\ii COMITT. \TIMN IMLES. 



FUNDAMENTAL PRINCIPLES. 



Retain everywhere enough places to correspond to two unreliable 

 places in the final result ; the direct object of this is to keep the first 

 place of unreliable figures in the final result substantially free from the 

 accumulated rejection errors. 



K\' BPTIONS. A final result is seldom stated to more than one 

 ;;iiu place unless the uncertainty of that place is small (say 

 plus or minus four or less). 

 K. cample: i, page xvii. 



Single direct measurements generally yield numbers extending to 

 only one uncertain place. This should not, however, be taken as a 

 reason for relaxing the application of the above rule to subsequent 

 steps of the computation, especially in deducing the mean or average 

 of several single observations. 



Final zeros occurring in decimal fractions should be retained 

 when any other digit in the same place would be retained. This is 

 of course essential to show that this place is known. 



The foregoing principles consistently carried out constitute en- 

 tirely sufficient rules. But more detailed instructions are usually 

 required at the outset. These are readily understood in view of the 

 two following propositions, which one can easily verify by algebra 

 or by numerical examples. 



PROPOSITION I. In multiplication or division, the percentage 

 accuracy of the product or quotient cannot exceed that of the factor 

 whose percentage accuracy is least. 



PROPOSITION II. In addition or subtraction, the result cannot 

 be accurate beyond the first decimal place which is inaccurate in any 

 component. 



A more general form of statement from which these follow is : 

 If several numbers are multiplied or divided, a given percentage 

 error in any one of them will produce the same percentage error 

 in the result. If several numbers are added or subtracted, a given 

 error or change in the digit in any decimal or other place will 

 produce an equal error or change in the digit in the same decimal 

 place in the result. 



