42 GRAPHICAL AND MECHANICAL AIDS TO CALCULATION 
sliderules, as it gives much greater accuracy than any other 
rule of the same length, is easier to work, and has a far 
greater range of possibilities in calculations, as for instance 
it allows with only one setting of the slide direct multipli- 
cation of three numbers or the finding of the quotient of 
a number divided by the product of two numbers. Calcu- 
lations like w=a.b., w=a.b.c., x=a.b.+¢, x=a+b e, 
a= ya, £=Va, xz—a.b?, x=a2~b, x=a: Vb, x= Vab, 
Me oa 7b, x=* Vad, x=a?—b?, r= Va?+b2, x= 
(va+ vb)? can be solved with the greatest of ease with one 
single movement of the slide. Special scales on the reverse 
of the slide give natural sines and tangents of angles, and 
allow trigonometrical calculations. 
Just to give one example of the use of the sliderule 
in technical calculations. In order to make the results 
of analyses strictly comparable the results of the analysis 
are calculated on to the percentage of dry substance. We 
find for instance a sample of sorghum containing after air 
drying 10.15 per cent. of moisture, to contain starch 23.80 
per cent., soluble carbohydrates 10.65 per cent., fat 2.56 
per cent., ash 7.06 per cent., woody fibre 36.60 per cent., 
nitrogen 1.225 per cent., and proteins 7.35 per cent., and 
with one setting of the slide by setting the 10 on the rule 
to 89.85 amount of dry substance on the slide (as on 
top of double rule, Plate 1II., B), we can read all the 
results off from the amounts taken on the shde with the 
coinciding figures on the rule and get 26.50 per cent., 11.86, 
2.85, 7.86, 40.75, 1.364, 8.18 per cent. respectively. 
Practical calculations are very much simplified by 
using conversion factors or gauge points, for instance, to 
convert feet into metres we use the proportion feet : metre as 
292:89 or the factor .3048. The relation between the cir- 
cumference of a circle and its diameter is very accurately 
expressed by the factor 710:226. If we read an Kuropean 
work on agriculture we find all the results of harvest 
expressed in hectolitres per hectare, and we can convert 
this into bushels per arce by multiplying the numbers 
by the factor 1.1133, or setting the slide to the propor- 
tion 180/167. 
Every user of the sliderule, after becoming once familiar 
with the instrument, will find that certain factors are mostly 
