20 The Realm of Nature CHAP. 



hour. This is because we look at the hand from different 

 points of view and at different angles with the direction in 

 which we are going. By measuring the angles, and the 

 distance between the two points of observation, it is possible 

 to calculate the distance of the object by trigonometry the 

 part of mathematics dealing with triangles. Suppose that 

 in Fig. 3 the distance from A to B, which is called the base- 

 line, is 100 yards, and that by means of a sextant the angles 

 PAB and PBA are measured, then since all the angles of a 

 triangle are equal to two right angles, the angle at P can be 

 got by a simple subtraction, and an easy calculation would 

 give us the distance of P from the eye. The more nearly 



FIG. 3. Angular measurement of distance. AB, base-line, P, Q, vertical angles. 



equal the three angles of APB, the more accurately can this 

 distance be found. For example, from the same base-line 

 the angles to the hand of a much more distant clock would 

 scarcely differ from right angles ; the angle at Q would be 

 so minute that the least mistake in measuring the two large 

 angles would put the calculation all wrong. The more 

 nearly the base-line is equal to the other sides of the triangle, 

 the more exact is the trigonometrical measurement of 

 distance. In this illustration the angle at P might be 

 measured without a sextant by noting the amount of dis- 

 placinent of the long hand of the clock on the dial. In 

 the distant clock the displacement would be too slight for 

 the eye to detect. 



34. Exclusiveness is a term descriptive of the way in 

 which matter occupies space. It means that when one 

 portion of matter is in a certain space no other portion of 

 matter can be in the same space. The fact that a quantity 

 of water can be absorbed by a sponge without much in- 

 creasing the volume is no argument against this statement, 



