38 GRAPHICAL AND MECHANICAL AIDS TO CALCULATION 
1. Length of chord BC=200 x chord 31.4 degrees=2 x 54.12 
=108.24 yards ; 
2. Height of arc FS=200, height of arc 31.4=2x3.73= 
7.46 yards , 
3. Length of arc, curve CFB degrees=200 x are 31.4= 
200 x .548=109.67 yards ; 
4. Surface of segment=200? seg. 31.4 degrees = 40000 x 
.0134=536 sq. yards ; 
5. Distance CD and DB=200 x tang. 15.7 degrees = 
200 x .281=56.2 yaras ; 
6. Distance DM=200 x sec. 15.7 degrees=200 x 1.038 x 
207.6 yards. 
1 will now pass to the mechanical aids to calculation 
and draw first attenticn to the simplest of all such instur- 
ments the ordinary ball frame, which is still extensively 
used in all business houses in Russia, and is also in common 
use in China and a few other countries. It is quite a reve- 
lation to see a Russian bank clerk doing all his adding up 
and other calculations with the help of a ball frame, with 
the greatest of speed and absolute accuracy, and with the 
great advantage that he may be interrupted at any time 
during his calculations without affecting the result. Some 
years back a small portable instrument was patented in 
America, the ‘‘ Locke Adder,’ which is based on the same 
principle as the ball frame, and is worked in exactly the 
same manner. It is of great advantage for adding up, 
but not so easily applicable to our system of money with 
its pound, shillings and pence. With practice any arith- 
metical operation addition, subtraction, multiplication 
and division may be done with the little instrument. 
By far the most general usefu] of all the mechanica] 
devices invented to aid calculation are sliderules, of which 
a great many forms exist. In 1624, ten years after the 
invention of logarithms by the Scotchman, John Napier, 
who published the first table of his natural or hyperbole 
logarithms in 1614, the English mathematician, Edmund 
Gunter, constructed a rule which he divided in proportion 
with the Joragithms of numbers, with which he used a pair 
of compasses to obtain results of multiplication and division. 
Gunter was a colleague of Prof. Henry Briggs, of Gresham 
College, London, who was the originator of the more gener- 
