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LETTERS To the Editor: The formula of Crayton 11. Crawford [J. CHEM. EDUC.,42,669 (1965)l for finding the rest point, P, of a balance,
where R1,Ra,and Ra are three successive turning points, is known in numerical analysis as "Aitken's 62extrapolation formula."' As we shall see, practically the same rest point values are obtained using the much simpler formula P = I/, (R, f 2R2 R3) (2) which can be obtained from eqn. (1) as follows:
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of the average of (n 1) turning points on one side of the rest point and the average of the intervening n turning points on the other side. The above derivation of eqn. (Z), original with the author, is much simpler than the derivation of the general rule for any odd number (%n 1) of successive turning points, even though both derivations are based on the postulate of constant d a m p ing.= I\lany laboratorians appear to feel that a t least five successive turning points should be taken in order to obtain sufficient accuracy. The following table, based on Crawford's data, shows that three are adequate:
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Comparison o f Equations ( 1 ) and (2)
These results also demonstrate that there is no advantage in using eqn. (1) despite the fact that it is exact if the postulate of constant damping is correct. MICHIGAN TECHNOLOGICAL UNIVERSITY 49931 HOUGHT~N, MICHIGAN 'See, for example, the discussions of Aitken's 6 % process by John Todd (p. 5) and by Urs Hochstrasser (p. 260) in "Survey of Numerical Analysis," (Editor: TODD,J.), McGraw-Hill Book Co., Inc., New York, 1962. %Fora derivation of the traditional rule. see. for examole.
where
Equation (2) is the simplest instance of the traditional rule that the rest point of a balance is the grand average
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Journal o f Chemical Education
