66 PLEASANT WA YS IN SCIENCE. 



common centre of gravity of herself and the moon. This 

 orbit has a diameter of about six thousand miles ; and as 

 the earth travels round it, speeding swiftly onwards all the 

 time in her path round the sun, the effect is the same as 

 though the sun, in his apparent circuit round the earth, were 

 constantly circling once in a lunar month around a small 

 subordinate orbit of precisely the same size and shape as 

 that small orbit in which the earth circuits round the moon's 

 centre of gravity. He appears then sometimes displaced 

 about 3000 miles on one side, sometimes about 3000 miles 

 on the other side of the place which he would have if our 

 earth were not thus perturbed by the moon. But astrono- 

 mers can note each day where he is, and thus learn by how 

 much he seems displaced from his mean position. Knowing 

 that his greatest displacement corresponds to so many miles 

 exactly, and noting what it seems to be, they learn, in fact, 

 how large a span of so many miles (about 3000) looks at the 

 sun's distance. Thus they learn the sun's distance precisely as 

 a rifleman learns the distance of a line of soldiers when he has 

 ascertained their apparent size for only at a certain distance 

 can an object of known size have a certain apparent size. 



The moon comes in, in another way, to determine the 

 sun's distance for us. We know how far away she is from 

 the earth, and how much, therefore, she approaches the sun 

 when new, and recedes from him when full. Calling this 

 distance, roughly, a 3Qoth part of the sun's, her distance 

 from him when new, her mean distance, and her distance 

 from him when full, are as the numbers 389, 390, 391. Now, 

 these numbers do not quite form a continued proportion, 

 though they do so very nearly (for 389 is to 390 as 390 to 

 391^7). If they were in exact proportion, the sun's disturb- 

 ing influence on the moon when she is at her nearest would 

 be exactly equal to his disturbing influence on the moon 

 when at her furthest from him or generally, the moon would 

 be exactly as much disturbed (on the average) in that half oi 

 her path which lies nearer to the sun as in that half which 

 lies further from him. As matters are, there is a slight 



