THE BOUNDARIES OF ASTRONOMY. 95 



The doctrine to which we refer is known as the law of universal gravi- 

 tation. It is customary to enunciate this law in the proposition that 

 every particle of matter attracts every other particle with a force 

 which varies directly as the product of the masses and inversely as 

 the square of their distance. It is no doubt convenient to enunciate 

 the great law in this very simple manner. It might seem awkward 

 to have to specify all the qualifications which would be necessary if 

 that enunciation is to assert no more than what we absolutely know. 

 Perhaps many people believe, or think they believe, the law to be 

 true in its general form ; yet the assertion that the law of gravitation 

 is universally true is an enormous, indeed, an infinite, exaggeration of 

 the actual extent of our information. 



To make this clear, let us contrast the law of gravitation as gen- 

 erally stated with the proposition which asserts that the earth rotates 

 on its axis. No one who is capable of understanding the evidence on 

 the question can doubt that the earth really does rotate upon its axis. 

 I purposely set aside any difficulties of a quasi-metaphysical character, 

 and speak merely of words in their ordinary acceptation. In stating 

 that the earth rotates upon its axis, we assert merely a definite propo- 

 sition as regards one body, all the facts which the assertion involves 

 are present to our minds, and we know that the assertion must be true. 

 Equally conclusive is the evidence for the statement that the earth 

 revolves around the sun. Concrete truths of this kind could be multi- 

 plied indefinitely. "VVe can make similar assertions with regard to the 

 planets. We can assert that the planets rotate upon their axes, and 

 that the planets revolve around the sun. But the law of gravitation 

 is a proposition of quite a different nature. Let us examine briefly 

 the evidence by which this law has been established. 



The science of dynamics is founded upon certain principles known 

 as the laws of motion. The simplest of these principles asserts that 

 a body, once set moving in a straight line, will continue to move on 

 uniformly forever in the same straight line, unless some force be per- 

 mitted to act upon that body. For nature as we know it, this law 

 seems to be fully proved. It has been tested in every way that we 

 have been able to devise. All these tests have tended to confirm that 

 law. The law is therefore believed to be true, at all events through- 

 out the regions of space accessible to us and to our telescopes. Assum- 

 ing this law and the other principles analogous to it, we can apply 

 them to the case of the revolution of the earth around the sun. As 

 the earth is not moving in a straight line, it must be acted upon by 

 some force. It can be shown that this force must be directed toward 

 the sun. It will further appear that the intensity of this force will 

 vary inversely as the square of the distance between the earth and the 

 sun. The movements of the planets can be made to yield the same 

 conclusions. All these movements can be accounted for on the sup- 

 position that each planet is attracted by the sun with a force which 



