484 



SCIENTIFIC RECREATIONS. 



Therefore, as A M, the tangent of the circle stands at right angles to the 

 radius, A C, the angle at A is a right angle, and the magnitude of the angle at 

 C is found by means of the arc, A B, the distance of the two observers from 

 each other. As soon, however, as we are acquainted with the magnitude of 

 two angles of a triangle, we arrive at that of the third, because we know that 

 all the angles of a triangle together equal two right angles (180). The 

 angle at M, generally called the moon's parallax, is thus found to be fifty-six 

 minutes and fifty-eight seconds. We know that in the right-angled triangle 

 MCA, the measure of the angle, M = 5 6' 5 B", and also that A C, the semi- 

 diameter of the earth = 3,964 miles. This is sufficient, in order by trigono- 

 metry, to obtain the length of the side, M C ; that is, to find the moon's 

 distance from the earth. AC is the sine of the angle, M, and by the table 



Fig. 524. Parallax explained. 



the sine of an angle of 56' 58" is equal to T^OO ; or, in other words, if 

 we divide the constant, M C, the distance of the moon, into 1 00,000 equal 

 parts, the sine, A C, the earth's semi-diameter = 1,652 of these parts. And 

 this last quantity being contained 60 times in 100,000, the distance of the 

 moon from the earth is equal to 60 semi-diameters of the earth, or 

 60 x 3964 = 237,840 miles. 



In a similar way the parallax of the sun has been found - 8"'6, and 

 the distance of the sun from the earth to be 91,000,000 miles. 



Let us first see how we can obtain the distance of any inaccessible or 

 distant object. We have already mentioned an experiment, but this method 

 is by a calculation of angles. The three angles of a triangle, we know, are 

 equal to two right angles ; that is an axiom which cannot be explained 

 away. We first establish a base line ; that is, we plant a pole at one point, 



