C4G Professor A. Fowler [March 31, 



o 



where A. is the wave-length in Angstrom units (10" '^^ metre), and m 

 takes the value 3 for Ha, 4 for R^, and so on. 



It is instructive to re-write the equation in the form 



A =364C' U+Mii-yjli 

 m^-4 



from which we see at once that there can be no members of this 

 series beyond A 3646 • 14, for this is the value of A when m is infinite. 

 The wave-length 3646 • 14 is thus the end, or " limit," of the Balmer 

 series. 



In such formulae there are often very definite advantages in ex- 

 pressing the positions of the lines in wave-numbers rather than in 

 wave-lengths, the wave-number being 10^ /x, or the number of waves 

 per centimetre, corrected to vacuum. In these terms, the Balmer 

 formula becomes 



^^ ,,Q ^- 109,675 

 n = 2 / , 41 8 • < - — -^ — 



or 



71 = 100,675 



V2- ~ my 



Balmer's formula clearly permits the calculation of an indefinitely 

 great number of lines, but in laboratory experiments even ten or a 

 dozen are not obtained without a little trouble. Sir James Dewar has 

 found that admixture with helium tends to the better development of 

 the ultra-violet members of the series, but it is in the white stars and 

 in the sun's chromosphere that the Balmer series is most completely 

 exhibited. In some of the stellar spectra photographed by Sir 

 William Huggins we can count up to about the 20th member. In I 



the chromosphere, during eclipses, the Astronomer Eoyal has photo- 

 graphed as far as the 28th, and Professor Mitchell as far as the 34th 

 line. The Balmer formula continues to represent the lines with 

 astonishing accuracy, so that no one hesitates to attribute the ultra- 

 violet members to hydrogen, although experimental proof of their 

 hydrogen origin is entirely wanting. 



Besides the Balmer series there are other lines of the primary 

 spectrum of hydrogen which do not come within the range of 

 ordinary observation. There is an infra-red series which was 

 predicted by Bitz and observed by PascTien ; and another series in 

 the extreme ultra-violet which has been partially recorded by Lyman 

 with a Schumann spectograph. These two series run parallel to the 

 Balmer series and are simply related to it, as we shall see later. 



The number 109,675 which occurs in the Balmer formula is an 

 important physical constant, and at the Imperial College Mr. Curtis 

 has taken a great deal of trouble to ascertain its precise value. He 

 obtained a fine series of photographs with the 10-foot concave 



