22 



Prof. Cayley on the 



[Nov. 16, 



applicable through the entire range of Kirchhoff's lines, and actually to 

 apply the corrections to those computed wave-lengths which relate to 

 spectral lines produced by the atmosphere and by many metals. 



Adopting as foundation the comparisons with Angstrom's and Ditschei- 

 ner's measures given in the former paper, and laying these down graphi- 

 cally, the author remarks that in some parts of the spectrum the agreement 

 of the two experimenters is very close, that in some parts they are irrecon- 

 cilable, and that in one part (where they agree) there is a peculiarity 

 which leads to the supposition that some important change was made in 

 Kirchhoff's adjustments. He then explains the considerations on which 

 he has drawn a correction-curve, whose ordinates are to give the correc- 

 tions applicable to his former computed numbers. A. general table of 

 corrections is then given, and this is followed by tables of the Lengths of 

 the Light- Waves for the air and metals as corrected by the quantities 

 deduced from that general table. 



The author remarks that he has not yet succeeded in discovering any re- 

 lation among the wave-lengths for the various lines given by any one 

 metal &c. which can suggest any mechanical explanation of their origin. 



V. "Corrections and Additions to the Memoir on the Theory of 

 Reciprocal Surfaces, Phil. Trans, vol. clix. (1869)." By Prof. 

 Cayley, F.R.S. Received July 22, 1871. 



1. I am indebted to Dr. Zeuthen for the remark that although the " off- 

 points " and " off-planes," as explained in the memoir, are real singulari- 

 ties, they are not the singularities to which the 0, 0' of the formulae refer. 

 The most convenient way of correcting this is to retain all the formulae with 

 0, 0' as they stand, but to write w, w' for the number of " off-points" and 

 <( off-planes " respectively ; viz. we thus have 



to, off-points, 



6, unexplained singular points, 



and 



to', off-planes, 



0', unexplained singular planes, 



the formulae as they stand, taking account of the unexplained singularities 

 and 0', but not taking any account at all of the off-points and off-planes 

 a-, w\ The extended formulae in which these are taken into account are : — 



a(n - 2) =k — B +p + 2a + 3w, 



b(n—2)=- p + 2/3-f-3y + 3£, 



c(rc_2) = 2<7+4/3 + y + + w, 



«(» — 2)(»— 3)=2(S— C— 3to) + 3(«c— 3*7— x - 3u) ) + 2 ( ab — 2 P— f)> 

 b(n— 2)0— 3)= 4k + (ab— 2 P —j) + 3(bc-3(3— 2y-i), 

 cQi— 2)0— 3)= Gh +(ac— 3<r— x— 3w) + 2(6c— 3/3— 2y— 0, 

 which replace Salmon's original formulae (A) and (B). 



