i8yi.] Molecules, Ultimates, Atoms, and Waves. 353 



calculated from the wave-length of E alone, but that of the 

 seven equations b}' which these are determined the sum of 

 the first three is equal to that of the remaining four, — will be 

 more fully appreciated by those who are able to estimate the 

 vast amount of the probabilities against the existence of 

 such a coincidence. It is also a curious, though accidental, 

 coincidence that the wave-length of E expressed in ten- 

 thousandths of the millionth of a millimetre is almost ex- 

 actly equal to the tangent of an angle of 27 47', namely, 

 5268685 — the difference, 0000015, tying much within the 

 limits of probable errors of observation, which are more than 

 sixty times greater.* This tangent might accordingly be 

 assumed as the value of e without affecting the relations of 

 the wave-lengths to each other. 



Having thus obtained the wave-lengths of the principal 

 lines, it is easy to calculate the periods of time which the 

 wave motion takes to traverse each wave-length in parts of 

 the billionth of a second. For, seeing the motion is propa- 

 gated at the rate of 11,721 millionths of an inch in the 

 billionth of a second, we have only to divide this number by 

 each wave-length, as given in the last table, to obtain the 

 times. The following table exhibits the results in parts of 

 the billionth of a second : — ■ 



A. One 391st. E. One 565th. 



B. One 433rd. F. One 612th. 



C. One 453rd. G. One 691st. 



D. One 505th. H. One 756th, 



The wave-length being the space traversed by the wave 

 motion travelling onwards in a right line, while each ethereal 

 particle embraced in it is performing a single vibration in a 

 transverse direction, the above times are also the periods of 

 vibration of the individual particles involved in each wave. 

 It remains to ascertain what amount of motion the particles 

 perform during the above minute fragments of time. 



By comparing the speed of sound in traversing the air with 

 that of light in passing through the ether, we learn that the 

 elastic energy, operating in the latter case, exceeds in inten- 

 sity that of terrestrial gravitation, operating in the former 

 case 1,137,156 millions of times — the forces being to each 

 other as the squares of the speeds. Terrestrial gravity 

 being capable of dragging a particle through 193 inches in a 



* The wave-lengths of f, when stated in hundred thousand millionths of an 

 inch, makes a still nearer approach to being equal to the versed sine of an 

 angle of 36° 3' 1" = 1914962, which might be adopted as the value of the wave- 

 length of f without affeding any of the calculations. 



VOL. VIII. (O.S.) — VOL. I. (N.S.) 2 Z 



