The Calculimetre. 85 



are required by architects, engineers, surveyors, analytical 

 chemists, actuaries and statisticians, mechanics, mathe- 

 maticians, students and others, the circular rule now 

 exhibited u'ill doubtless prove of valuable assistance. 



A considerable amount of time and labour is constantly 

 being wasted in the present day, by making long calculations 

 out of all proportion to the accuracy of the data involved. 

 Take surveyors' calculations for example. A good ordinary 

 — say a 6-inch — theodolite is divided to twenty minutes of 

 a degree (20'), in which case the lines would be only about 

 /^th of an inch apart. It is quite within the bounds of 

 possibility, therefore, that a rough observation might] be 

 liable to an error of 10', which would be equivalent to an 

 error in the sine, varying (in the case of angles under 70°) 

 from "001 to 'OOo, according to the mao-nitude of the anfyle. 

 The error would be thus in the third place, and what can 

 be the use of employing tables of sines calculated to six or 

 seven places when the observation is, in the case supposed, 

 not correct to even three. By means of the vernier, 

 in like manner the same instrument may, by careful 

 observation, be read to say within one minute of a degree 

 (]') ; then the error in the sine of the angle would vary 

 from 0001 to -0003, which involves an error in the fourth 

 place, and so on, according to the accuracy of the 

 observation, and the precision of the particular instru- 

 ment used. 



I think it may be laid down as a general rule in arith- 

 metical operations that a computer is justified in accepting 

 as correct only as many figures (digits) in the product or the 

 quotient, as there are reliable figures in either of the factors, 

 or in either the divisor or dividend, by which such product or 

 quotient respectively was obtained. For example, supposing 

 it was required to find a death-rate at a particular age, i.e., 

 deaths divided by population, assvnning the deaths to be 

 . fairly correct, and the population to be uncertain beyond 

 (say) the third figure, any death-rate based on such figures 

 would be incorrect beyond the third figure. It is the same 

 in the case of products, the number of reliable figures in the 

 result being solely dependent on the number of reliable 

 figures in the most uncertain of its factors. 



In using logarithms, likewise, a similar general rule might 

 be applied, i.e., to use logarithms to as many places only* as 



* In special cases one place more might be used, so as to ensm-e of the last 

 figure but one being as accurate as possible. 



