THE BOOK OF NATURE STUDY 



and show that the view from A, the lower point, is necessarily 



less extensive than that from B, the higher. 



To calculate the radius of the circle of the horizon proceed as 



follows (Fig. i). Let P 

 be the point where the 

 line of vision drawn 

 from A touches the sur- 

 face, and let C be the 

 centre of the earth. 

 Join CA and CP. Now 

 the angle at P being a 

 right angle, by Euclid 

 I. 47, AP 2 = AC 2 -CP 2 , 

 or calling the earth's 

 radius r, the height of 

 the mountain a, and 



the required distance oc y we have 



therefore x z = a (zr+a). Taking the earth's radius as roughly 

 3975 miles, it will be found that a hill 800 feet high should 

 give theoretically a range of view of about 34 miles in every 

 direction. The actual view will depend upon the day, the 

 amount of haze present, and so forth. 



While the class is engaged in these observations, the colour 

 of the sky will naturally come in for study. If the day is fine, 

 and such a day would naturally so far as possible be chosen, we 

 should note the clear blue of the sky overhead. We should 

 also notice that this blue fades towards the horizon, where 

 the sky becomes whitish. The opportunity might also be taken 

 for some incidental observations on the meaning of certain 

 terms. Standing on the summit of a hill we should naturally 

 notice that if a line were supposed to be prolonged indefinitely 

 above our heads to reach the sky, this line would pierce the centre 

 of the great vault. This would be a useful opportunity to ex- 

 plain the meaning of the term zenith. Such little remarks as that 

 wherever we stand we are beneath the centre of the arch of 

 heaven, are then worth making. To attempt to explain the 



