354 Molecules, Ultimates, Atoms, and Waves. [July, 



second, a force of the above number of times greater inten- 

 sity would, in the same time, drag or drive it through nearly 

 219 billions of inches, or 219 billionths of an inch in the 

 billionth of a second—the spaces being as the squares of the 

 times. 



The extreme distance to which a vibrating particle will 

 depart from its point of rest will be that through which it 

 may be dragged or driven by the returning force in the fourth 

 part of the period of vibration. In the case of the wave a, 

 it will be that through which it maybe dragged or driven in 

 the 1564th part of the billionth of a second. This gives the 

 11,169th part of the billionth of an inch for the departure of 

 the particle from its point of rest. The length of the wave A 

 being 29,956,800 billionths of an inch, this length is to the 

 departure of each particle involved in that wave from its 

 point of rest in the ratio of 334,600 millions to 1. 



Seeing the spaces vary as the squares of the times, the 

 ratio which the wave-lengths bear to the departure of the 

 particles involved in them from their points of rest will be 

 inversely proportional to the wave-lengths themselves. The 

 shorter the wave the higher the ratio. The following 

 table exhibits the ratio for the wave-lengths corresponding 

 to the eight principal lines : — 



A. 334,600 millions to 1. E. 482,885 millions to 1. 



B. 370,470 „ 1. F. 523.390 » 1- 



C. 387,708 „ 1. G. 59°>647 „ i- 

 D - 43i>555 » i« H. 646,881 „ 1. 



A better notion of this immense excess of the length of 

 the wave over the departure of the individual particles from 

 their points of rest may be obtained by imagining both to be 

 magnified a million of billions of times. The length of the 

 A wave would then be nearly 473 millions of miles, while the 

 departure of each particle involved in that wave from its 

 point of rest would be only about 7J feet. In the 

 case of the H wave, its length would be about 245 mil- 

 lions of miles, while the departure of each particle involved 

 in that wave from its point of rest would be only about 2 feet. 



This great excess of the wave-length over the departure 

 from the point of rest shows the latter motion to be rateably 

 very much slower than the speed with which the motion of 

 translation runs along the wave-lengths from particle to 

 particle — in other words, than the velocity of light. Thus 

 in the case of the A wave the particles move the 11,169th part 

 of the billionth of an inch in the 1564th part of the billionth of 

 a second. Supposing the motion to be uniform, this rate is 





