18 
was by means of boards and counters. On the boards were 
lines, the lowest representing units, the next above tens, the third 
hundreds, and so on, working upwards. As many counters were 
placed on each line as were needed for the required number, and 
a counter placed between the lines represented five counters on 
the line next below. This calculating board was gradually super- 
seded by the Arabic notation, which is now in use. The struggle 
between these two systems was illustrated by throwing on the 
screen a print taken from an old arithmetic book, showing two 
men sitting side by side working each on his own method. 
With regard to division in arithmetic, which was the chief 
subject of the lecture, Mr. Harding showed that the modern method 
of working had only been in general use since the time of Cocker. 
The Hindoos had worked their long division sums by repeatedly 
subtracting the divisor, doing this from left to right, instead of 
from right to left as we do now. They worked in sand and erased | 
every figure that was done with as they went along. The Arabians 
copied their method, but, as they used tablets and not sand, they 
scratched through their figures instead of erasing them. This 
system of division continued in England until Cocker’s time, and 
can be seen in many of the earlier arithmetic books. Edward 
Cocker and his contemporary, James Hodder, were writing masters, 
who kept rival schools for the teaching of writing and arithmetic. 
They were both popular at the time, but Cocker is noted for having 
used the modern method of division, whereas Hodder kept to 
the old ’“‘ scratch division ” as it is called. Pepys in his celebrated 
Diary mentions going to visit Cocker ; and Boswell tells us how 
Dr. Johnson gave a copy of Cocker’s Arithmetic book as a tip to 
a servant girl in the Highlands. 
The lecture was illustrated by many lantern views. There were 
shown portraits of some of the great arithmeticians ; sample pages 
of woodcuts which illustrated old arithmetic books, English, 
German and Italian; pages from some of Cocker’s copy-books, 
which were ornamented by wonderful designs in scroll-work ; 
and also examples of sums done on the old scratch method. Dr. 
Womack also illustrated the lecture by working sums by this 
method at the lantern. 
On Friday, April 2nd, a special meeting was held to consider 
the proposal to establish an Astronomical Observatory and Meteoro- 
logical Station, Mr. P. E. Vizard, Vice-President, in the chair. 
The proposal was unanimously approved. 
