60 Lord Rayleigh on the remarkable Case of 



Using these we have 



JW(|)>-w"o 



+ 7, 2 )- 



5. General Conclusion. — By combining the above we 

 obtain the value o£ 



JV(f)> 



for a bar under any terminal conditions whatever expressed 

 in terms of (f> and <f>', where 



(f> = A cos 7jf + B sin 7, £. 



Thus the changes needed in the notes, in the form and 

 relations of the normal functions and in the equation 

 determining the influence of a generalized force have been 

 fully dealt with for the case in which rotatory inertia terms 

 are retained. It will be seen at once, that while the analysis 

 is somewhat lengthy, the results reached are not of a very 

 complicated character. 



My best thanks are due to Prof. Karl Pearson, both for 

 suggesting the above investigation and for his constant help 

 during the progress of the work. 



III. Note on the remarkable Case of Diffraction Spectra 

 described by Prof . Wood. By Lord Rayleigh, O.M.,P.R.S* 



IN the Philosophical Magazine for Sept. 1902 Prof. Wood 

 describes the extraordinary behaviour of a certain grating 

 ruled upon speculum metal which exhibits what may almost 

 be called discontinuities in the distribution of the brightness 

 of its spectra. Thus at a certain angle of incidence this 

 grating will show one of the D-lines of sodium, and not the 

 other. In fig. 1, p. 398, Prof. Wood gives ten diagrams 

 fixing the positions (in terms of wave-length) of bright and 

 dark bands in the spectrum at various angles of incidence 

 ranging from 4° 12' on the same side of the normal as the 

 spectrum to 5° 45' on the other side. In general there may 

 be said to be two bands which approach one another as the 

 angle of incidence diminishes, coincide when the incidence is 

 normal, and open out again as the angle increases upon the 

 other side. In the tenth diagram there is a third band whose 

 behaviour is different and still more peculiar. In the move- 

 ment of the two bands the rate of progress along the normal 

 spectrum is the same for each. The above represents the 

 cycle when the grating is in air. " If a piece of plane-parallel 

 glass is cemented to the front of the grating with cedar-oil 



* Communicated by the Author. 



