516 Prof. Helmholtz on the Interaction of Natural Forces, 



generations after us we have nothing to fear. But the same 

 forces of air and water, and of the volcanic interior, which pro- 

 duced former geological revolutions, and buried one series of 

 living forms after another, act still upon the earth's crust. They 

 more probably will bring about the last day of the human race 

 than those distant cosmical alterations of which we have spoken, 

 and perhaps force us to make way for new and more complete 

 living forms, as the lizards and the mammoth have given place 

 to us and our fellow-creatures which now exist. 



Thus the thread which was spun in darkness by those who 

 sought a perpetual motion has conducted us to a universal law 

 of nature, which radiates light into the distant nights of the 

 beginning and of the end of the history of the universe. To 

 our own race it permits a long but not an endless existence ; it 

 threatens it with a day of judgment, the dawn of which is still 

 happily obscured. As each of us singly must endure the thought 

 of his death, the race must endure the same. But above the 

 forms of life gone by, the human race has higher moral pro- 

 blems before it, the bearer of which it is, and in the completion 

 of which it fulfils its destiny. 



Note to Paire 506. 



I must here explain the calculation of the heat which must be pro- 

 duced by the assumed condensation of the bodies of our system from 

 scattered nebulous matter. The other calculations, the results of 

 which I have mentioned, are to be found partly in J. R. Mayer's 

 papers, partly in Joule's communications, and partly by aid of the 

 known facts and method of science : they are easily performed. 



The measure of the work performed by the condensation of the 

 mass from a state of infinitely small density, is the potential of the 

 condensed mass upon itself. For a sphere of uniform density of the 

 mass M, and the radius R, the potential upon itself V — if we call 

 the mass of the earth m, its radius r, and the intensity of gravity 

 at its surface g, — has the value 



„_ 3 r^M- 



5 Rm 



Let us regard the bodies of our system as such spheres, then the 

 total work of condensation is equal to the sum of all their potentials 

 on themselves. As, however, these potentials for different spheres 



are to each other as the quantity — , they all vanish in comparison 



with the sun ; even that of the greatest planet, Jupiter, is only about 

 the one hundred-thousandth part of that of the sun ; in the calcula- 

 tion, therefore, it is only necessary to introduce the latter. 



