294 Prof. P. E. Chase on Undulation. 



Denominators. Nodal divisions. Quotients. Observed. 



1 1-0000 761-20 A 761-20 



a + c(f) 1*1071 687-56 B 687-49 



[1-1530 660-19] C 656-67 



a + 2c 1-1989 634-92 



a + 3c(f) 1-2907 589-76 D 589-74 



a + 4c 1*3825 550-60 



[1-4437 527-26] E 527-38 



a + 5c 1-4743 516-31 b 517-70 



a + 6c(f) 1*5661 486-05 F 486-52 



a + lc 1*6579 459*13 



a + Sc ...... 1-7497 435-05 G 431*03 



[1-7650 431-27] 



a + 9c 1-8415 413*37 



[1*9180 396*87] H 397*16 



a + 10c(/) 1*9333 393*73 H 393*59 



The harmonic interferences which are indicated by the series 

 marked (/) are the most interesting, both on account of the 

 close accordance between the theoretical quotients and the 

 corresponding observed values, and because the successive 

 denominator-increments are figurate. Moreover the figurate 

 series (1, 3, 6, 10) is the same as I pointed out in my equa- 

 tion of products of triangular powers, which is applicable both 

 to vector radii and to masses: — 



^x^x^xV -10 ^*- 



Of the six remaining lines, three (A, b, Gr) approximate so 

 closely to the corresponding harmonic quotients, the greatest 

 deviation being less than one per cent., that they may be pro- 

 perly regarded as illustrations of secondary interferences. The 

 bracketed divisors and quotients indicate tertiary harmonics, 

 based on denominative differences of c f = a — 1 = *0153, 1*1539 

 = l + 10c', 1*4437 = 1 + 29 c', 1-7650 = 1 + 50c', 1-9180 = 1 

 + 60c'. The greatest difference between the theoretical and 

 observed values is less than ^ of one per cent. ; all the other 

 differences range between -^ and Jj- of one per cent. 



Among the subordinate spectral lines there are some which 

 are closely represented by the quotients of 761*20 by the de- 

 nominators a + 2c, a + 4:C, a + 7c, a + 9c. But, on account of 

 the great number of faint lines, such accordances are less satis- 

 factory than those which can be found in the lines that are 

 more widely separated and more prominent. 



* Phil. Mag. for June (Supplement) 1876. 



