30 Domestic Science 



made in counting the larger fractions as whole squares 

 will be balanced by that made by leaving out of account 

 the smaller fractions. This will not of course be always 

 the case, but the error in the value of an area obtained 

 by this method of counting, where the paper is divided 

 into squares which are small, and the area itself is 

 large compared with the area of 1 square, is not very 

 great. 



Example. In the irregular figure MNOPQR (Fig. 9) 

 there are 16 complete large squares, each containing 

 25 small ones, contained within the boundary of the 

 figure. These are numbered 1 to 16 (No. 8 is con- 

 sidered a complete square, because the small portion 

 outside the figure is less than half a small square). 

 Within the portions of large squares also contained 

 in the figure are marked in smaller type the numbers of 

 small squares each such portion contains, the fractions 

 of small squares being estimated by the second method 

 described above. 



Thus the whole area of the figure MNOPQR is equal 

 to that of 



(16 x 25) + 6 + 6 + 15 + 21+ 11 + 2 + 5+ 11 

 + 1 + 12-5 + 10 + 20 + 7 + 15-5 + 23 

 + 1 + 3 + 7+15 + 5 = 597 small squares. 

 Hence the area of the figure MNOPQR is 



(597 x O'Ol) sq. in. = 5*97 sq. in. 

 For practice in this method of estimating areas, 

 perform the two simple experiments which follow. 



EXPERIMENT 8. On a sheet of squared paper 

 divided as described above, draw with a pair of com- 

 passes a circle as large as the paper will allow. Draw 

 any radius of this circle, and on this radius describe 

 a square. (See Fig. 10.) ' 



