THE BOUNDARIES OF ASTRONOMY. 99 



the confines of the solar system. Does Sirius, for instance, attract the 

 pole-star ? We really do not know. Nor can we ever expect to know. 

 If Sirius and the pole-star do attract each other, and if the law of their 

 attraction be the same as the law of attraction in the solar system, it 

 will then be easy to show that the effect of this attraction is so minute 

 that it would he entirely outside the range of our instruments even to 

 detect it. Observation is hopeless on such a matter. If we can not 

 detect any attraction between a star in one constellation and a star in 

 another, no more can we detect any attraction between our sun and 

 the stars. Such attractions may exist, or they may not exist : we have 

 no means of knowing. Should any one assert that there is absolutely 

 no gravitation between two bodies more than a billion miles apart, we 

 know no facts by which he can be contradicted. 



If we know so little about the existence of gravitation in the space 

 accessible to our telescopes, what are we to say of those distant regions 

 of space to which our view can never penetrate ? Let a vast sphere be 

 described of such mighty dimensions that it embraces not only all the 

 objects visible to the unaided eye, not only all the objects visible in 

 our most powerful telescopes, but even every object that the most 

 fertile imagination can conceive, what relation must this stupendous 

 sphere bear to the whole of space ? The mighty sphere can only be an 

 infinitely small part of space. It must bear to the whole of space a 

 ratio infinitely less than the water in a single dew-drop bears to the 

 water in the Atlantic Ocean. Are we then entitled to assert that every 

 particle in the universe attracts every other particle with a force which 

 is proportional to the product of their masses, and which varies in- 

 versely as the square of their distance ? We have, indeed, but a slen- 

 der basis of fact on which to rest a proposition so universal. Let us 

 attempt to enunciate the law of gravitation so as to commit ourselves 

 to no assertion not absolutely proved. The statement would then run 

 somewhat as follows : 



Of the whole contents of space we know nothing except within 

 that infinitely small region which contains the bodies visible in our 

 telescopes. Nor can we assert that gravitation pervades the entire of 

 even this infinitely small region. It is true that in one very minute 

 part of this infinitely small region the law of gravitation appears to 

 reign supreme. This minute part is of course the solar system. There 

 are also a few binary stars in this infinitely small region whose move- 

 ments would admit of being explained by gravitation, though as yet 

 they can hardly be held to absolutely prove its existence. 



It must then be admitted that, when the law of gravitation is spoken 

 of as being universal, we are using language infinitely more general 

 than the facts absolutely warrant. At the present moment we only 

 know that gravitation exists to a very small extent in a certain in- 

 definitely small portion of space. Our knowledge would have to be 

 enormously extended before we can assert that gravitation extended 



