect. Could the redshift be from something other the object moving away.Since empty space is not empty, there is a lot of stuff for light to go through and be shifted. Simply put, there is interactions and phenomena in the subjects of radiative transfer and physical optics which - CAN result in shifts in the wavelength and frequency of electromagnetic radiation. The greater the distance light travels through stuff in space and is shifted, The shifts can be due to things such as:the greater is the shift... DUH. - coherence effects - scattering of electromagnetic radiation – from charged elementary particles, – from particulates, – from fluctuations of index of refraction - entropy - Wolf effect - Brillouin scattering - and other things in empty space that is not empty. Thus, we see that Hubble variable constant expansion is not supported by redshift or any other supporting observations. Stuff in space moves like in musical chairs without removing a chair. There are places and stuff moved from place to place. Space is constant. Time progresses or builds on it's self at a constant rate. Copyright Don E. Sprague 2007 updated 11 oct 2011 |

At any instant, any observer in any location is an equally valid observer and the conditions are without information has the potential of being an equally valid observer when they collect and use all information that all other observers have. When time is frozen, all things are absolutely frozen in space. Any imaginary people can wander around and measure all things. Things do NOT change shape based on direction of travel. In the Lotentz contraction contradiction: - The ladder supposedly shrinks to the garage observer - The garage supposedly shrinks to the ladder observer. In reality neither shrinks. Using thought cameras on both the garage and the ladder, we see that the ladder and the garage do not simultaneously shrink based on motion of direction of travel of the observer or the observed. With the ability to freeze time in thought experiment, we are able to examine conditions of all things at an instant in time. Consider a person on a train going 65 mph. Consider two strobe 2 miles away from the person in the train. Both lights flash. We froze time exactly when the light flashed. While time is frozen, the person gets off the train and walks around. He or she finds that there are a few hundred other people walking around examining things. They all find that the lights flashed simultaneously regardless of where the observers were when time was frozen. This thought experiment to freeze things shows that conditions are absolute at an instant regardless of the position of the observer. This goes to the heart of Einstein’s known fundamental singularity flaw. His theory leads to time ending and gravity going to infinity. Time only varies to end as a result Einstein variable time as established in section 9 of his paper where he claims a person can NOT know they are on a moving train. Even a child can know they are on a moving train. It is obvious that the simultaneous lights did occur simultaneously. The event conditions are absolute for all observers in all frame. An observer’s lack of information or skill doesn’t alter reality. Section 20 of Einstein’s paper is another illusion that supposedly makes acceleration the same as gravity. That uninformed observer’s mistake does not translate to fact. Einstein section 9 and 20 are wrong. Time progresses at a constant rate in all places. Space is constant. It is just a bunch of places for stuff that moves or plays musical chairs. Classical mechanics is accurate but needed additions. I provide that in ChR. Copyright |