86 Proceedings of the Royal Society of Victoria. 



correspond to the number of correct digits in the numerical 

 data involved. For example, it would be useless labour to 

 use the log. sines of angles observed with an error of one 

 minute of a degree to six or seven figures of decimals, when 

 a table of four figure logarithms would answer equally well. 



When these things are well understood and appreciated, 

 the more extended tables of logarithms will Vie used less and 

 less, and slide-rules will come into more general use. 



For results to the second and third figure, the small 

 circular slide-rule is best adapted; and for results to the 

 fourth figure, the spiral slide rule is most invaluable ; but 

 for results beyond the fourth, we must still resort to 

 mathematical tables or the arithmometre. 



The great advantage of slide-rules over logarithmic tables 

 are obvious. To find a product by logarithms, no less than 

 seven operations* are necessary, and then there is the liabil- 

 ity to eri-or as well as loss oi' time in transcribing the 

 logarithms, after finding the differences, and in adding them. 

 With the slide-rule, only the natural numbers are dealt with, 

 and it is merely necessary to bring the indices to the factors 

 and the results may read oft' immediately by inspection, 



I should mention, that I described in my paper on Fuller's 

 Calculating Slide Rule, a circular rule somewhat similar to 

 the calculimetre, called the Cercle a calcid.f The cercle a 

 calcul more nearly resembles a watch, the calculations being 

 performed by two hands — the one movable, and the other 

 fixed. The cercle a calcul is in some respects the better 

 instrument, but it is about three times the cost of the other, 

 which is only about ten or twelve francs. 



* Multiplying a x b; (1) find a in log. book ; (2) then log. a and transcribe ; 

 (3) find b; (4) then lug. b and transcribe; (5) find sum; (6) find same in log. 

 book ; and (7) find colog. a b. 



i A similar instrument made in England is known by the name of 

 " Boucher's Pocket Calculator." 



