60 Fuller's Calculating Slide-Rule. 



required ; also in the calculation of logarithmic or other 

 series. But the Spiral Slide-Rule decidedly supersedes the 

 use of all three when results involving not more than four 

 figures are required. And when it is considered that few 

 calculations — at all events actuarial or statistical ones — can 

 be carried, to any purpose, beyond the fourth or fifth figure, 

 chiefly on account of the unreliability of the data, the 

 universal utility of this rule will be at once recognised. 

 Take, for example, the calculation of a death-rate based on 

 the population of a country. No one would surely imagine 

 that the number showing the population is correct in the 

 unit's or ten's place, and even the figures in the hundred's 

 and thousand's place can seldom be relied on. In deducing 

 a result of any value, it would therefore be necessary that 

 the number of figures in the result (quotient) should not 

 •exceed the number of reliable figures in the divisor (or 

 population) ; in fact, it ought to be one less. 



ADDENDUM. 



[Written 6th November, 1885.] 



An objection often raised to the use of Slide-Rules gener- 

 ally is the trouble experienced (although there is no doubt 

 that in the great majority of cases it may be done simply by 

 inspection) in finding out where to place the decimal point 

 in the result; but in the Spiral Slide-Rule, by a simple device, 

 this difficulty has been overcome. 



In calculating with the Spiral Slide-Rule it is advisable 

 that the operations should be so arranged that the result 

 may always be found at the fixed index. In using 

 u constant" multipliers or divisors (as in the calculation of 

 percentages, &c.), moreover, it will be found advantageous to 

 set the " constant" once for all the operations in which it may 

 be required. In the following examples of multiplication 

 and division let C be constant : — 



(1.) Multiplication ivith a Constant Factor. 

 C x d = x, C x d' — x, C x d"= x", &e., may be resolved into 

 (1\ d d' d" p 

 \CJ xxx 



i.e. (log. 1 — log. G) = log. dj — log. x = log. d r — log. a?'r=&c. 



