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 

 Lillebammer the tourist may proceed northwards to 

 Trondbjem, 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 hia 

 powers of memory and calculation must 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 answered he amused 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 we're 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 enjoyed 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. t 

 No. 21, p. 179, and were republished in the Spectator of January 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, 00000, 00000, 00000, which I found to be 1,77205, 08075, 68077, 29353, 

 /er5, and did the next day commit it to writing.' 



4 February 18, 1670. Joannes Georgius Pelahower (Regioinontanus Borussus), 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 

 1S201719212-2242628302325272931, of which I extracted the square root in 27 places 

 15710301687148-2805817152171 proorimt, 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 successful in life. The correspondent of 

 the Spectator remarks : 'The naivetd of the/ere and proximt 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 mental calculation.' 



