BOOK V. 

 EXPERIMENTAL METHODS. 



CHAPTER I. 



MEASUREMENTS : INSTRUMENTS. 



193. Measurements and Errors. Under the heading of Experi- 

 mental Methods will be set forth the elements of experimental 

 measurements and the instruments already mentioned will be 

 described. A measurement is never absolutely correct ; an error, 

 no matter how small, always exists, no matter with what care the 

 measurement is carried out, or however perfect the instruments. 

 The art of measurement consists in knowing how to reach the 

 extreme limit of experimental exactitude, or the smallest error. 

 The difference between the value found and the real value is 

 called the absolute error. Suppose, for example, it is desired to 

 determine the exact weight of a man of 65 kilogrammes. If the 

 scales indicate 64-900 kg., there is an absolute negative error of 

 0-100 kg. If they indicate 65-100 kg. there is again an absolute 

 positive error of 0-100 kg. The reduction of absolute errors 

 depends on the degree of perfection of the instruments. 



The relation of the absolute error to the total dimensions to be 

 measured is called the relative error. In the preceding example 



it is - - = ^ r. It will be seen that the relative error decreases 

 oo boO 



in proportion as the total quantity increases. For a weight of 

 130 kilogrammes, it would be : 



0-100 1 



130 " 



In experiments the permissible relative error depends on the end 

 in view. Thus, if a gas meter had a constant error of half a 

 litre (minus), 100 litres of gas would be read as 99-5 litres. The 

 error being -5% (half of 1%), which would be permissible. The 

 same error in a measurement of 10 litres would amount to 5%, 

 which would not be permissible. 



A variable and increasing error can also be introduced by wear 

 in the moving parts of the instrument. Also, in the course of 

 any experiment, errors may occur owing to external interference. 

 Thus, in delicate measurements of temperature, the heat of the 



