1871.] Molecules, Ultimates, Atoms, and Waves. 351 



scale — in which the lines are laid down as they appear to 

 the eye when viewed through the spectroscope. But from 

 the circumstance above explained, these positions are true 

 only for the particular instruments employed in the observa- 

 tions. The positions given in this plan are also very diverse 

 from those laid down in M. Angstrom's atlas, which is con- 

 structed on a totally different principle, the lines being re- 

 presented, not in the positions in which they appear to the 

 eye, but in positions corresponding to their wave-lengths in 

 ten-millionth parts of a millimetre. It would be desirable 

 that a fresh plan were constructed combining both /princi- 

 ples. The plan and the atlas both give the names of the 

 vapours and gases by which the lines are supposed to be 

 produced, in so far as these have been ascertained ; but 

 there is great difficulty in identifying any of the lines in the 

 atlas with those on the plan, except in the case of the most 

 conspicuous lines. 



In 1859, when only the measures of Fratinhofer were 

 known, it was shown in a paper inserted in the " Philo- 

 sophical Magazine" for i860, p. 437, that, assuming those 

 measures to be approximately correct, it is probable that 

 the wave-lengths of the principal lines are so connected by 

 a law as to render their observed values a check one upon 

 another. It has accordingly become interesting to ascertain 

 how far this probability is confirmed by the more recent 



o m 



observations of M. Angstrom. On investigation it is found 

 that the measurements of the Swedish philosopher do follow 

 siich a law, but one differing from that which appeared dedu- 

 cible from those of Fraiinhofer. A careful analysis of 



o 



M. Angstrom's measurements has proved the wave-lengths to 

 be so mutually related that from the one corresponding to 

 the more refrangible e, all the others may be accurately cal- 

 culated by simple formulas ; while of the seven equations by 

 which those values may be determined, the sum of the first 

 three is equal to that of the remaining four, thus showing 

 that all the wave-lengths are inter-dependent, each one upon 

 the whole. These curious relations have been already enun- 

 ciated in a memorandum added to a work recently pub- 

 lished.* Craving reference to that memorandum for the 

 formulas by which they are expressed, it will suffice here to 

 give the general result, by exhibiting in the following table 

 the values of the wave-lengths, as calculated from those for- 

 mulas, and as given by M. Angstrom from his observations, 



* The Beginning ; Its When and its How. Longmans and Co. 



