74 



THE WORLD MACHINE 



by the post, measure the angle between the plumb-line and 

 the slant of the shadow thus : 



FIG. 3. 



It is evident enough that, if the earth is round and the sun 

 at a very great distance, the angle that is marked A will be 

 to all intents the same as if it were taken from the centre of 

 the earth. But this means that the angle will cut out the same 

 arc in the circle of the sky as, from the centre of the earth, it 

 would cut out of the circle of the earth's circumference, as 

 another figure will make clear enough : 



FIG. 4. 



The line B Z is my zenith, the direction of my plumb-line. 

 The angle I have measured is the angle marked A, and for a 

 rough calculation is the same as the angle C at the earth's centre. 

 The arc of the circle S Z is the same as the arc A B on the surface 

 of the earth. If the angle A is about 7 12' ', the arc A B is one- 

 fiftieth of the earth's circumference. If the distance from A 

 to B on the earth is 500 miles, then the earth is 25,000 miles 

 around. The globe has been measured in half-an-hour. What 

 could be simpler ? 



I said above " It is evident enough." Laplace used to use 

 this phrase rather freely in his expositions. Sometimes he 



