BENJAMIN PEIRCE. 453 



maJe some progress in the investigation of the laws of non-associative 

 algebras. 



Professor Peirce could not fail to be interested in all questions that 

 concern the equilibrium, the history, and the development of the solar 

 system. At first he was loth to accej^t the nebular hypothesis in any 

 form. But the results of his studies led him, at last, to defend its 

 main propositions as the true laws of creation. 



The rings of Saturn are of prime import in any explanation of 

 ])lanetary development. The discovery by Professor Bond in 1850 

 of the dusky ring, and his announcement of reasons for believing 

 that the rings were fluid, multiple, and variable in number, led Pro- 

 fessor Peirce to take up the mathematical theory of the rings. He 

 announced as the result of his analysis that the rings could not be 

 solid, that a fluid ring could not have its centre of gravity con- 

 trolled by its primary, and^ that it must be supported by the satellites. 

 The principles of the solution were indicated in an article, published 

 in "Gould's Astronomical Journal" in 1851. At diff"erent times 

 in the following years some portions of his theoretical treatment 

 of the problem were published. The mathematical possibility of a 

 large number of narrow solid rings was admitted. In the " Memoirs 

 of the National Academy of Sciences" he published, in 18G6, the 

 formulas -for the potentials and attractions of a ring. This problem 

 has peculiar interest, from the mode of development of the formulas. 



The place of comets in the solar system was a subject of his thought 

 even earlier than the rings of Saturn. The discussions and the com- 

 putation of orbits of various comets in the years 184G-1849, were fol- 

 lowed in the latter year by an argument that the comets must have 

 always been parts of the solar system. 



In 1859 he applied the theory of solar repulsion of the matter of 

 the comets' tails to the observed form of the tail of Donati's comet, 

 and deduced the strength of the repulsive forces that drove off the 

 nebulous matter. 



In 1861 he made a communication to this Academy, suggesting the 

 meteors as a cause of the acceleration of the moon's mean motion. The 

 paper was not printed, and it does not appear whether he referred to 

 the direct impact of the meteors upon the moon, or to the resistance 

 due to the action of the moon in turning the meteors out of their 

 paths. Probably he included both causes, since each has the effect, 

 to a limited degree, of a resisting medium. 



In the last two years of his life he presented to this Academy sev- 

 eral communications upon the internal structure of the earth, and the 



