## Elements of the Precision of Measurements and Graphical Methods |

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0.5 per cent ammeter amperes angle arithmetical mean Atomic weight average deviation axis best representative line Boyle's law calorimeter candle power cision coil components corrected corresponding criterion curve desired determined deviation measure deviation or precision diameter direct plot equal effects equation expressed factor final result formula fractional deviation fractional method fractional or percentage galvanometer grams graphical method ILLUSTRATIVE PROBLEMS inch index of refraction inspection law of tangents Least Squares length logarithmic plot magnitude meas meter method of Least negligible number of observations number of significant obtained ohms ordinates and abscissae pendulum percentage deviation percentage precision place of figures plotting-paper points precision discussion precision measure probable error produce quantity reliable residual plot resistance respectively resultant deviation resultant effect retained Rule scale significant figures single observation SOLUTION OF ILLUSTRATIVE specific gravity standard candle straight line Suppose tangent temperature uncertain value of g variables voltmeter volts

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Page 118 - STAMPED BELOW AN INITIAL FINE OF 25 GENTS WILL BE ASSESSED FOR FAILURE TO RETURN THIS BOOK ON THE DATE DUE. THE PENALTY WILL INCREASE TO SO CENTS ON THE FOURTH DAY AND TO $1.OO ON THE SEVENTH DAY OVERDUE.

Page 22 - Thus aero may be a significant figure when it is written, not merely to locate the decimal point, but to indicate that the quantity in the place in which it stands is known to be nearer to zero than to any other digit. For example, if a distance has been measured to the nearest hundredth of an inch, and found to be 205.46 inches, all five of the figures, including the zero, are significant. Similarly, if the measurement had shown the distance to be nearer to 205.40 than to 205.41 or to 205.39, the...

Page 21 - ... value widely discordant from the others has undue weight on the value of the mean. A good criterion to follow in such cases is the following: Compute the mean and the average deviation ad omitting the doubtful observation. Compute also the deviation d of the doubtful observation from this mean. If d = 4 ad, reject the observation since it can be shown that the probability of the occurrence of an observation whose deviation is equal to four times the average deviation, is only one in a thousand....

Page 19 - The probable error of an observation is of such a magnitude that the probability of making an error greater than it is just equal to the probability of making one less than it, both probabilities being one-half.

Page 22 - ... zero would be also significant, and should invariably be retained, since its presence serves the most useful purpose of showing that this place of figures had been measured as well as the rest. If in such a case the quantity had been written 205.4 instead of 205.40, the inference would be drawn either that the hundredths of an inch had not been measured, or that the person who wrote the number was ignorant or careless of the proper numerical usage. Failure to follow this simple rule is a common...

Page 22 - However, good judgment is essential in rounding the figures presented, in order that essential data are not lost. "A significant figure is any digit to denote or signify the amount of the quantity in the place in which it stands. Thus zero may be a significant figure when it is written, not merely to locate the decimal point, but to indicate that the quantity in the place in which it stands is known to be nearer to zero than any other digit. For example, if a distance has been measured to the nearest...

Page 23 - In rejecting superfluous figures, increase by _1 the last figure retained, _if the following rejected figure i_s five or over. RULE II: In all deviation and precision measures, retain only two significant figures. The reason for this rule is as follows: Suppose a length m is measured to be 122.48 cm. with an AD of 0.12 cm. The significance of the AD is that the place of figures in m occupied by the four is uncertain by 1 unit, and the next place is uncertain by 12 units, while the third unit would...

Page 8 - Classification of Errors. — When any quantity is measured to the full precision of which the instrument or method employed is capable, it will, in general, be found that the results of repeated measurements do not exactly agree. This is true not only of results obtained by different observers using different instruments and methods, but also of results obtained by the same observer under similar conditions. The cause of these discrepancies lies in various sources of error to which all experimental...

Page 22 - ... if the measurement had shown the distance to be nearer to 205.40 than to 205.41 or to 205.39, the final zero would be also significant, and should invariably be retained, since its presence serves the most useful purpose of showing that this place of figures had been measured as well as the rest. A zero, when used merely to locate the decimal point, is not a significant figure in the above sense; for the position of the decimal point in any measurement is determined solely by the unit in which...

Page 25 - ... a 10-inch slide rule. For greater precision, logarithm tables should be used. If the old-style method of multiplication or division must be resorted to, reject all superfluous figures at each stage of the operation. Rule VI. In carrying out the operations of multiplication or division by the use of logarithms, retain as many figures in the mantissa of the logarithm of each factor as are properly contained in the factors themselves under Rule IV. Thus, in...