By Arthur J. Lyon and W. Ashhurst (Auth.)
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Just as maps can be made on various scales and with varying amounts of detail, so various mathematical models can be constructed for any physical situation which will represent it in various degrees of approximation or completeness. 10. ILL-DEFINED MAGNITUDES Finally, we consider an experiment of a slightly différent sort, where again our theoretical model is too simple to match the complexity of the actual situation. A rectangular piece of 28 DEALING WITH DATA glass is placed under strain by weights suspended at its ends and a piece of optically flat glass is placed on top of it.
The remaining results required are: jc2 = 16, 1/x = 0-25, V* = 2, 2π<ν/6Ix = 7-7, <3(JC2) = 4% of 16 = 0-64, d(l/x) = - 2 % of 0-25 = -0-005, <3(V*) = 1% of 2 = 0-02, d[2my/(6/x)] = - 1 % of 7-7 = -0-077. (c) If x = 4-00+0-05, the maximum error is ±1-25%. Hence the maximum relative error in 5x2 is ±2-5%, and 5x2 = 80; hence its maximum absolute error is ± 2-5 X 80/100, or ±2. SO5JC2 = 80±2. Similarly, 1/5JC = 0-05, and its maximum error is ±1-25% of 005 = ±0-000625. So 1/5JC = 0-0500+0-0006 approximately.
In other words these errors occur because it requires a finite and inevitably somewhat variable time, of the order of 0-1 sec, for the tick of a clock to reach the observer's consciousness, and for the muscular response which finally leads to the depression of the button of the stopwatch to occur and take eifect. Errors due to the observer—which are often characteristic of a particular observer—are known as personal errors. An experiment of the kind just described can be used to study the precision and accuracy of a given observer's timing.
Dealing with Data by Arthur J. Lyon and W. Ashhurst (Auth.)