146 



SCIENCE. 



for the great body of our fellow creatures that high 

 improvement, which both their understanding and 

 their morals fit them to receive, is an object suffi- 

 ciently brilliant to allure the noblest ambition. With- 

 out claiming such lofty aspirations, the promoters of 

 " Science " yet look forward to the time when their 

 efforts to establish this journal may be recognized as 

 at least a step in that direction. 



ON THE AMPLITUDE OF VIBRATION OF 

 ATOMS. 



Prof. A. E. Dolbear, Tufts College, Mass. 

 There is now sufficient evidence for the belief that 

 the kinetic energy of atoms and molecules consists of 

 two parts, one of which is the energy of translation or 

 free path, the other of a change of form due to vibra- 

 tions of the parts of the atom or molecule toward or 

 away from its centre of mass. The pressure of a gas 

 is immediately due to the former while the tempera- 

 ture of the gas depends solely upon the latter. These 

 two forms of energy must indeed be equal to each 

 other in a gas under uniform conditions ; for if one 

 exceeded the other in energy when there is as free a 

 chance for exchange as among the atoms of a gas, 

 there would result an increase of pressure on the one 

 hand, or an increase of temperature on the other. 

 Now the kinetic energy of a mass m and velocity v 



is expressed by — — and applies as well to an atom 



as to a musket bullet, and if we take the mass of the 

 hydrogen atom as unity and employ the calculated 

 velocity of hydrogen atoms at o" Cent, and 760 mm. 

 pressure, namely i860 metres per second, the energy 



will bei^ 60 ! 2 - 

 2 



We know also how many times the hydrogen 

 atom vibrates per second, by dividing the velocity of 

 light per second by some chosen wave length ?. ; so 



that n = If attention be now directed to the vi- 



A 



brating atom possessing the same energy as in the 

 free path movement, it will be seen that its velocity of 

 vibration must also be equal to i860 metres per 

 second. But vibratory velocity is the product of a 

 number n into an amplitude a , so that v — n& — 

 i860. 



Adopting the vortex-ring theory of matter, the dark 

 ring represents the atom which, when executing its 

 simplest vibration assumes consecutively the conju- 

 gate ellipses and any point a in the circumference 

 will move over the line b d, the latter distance consti- 



tuting the amplitude of the vibration. The limits to 

 this movement must clearly be between b d = o when 

 there is no vibration, the absolute zero of the atom 

 and c e which can never exceed \ ttt and indeed 

 must always be less than that value ; for when half 

 the major axis of the ellipse is equal to that it has 

 become a straight line. As atomic vibrations result in 

 undulations in ether it is evident that amplitude b d 

 will give an undulation a f shown in continuous line, 

 while maximum amplitude c e would give same wave 

 length shown in broken line. The greater the actual 

 thickness of the ring the less must be the possible maxi- 

 mum amplitude. 



The amplitude then becomes comparable with the 

 diameter of the atom, and in this discussion the as- 

 sumed diameter is the one given by Maxwell, namely 

 .0000005 mm - 



The numerical value of \ ?rr for such a diameter 

 is .0000004 mm - which represents the theoretical 

 maximum amplitude for a hydrogen atom. 



If any hydrogen wave length be taken, say C = 



.0006562 mm. the ratio of wave length to maximum 



. .0006562 . ... 



amplitude is - = 1640, that is wave length is 



1 .0000004 ^ ' 



1640 times such amplitude. But hydrogen C is not 



the fundamental vibration, but according to Stoney 



is the 20th harmonic of a fundamental having a wave 



.013127714 



length of .013127714 mm. and "^oo^" = 3 z8l 9- 

 That is, it is 32819 times greater than the amplitude. 



Now, Sir William Thomson, in his calculations on 

 the amount of energy in the ether, assumed that the 

 amplitude should not exceed one-hundredth of the 

 wave length, but that value is evidently very many 

 times too large. An undulation with the wave length 

 of this fundamental for hydrogen is nearly twenty 

 times longer than the longest one that can be seen ; 

 and as the sensation of light depends upon wave 

 length and not upon amplitude, or what the energy 

 of the ray, it follows that Dr. Drapers' deductions 

 concerning the temperature of bodies beginning to be 

 luminous will not necessarily apply to gases, for when 

 extra energy is imparted to the atoms of a gas it is the 

 amplitude of their vibrations that is affected, and if 

 the impacts are sufficiently frequent some of the har- 

 monic vibrations may appear continously, but they 

 will not thereby necessarily indicate a higher tempera- 

 ture, but show that the energy is distributed in two or 

 more periods, some of which have resulting undula- 

 tions which may be seen ; but this will depend upon 

 the density of the gas. Suppose a body capable of 

 vibrating a times per second for its fundamental, be 

 struck b times per second ; then will the rate of vi- 

 bration be interfered with - times. If b be less 



b 



than a, then will the fundamental vibration have more 

 than its required interval between impacts, and a cer- 

 tain number of these fundamental vibrations will be 

 made per second. If b be equal to a, then, after the 

 first impact, a will vibrate in its own period with in- 

 creasing amplitude, without interference. If b be 

 greater than a then will the impacts interfere in all 

 phases of the vibrations, the fundamental will be 

 destroyed, and only some harmonics and irregular 

 vibrations will be possible ; but the number of impacts 



