48 



a picture : known forms are seen in definite group- 

 ings ; tlieir relative positions, or perspective as it 

 may be called, tlieir very liglit and shadow, convey 

 their meaning almost as much through the artistic 

 faculty as through any conscious ratiocinative process. 

 Few principles have been more suggestive of extended 

 ideas or of new views and relations than that of which I 

 am now speaking. In order to pass from questions 

 concerning plane figures to those which appertain to 

 space, from conditions having few degrees of freedom to 

 others which have many — in a word, from more restricted 

 to less restricted problems — we have in many cases 

 merely to add lines and columns to our array of letters 

 or symbols already formed, and then read ofi" pictorially 

 the extended theorems. 

 Mechanical Next as to mechanical appliances. Mr. Babbage, when 

 speaking of the difficulty of ensuring accuracy in the 

 long numerical calculations of theoretical astronomy, 

 remarked, that the science which in itself is the most 

 accurate and certain of all had, through these difficulties, 

 become inaccurate and uncertain in some of its results. 

 And it was doubtless some such consideration as this, 

 coupled with his dislike of employing skilled labour 

 where unskilled would suffice, which led him to the 

 invention of his calculating machines. The idea of 

 substituting mechanical for intellectual power has not 

 lain dormant ; for beside the arithmetical machines whose 

 name is legion (from Napier's Bones, Earl Stanhope's 

 calculator, to Schultz's and Thomas's machines now in 

 actual use) an invention has lately been designed 

 for even a more difficult task. Prof. James Thomson 

 has in fact recently constructed a machine which, 

 by means of the mere friction of a disk, a cylinder, 

 and a ball, is capable of effecting a variety of the 



methods. 



