I'm still working on improving documentation on A.A. Michelson's speed of light experiments in Southern California in the 1920s and have become confused by accuracy reports of the survey performed in support of the experiment. The authors use both "probable error" and "actual error".
For example,?ÿin "Measurement Of The Velocity Of Light Between Mount Wilson And Mount San Antonio" by A.A. Michelson, Appendix III by William Bowie, 1927. it states midway through that:
The methods adopted for the field measurements and the office computations were such as to assure the attainment of an accuracy, for the straight-line distance between Mount Wilson and San Antonio Peak, corresponding to a probable error of about 1 part in 2,000,000, derived from field measurements and observations alone, and to an actual error surely less than 1 part in 300,000. It is the feeling of those who have been engaged in the work that the actual error is somewhere between 1 part in 500,000 and 1 part in 1,000,000.
Underlined by me. Then, in the appendix's conclusion Bowie states:
The probable error of the straight-line distance from Mount Wilson to San Antonio Peak is 1 part in 6,800,000 from field measurements and observations alone.
Huh?? Bowie has tossed around a number of values for accuracy which have left me scratching my head. And I'm especially confused as to the distinction between probable and actual error. Is probable one or two standard deviations, or something completely different? I'm really just looking for the probable error range in the final straight line measurement between the two stations and the more I focused on this aspect, the more bewildered I've become. I'd be grateful for any clarity someone might offer.
Tom
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Probable error can be estimated by analyzing the data observation steps with all possible setup errors without ever making an observation.
Actual error can only be known until after you have actually made the observations. The goal is to have your actual errors be less than your probable errors. If not you must rethink your probable error estimates with more thought?ÿand redo your field work with more care.
The fact that he mentions an actual straight line distance from one point on the earth to another point on the earth is an imagined fiction.
Paul in PA
Paul, thank you for your comments. If I'm understanding what you're saying, the probable error is sort of a theoretical error based upon how something is measured, while the actual error is what you end up with in fact?
That makes sense to me, but seems to run counter to the way the appendix was written. The appendix closes with Bowie highlighting what he considered to be an impressive probable error of 1 part in 6,800,000. But he states the actual error number, mentioned in the middle of the report, is far worse number of 1 part in 500,000 to 1,000,000. Why tout something that's theoretically wonderful if in practice only a fraction of it was attained? I have the sense that I'm missing something obvious here, but I can't get my head around what it is. But I'll probably be suitably embarrassed when it finally hits me.
The US Coast and Geodetic Survey's final product to Michelson was in fact a straight line distance (chord length) between two points in space, each on a mountain peak. Since Michelson was intending to reflect a beam of light between these two points he needed to know the straight line distance over which the light would travel (which ended up being 35,385.53 meters). Now if I could only figure out how accurate they figured that to be....
Tom
Since I first posted my query I've been going through surveying books from the early 1900s and finally worked out the answer, which I'll post here to close out this thread. Succinctly put, probable error is a measure of precision while actual error is a measure of accuracy. Or, another way, probable error is how well a survey team performed a survey (which is why it's often played up) while actual error is how close they came to the "correct" answer.
Probable error (also known as the 50% error) isn't used much anymore, being replaced by standard deviation methodology. Probable error was defined as the value providing a 50% chance of being either plus or minus of the most probable value of a measurement. The center half of a bell curve, so to speak. Today's standard deviation is +/-68.3% of the most probable value and an old school probable error value is equal to 0.674 of a standard deviation. The final important point of probable error is that it's purely the mathematics of a group of measurement values and easily calculated.
Actual error is a bit more.....squishy. Since we can't ever know the true, absolutely correct value for a measurement, we can't really know the actual error. But based upon a survey team's knowledge and professional experience, they can usually come up with an estimate. Actual error seems to be due more to things outside of a survey team's expertise, with things like refraction often being cited. It was also stated the the actual error may be larger than the probable error in these cases.
Tom
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