﻿On the Highest Wave of Permanent Type. 351 



until the desired part of the spectral field is brought into the 

 observing eyepiece. If the spectrum is now either too high 

 or too low, it shows that the refracting edge of the prism is 

 slightly inclined to the mirror-face, and the screw c is turned 

 until the spectrum is centred. Then, if all the preliminary 

 adjustments have been properly made, the angular deviation 

 of the central ray in the field will be given by the relation 



= 2(0- (90° + *)), 

 where /3 is the circle-reading for a deviation 0, and a is the 

 zero-reading determined as already described. 



In very accurate spectrometric work it is important to 

 determine just what degree of accuracy is required in making 

 the various adjustments of parts to each other in order to 

 attain a given degree of accuracy in the final result. The 

 theory of these adjustments is comparatively simple, but some- 

 what lengthy, and it will therefore be briefly indicated in a 

 future paper. 



Astro-Physical Observatory, 

 Washington, D.C, March 1893. 



XXXIX. On the Highest Wave of Permanent Type. 

 By J. McCowan, M.A., D.Sc, University College, Dundee*. 



IN a previous communication f, in which I discussed the 

 general theory of the class of waves in water or other 

 liquid which have no finite wave-length but which are of 

 permanent type, that is to say, which are propagated with 

 constant velocity without change of any kind, I gave a rough 

 estimate of the maximum height to which such waves might 

 attain without breaking. The paper dealt chiefly with an 

 approximation which was specially suitable for waves of small 

 or moderate elevation, and it is the object of the present 

 paper, therefore, to supplement this by investigating an 

 approximation better adapted to the discussion of the extreme 

 case of the wave at the breaking height, and sufficiently exact 

 for ordinary purposes. I trust, however, to be soon able to 

 communicate a fuller discussion of the general theory of the 

 solitary wave which I have almost completed. 



1. The General Equation of the Motion. 

 The highest wave which can be propagated without change 

 in water of any given depth is obviously the highest solitary 



* Communicated by the Author, having been read before the Edin- 

 burgh Mathematical Society, June 8, 1894. 



t "On the Solitary Wave," Phil. Mag. July 1891. 



