Chase.] ^^ [July 21. 



familiar, which lead us to similar results. At present the discoverj^ of these 

 relations has been very much confined to those subjects to which mathe- 

 matics apply."* At a later session of the same meeting, Peirce presented 

 a "Mathematical Investigation of the Fractions which occur in Phyllo- 

 taxis." After showing the influence of an identical law in the arrange- 

 ment of plants and planets, he asks: "Whence could this extraordinary 

 coincidence have arisen but from the action of a single mind"? and what 

 does it indicate but that the same Word which created the planet, is ex- 

 pressed in the planet ? May I close with this remark, that the object of 

 geometry in all its measuring and computing, is to ascertain with exactness 

 the plan of the great Geometer, to penetrate the veil of material forms, and 

 disclose the thoughts which lie beneath them '! When our researches are 

 successful, and when a generous and heaven-eyed inspiration has elevated 

 us above humanity, and raised us triumphantly into the very presence, as 

 it were, of the Divine intellect, how instantly and entirely are human 

 pride and vanity repressed, and by a single glance at the glories of the in- 

 finite mind, we are humbled to the very dust."f 



On the second of January, 1849, in a communication "On the Funda- 

 mental Principles of Mechanics,"^ Peirce had already shown that "a 

 system of bodies in motion must be regarded mechanically as a system of 

 forces or powers which is a perfect representative of all the single powers 

 of which the system is compounded, and this, too, at whatever time or 

 times the component powers may have been introduced into the system. 

 The question of the simultaneous introduction of the partial powers is of 

 no importance. Any power which is at any time communicated to the 

 system is preserved in the system unchanged in amount or direction." 



At the same meeting of the Academy, Professor Joseph Lovering read a 

 paper "On the Law of Continuity, "§ in which he said, "the method of 

 analysis which began with Leibnitz and Newton, and which in England 

 has been known under the name of fluxions, rests upon this law of continuity. 

 If we admit the usefulness of the principle only in cases of motion, we 

 still give it a wide range ; since so many problems, not strictly dynamical, 

 are reduced to cases of motion when investigated by the rules of modern 

 analysis." 



On the 4th of Feb. 1851, | " Professor Peirce gave an argument, which he 

 thought to be new, against the principle which is usually adopted in theo- 

 retical works, that the force of a body in motion is its vis inerticB. He 

 believes, on the contrary, that the time is at hand when the vis viva will 

 be universally recognized as the force of a moving body. His new argu- 

 ment is derived from the effect of a force in causing rotation, as well as 

 translation. By the old theory, no additional force is required to produce 

 rotation ; whereas, by the theory of the vis viva, just as much force is re- 



* Proc. A. A. A. S., ii, 129. 



t lb., p. 446. 



: Proc. A. A. S., ii, 111. 



? lb., p. 121. 



1 lb., p. 256. 



y 



