SIMILAR, IN A GEOMETRIC SENSE. 45 



" Being twice as near," said Lawrence, " would make 

 them give four times as much light. This is a case in 

 which the law of the squares of the distances comes in. 

 The square of two is four." 



Lawrence explained this principle to John as follows : 



"Light, as we all know, spreads itself in both directions 

 as it recedes from the luminous point that is, laterally, 

 which means from side to side, and also up and down. If 

 it spread only laterally, then the same light would, at 

 double the distance, fall on double the space, and would 

 consequently be weakened one half. But it spreads in the 

 other direction also that is, up and down ; so that at 

 twice the distance it will spread over four times the space." 



" That is curious," said John. 



"Yes," said Lawrence, "and it is more curious still, as it 

 is only a single case of a universal law. The two surfaces 

 that the same portion of light from a candle would shine 

 upon at different distances are similar, in the geometrical 

 sense. Do you know what the w r ord similar means, in a 

 geometrical sense ?" 



John said he supposed it meant alike, or somewhat 

 alike. 



"It means exactly alike inform? said Lawrence, " with- 

 out any regard to size. Thus an egg and a ball are simi- 

 lar, in common language, being both rounded, but they are 

 not similar in the geometrical sense, because they are not 

 exactly alike in form. A globe made to represent the 

 earth, if it was made a perfect sphere, would, in common 

 parlance, be similar to the earth. It would be made, in 

 fact, expressly in resemblance of it, but it would not bb 

 similar in a geometrical sense, for the earth is not a perfect 

 sphere. 



" So with surfaces. Two kites of exactly the same size 

 and nearly the same shape would be similar, in common 



