FORCE 687 



the absolute longitudes of the planets. If we deduce directly from 

 Newton's law the differential equations which define the variation of 

 these distances, these equations will not be of the second order. I mean 

 that if, outside Newton's law, we knew the initial values of these dis- 

 tances and of their derivatives with respect to time that would 

 not be sufficient to determine the values of these same distances at an 

 ulterior moment. A datum would be still lacking, and this datum 

 might be, for example, what astronomers call the area-constant. But 

 here we may look at it from two different points of view. We may 

 consider two kinds of constants. In the eyes of the physicist the 

 world reduces to a series of phenomena depending, on the one hand, 

 solely on initial phenomena, and, on the other hand, on the laws con- 

 necting consequence and antecedent. If observation then teaches us 

 that a certain quantity is a constant, we shall have a choice of two 

 ways of looking at it. So let us admit that there is a law which re- 

 quires that this quantity shall not vary, but that by chance it has 

 been found to have had in the beginning of time this value rather 

 than that, a value that it has kept ever since. This quantity might 

 then be called an accidental constant. Or again, let us admit on the 

 contrary that there is a law of nature which imposes on this quantity 

 this value and not that. We shall then have what may be called an 

 essential constant. For example, in virtue of the laws of Newton the 

 duration of the revolution of the earth must be constant. But if it is 

 366 and something sidereal days, and not 300 or 400, it is because of 

 some initial chance or other. It is an accidental constant. If, on the 

 other hand, the exponent of the distance which figures in the expres- 

 sion of the attractive force is eqiial to 2 and not to 3, it is not by 

 chance, but because it is required by Newton's law. It is an essential 

 constant. I do not know if this manner of giving to chance its share 

 is legitimate in itself, and if there is not some artificiality about this 

 distinction; but it is certain at least that in proportion as Nature 

 has secrets, she will be strictly arbitrary and always uncertain in their 

 application. As far as the area-constant is concerned, we are accus- 

 tomed to look upon it as accidental. Is it certain that our imaginary 

 astronomers would do the same? If they were able to compare two 

 different solar systems, they would get the idea that this constant 

 may assume several different values. But I supposed at the outset, as 

 I was entitled to do, that their system would appear isolated, and that 

 they would see no star which was foreign to their system. Under these 

 conditions they could only detect a single constant, which would have 

 an absolutely invariable, unique value. They would be led no doubt 

 to look upon it as an essential constant. 



One word in passing to forestall an objection. The inhabitants 

 of this imaginary world could neither observe nor define the area- 

 constant as we do, because absolute longitudes escape their notice; 



