482 THE PRINCIPLES OF SCIENCE [ch. xxi. 



and how to take proper account of inaccuracy in operating 

 with approximate decimal fractions. A simple investiga- 

 tion of the subject is to be found in Sonnet's Algehre 

 EUmentaire (Paris, 1 848) chap, xiv., " Des Approximations 

 Absolues et Eelatives." There is also an American work 

 on the subject.^ 



Although the accuracy of measurement has so much 

 advanced since the time of Leslie, it is not superfluous to 

 repeat his protest against the unfairness of afi'ecting by a 

 display of decimal fractions a greater degree of accuracy 

 than the nature of the case requires and admits.^ I have 

 known a scientific man to register the barometer to a 

 second of time when the nearest quarter of an hour would 

 have been amply sufficient. Chemists often publish results 

 of analysis to the ten-thousandth or even the milliouth 

 part of the whole, when in all probability the processes 

 employed cannot be depended on beyond the hundredth 

 part. It is seldom desirable to give more than one place 

 of figures of uncertain amount ; but it must be allowed 

 that a nice perception of the degi'ee of accuracy possible 

 and desirable is requisite to save misapprehension and 

 needless computation on the one hand, and to secure all 

 attainable exactness on the other hand. 



1 Principles of Approximate Calculations, hy J. J. Skinner, C.E. 

 (New York, Henry Holt), I876. 



2 LebUe, Inquiry into the Nature of Heat, p. 505. 



