of the Interrupted Spectra of Gases. 



C n =k sin 0, ^ 



C n+1 = 1c' sm(0 + lir), 

 C B+2 =Fsin(0 + §7r), 

 C tt+3 =F' sin (0 + §*-), 



C n+4 = ^sin{6 + i7r), 

 C n+5 = fcsm6. 



47 



(7) 



where 6 is some odd number of times -, and the Fs are coeffi- 



cients which only gradually change in passing from line to line. 

 13. This at once suggested a displacement-curve consisting of 

 a pair of lines repeated over and over, like the sides of the teeth 

 of a saw. Eor the equation of this displacement- curve is known 

 to be* 



And in this equation 



a — 3 . x 



smw- 



HK^-f)} 



(8) 



2tt 



«-/3_, 



sin ft -^> 



(9) 



71* 2 



which would assume the required form (5) if 



X i = -}7T±2€, 



e being small. The expression for C n then becomes 



u-/3 . f2ir , \ 

 C n = 27r — 2- . sin™ — ie L 



which would give the observed pattern in those regions of the 

 spectrum in which n has such values as make 



ne — an odd number of times =r- 



(using the symbol — to signify is nearly equal to). For these 

 parts of the spectrum 



\j n = 2tt . — 2~ cos n -—> 

 n o 



which gives the pattern represented in fig. (4). 

 14. Midway between two such regions 



ne = an even number of times ^ 



»* Equations (8) and (9) taken together represent the motion of a point 

 on a violin- string which is nearly, but not quite, two fifths of the length of 

 the string from one end. See Helmholtz's Lehre von den Tonempfindungen, 

 edition 1870, Beilage VI. 



