ECLIPSES. 63 



The conical shadow cast by the sun has a length calculable 

 by Rule of Three, because we know the distance of the earth 

 from the sun and the diameter of the sun and of the earth. 



From the extremities of the solar diameter draw straight 

 lines tangent to the earth. They will meet and form an isos- 

 celes triangle, the base of which is the diameter of the sun, 

 882,000 miles. This triangle is cut proportionally by the 

 diameter of the earth, 8000 miles, at a distance of 93,000,000 

 miles from the sun ; round numbers being given for the sake 

 of simplicity. Setting as x, unknown, the long side of the 

 isosceles triangle, it is clear enough that the side of the conical 

 shadow cast by the earth will be x — 93,000,000 miles. Solv- 

 ing the proportion, we get 93,851,258 miles for the long side, 

 and taking from this the distance of the sun, 93,000,000 

 miles, we have 851,258 for the length of the shadow. 



This shadow "lies floating on the floor," as it were, of 

 the ecliptic plane, always, of course, turned away from the 

 sun. The moon revolves about the earth, and supposing her 

 always to be in the ecliptic, she would be, every time she 

 came round, caught by this shadow and eclipsed ; that is, 

 would find her light, which is derived wholly from the sun, 

 screened off from her. She falls into the shadow at a distance 

 from the earth varying greatly, but averaging 240,000 miles ; 

 and, using the same triangles as before, 8000 miles at 851,258 

 miles is 5744 miles at 61 1,258 miles. For this distance of 5744 

 miles, then, the moon is in " solid " shadow. 



If the eclipse be central, that is, if she pass through the 

 axis of the shadow^ it will be two hours from the time of 

 complete immersion before she begin to emerge on the eastern 

 side. For though the moon moves eastward about her own 

 diameter in an hour, and the shadow diameter is 2.6 of the 

 moon diameter (the latter being 2160 miles) — yet, as a 

 moment's pondering will show, her centre at first internal 

 contact will be at half her diameter within the shadow, and 

 at second internal contact still half a diameter within the 

 shadow. Her centre, therefore, will be moving by the space 



