1876.] -^'^^ [Chase. 



American Philosophical Transactions. The following quotation tVom his 

 exordium is both prophetic and suggestive : 



"There are few branches of Mechanical Philosophy as interesting in every 

 p,:)int of view as the theory of Oscillatory Motion. From the minutest vibra- 

 tions of a harp-string to the magnificent oscillations of a planet's axis, there 

 are an infinite number of analogous phenomena remarkable for their curious 

 properties or important uses. The common pendulum, that little instru- 

 ment which has rendered such essential service to science and the arts, and 

 will soon, in the hands of the skilful observer, unfold to us the internal 

 constitution of our globe, and give a clue to the process b ,- which it has 

 acquired its present state, is itself indebted for its accuracy to the inces- 

 sant superintendence of a watchful mathematical analysis. The science of 

 Acoustics in all its parts, the varied phenomena of the tides, the theory of 

 Saturn's ring, that wonder of the solar system, and the philosophical ex- 

 planations of the stability and harmony, of the celestial motions, are in 

 fact, but different applications of this extensive branch of Demonstrative 

 Mechanics. What adds to the interest and value of this subject is tlje 

 circumstance that a large class of oscillatoiy motions, namely those of 

 any rigid system whatever whose points depart but little from the posi: 

 tion which they occupy when at rest, has been found susceptible of com- 

 plete determination, by means of which the position of the bodies compos- 

 ing the system may be expressed (to use the language of analysis) in finite 

 functions of the time." 



In 1843, Professor Stephen Alexander communicated to the American 

 Philosophical Society,* his observations upon physical phenomena which 

 accompany eclipses. Among those phenomena was a " dragging of 

 shadows," which he attributed, at the first meeting of the American Asso- 

 ciation (Philadelphia, 1848), to the inertia of the luminiferous aether. By 

 this, and other like "scientific uses of the imagination," he w-as led to the 

 discovery of a series of cosmical relations, some of which were laid before 

 subsequent meetings of the Association, the whole being filially embodied 

 in his " Statement and Exposition of Certain Harmonies of the Solar Sys- 

 tem."! 



At the second meeting of the American Association, (Cambridge, 1849), 

 Professor Benjamin Peirce read a paper "On the Relation between the 

 Elastic Curve and the Motion of the Pendulum." "On this subject Prof. 

 Peirce remarked, that the relations discovered merely by intellectual in- 

 vestigations, and not observed by the senses, are of peculiar interest, as 

 manifesting the fact that one intellect presides over the production of those 

 phenomena. Could we see in the moon a house like our own, we' should 

 say that it was built by men like ourselves, having similar wants, and us- 

 ing similar means to supply them, and we should say that the same being 

 who formed our minds created theirs also. We cannot make such observa- 

 tions, but Ave may trace relations between objects with which we are 



* Proc. Soe. Phil. Amer., May, 1843, vol. lii. 



t Amer. Nat. Acad. Sci., 1873-4; Smithsonian Contrib., 280. 



