LAKES, 91 
subsequently one of the great English lords of Norway, 
with a very eligible interest in that snug little railway and 
the Miosen navigation. 
Not far from the western extremity of the Miosen lake 
is the prettily situated village of Lillehammer. From 
Lillehammer the tourist may proceed northwards to 
Trondhjem, or westwards to Bergen and Hardanger, or 
through the Guldbransdal to’ Dovrefjeld. This is. 
described by Williams as a vast undulating moorland, 
then a pause. To test his memory, I then said to him, Do you remember the sum in 
addition I gave you?” To my great surprise he repeated the twenty-four figures with 
only one or two mistakes. It is evident, therefore, that in the course of two years his: 
powers of memory and calculation niust have been gradually developed. He could not 
explain the process by which he worked out long and intricate sums. He did not 
appear at all overworked. As soon as a question was ed he sed himself with 
whipping a top round the room, and when the examination was over he said to us, 
“* You have been trying to puzzle me, I will try to puzzle you. A man found thirteen 
cats in his garden. He got out his gun, fired at them, and killed seven. How many 
were left?” ‘‘ Six,” was the answer. ‘ Wrong,” he said,— “‘ none were left. The rest 
ran away.” I mention this to show that he was a cheerful and playful boy when he was 
about ten years old, and that his brain was not overtaxed.’ 
Such powers in a boy supply no indication that he will be distinguished in after life. 
Many have lost the trick by which the calculations are made while they are yet young, 
most have proved in after life nothing beyond more of average power, and none of them, 
it is said, have exhibited the slightest tincture of genius in mature life. 
Bidder, after being for a time a world’s wonder, had the good sense to study carefully ~ 
to qualify himself for the profession in which he engaged; he became a civil engineer 
of some eminence ; he evjoyed the confidence and esteem of Robert Stephenson; and 
rose to be president of the Institute of Civil Engineers. He has been dead for some. 
years. 
In further illustration of what has been done in mental arithmetic, I cite the follow- 
ing extracts from letters from Dr John Wallis, of Oxford, to Mr Thomas Smith, B.D.,- 
Fellow of Magdalene College, which are preserved in the Classical Journal, vol. xi., 
No, 21, p. 179, and were republished in the Sp tor of J: -y 4, 1879 :— 
‘December 22, 1669.—In a dark night, in bed, without pen, ink, or paper, or any- 
thing equivalent, I did by memory extract the square root of 30,000, ), , 
00000, 00000, , 00000, 00000, which I found to be—1,77205, 08075, 68077, 29353, 
Jeré, and did the next day commit it to writing.’ A : 
‘February 18, 1670.—-Joannes Georgius Pelshower (Regtomontanus Boruseus), giving 
me a visit, and desiring an example of the like, I did that night propose to myself in 
the dark, without help to my memory, a number in 53 places, 24681357910121411131516 
132017192122242628302325272931, of which I extracted the square root in 27 places— 
157103016871482805817152171 proximé, which numbers I did not commit to paper till he 
gave me another visit, March following, when I did from memory dictate them to him. . 
Yours, &c.’ : 
In Bayle Dr Wallis is described as a man of very great attainments, with a peculiar 
character for deciphering, and altogether very ful in life. The correspondent of 
the Spectator remarks :—‘The naivété of the feré and proximé is charming, and also the 
confession that he did not commit the appalling row of figures to paper, but dictated 
them a month afterwards to his friend from memory. These feats are perhaps not 
so difficult as multiplying 15 figures by 15, for while of course it is easy to remember 
such a number as three thousand billion trillion being nothing but noughts, so also it- 
may be noticed that there is a certain order in the row of 53 figures; the numbers 
follow each other in little sets of arithmetical progressior—(2, 4, 6, 8), (1, 3, 5,7, 9), 
(10, 12, 14), (11, 13, 15), (16, 18, 20), and so on; not regularly, but still enough so to 
render it an immense assistance to a man engaged in a tal calculation,’ % 2 
