76 THE PRINCIPLES OF SCIENCE. 



sea, every mine affords conclusive evidence. If the astro- 

 nomer is to make his calculations perfect, he must not 

 only take account of the Himalayas and the Andes, the 

 Atlantic and Pacific, but the attraction of every hill, nay, 

 every ant-hill, must be separately calculated, nor must the 

 attractive power of any grain of sand be neglected. So far 

 are they from having yet considered any local inequality 

 of the surface, that they have not yet decided upon the 

 general form of the earth; it is yet a matter of specula- 

 tion whether or not the earth is an ellipsoid with three 

 unequal axes c . If, as is probable, the globe is proved to 

 be irregularly compressed in some directions, the calcula- 

 tions of astronomers will have to be repeated and refined, 

 in order that they may approximate to the attractive 

 power of such a body. If we cannot accurately learn the 

 form of our own earth, how can we expect to ascertain 

 that of the moon, the sun, and other planets, in some of 

 which are probably irregularities of greater proportional 

 amount. 



The science of physical astronomy is yet in a further 

 way merely approximative and hypothetical. Given 

 perfectly homogeneous ellipsoids acting upon each other 

 according to the law of gravity, the best mathematicians 

 have never and perhaps never will determine exactly the 

 resulting movements. Even when three bodies simul- 

 taneously attract each other the complication of effects is 

 so great that only approximate calculations can be made. 

 Astronomers have not even attempted the general problem 

 of the simultaneous attractions of four, five, six, or more 

 bodies, resolving the general problem into so many dif- 

 ferent problems of three bodies. The principle upon 

 which the calculations of physical astronomy proceed, is to 

 neglect every effect which could not lead to any quantity 

 appreciable in observation, and the quantities rejected 



c Thomson and Tait, ' Treatise on Natural Philosophy,' vol. i. p. 646. 



