WASTED LIGHT. 



51 



Lawrence, moreover, explained to John that this same 

 principle of the effect of an increase in two dimensions, in 

 respect to any quantity, had a very wide application. It 

 applied, in fact, to all similar surfaces that is, similar in a 

 geometrical sense. If, for instance, we have two rooms, 

 and one is twice as long as the other, but is of exactly the 

 same shape that is, if it is twice as great in all its other 

 dimensions, it will take, not twice as much, but four times 

 as much carpet to carpet it. A person, without reflection, 

 might have said that it would have taken twice as much ; 

 but, with a little consideration, we see that if it had been 

 twice as long and only just as wide, it would have required 

 double the quantity of carpeting, but, being twice as long 

 and twice as wide both, it will take four times as much. 



It makes no difference what the shape of the two sur- 

 faces may be, provided that they are of similar shapes. A 

 boy has a kite a foot long. He wishes to make one of the 

 same shape two feet long. It will require four times as 

 much paper. If he requires his new kite to be three times 

 as long as the other, and every thing in proportion, it will 

 require nine times as much paper. 



So with the covering of a ball. There will be four times 

 as much leather in the covering of a foot-ball ten inches in 

 diameter as there would be in one of five inches ; for the 

 square of five is twenty-five, and the square of ten is one 

 hundred, and one hundred is four times twenty-five. 



It is true that the diameter of the balls are not lines in 



