246 On the Nodal Lines of a Square Plate. 



(a) Wood-like in structure, of a dull brownish-black colour, 

 cuts readily, and does not soil the fingers ; particles do not cake 

 when heated; sp. gravity T32 to 1*45; contains 17 to 18 per 

 cent, of hygroscopic water. This lignite makes a very good fuel, 

 but is not as rich in carbon as most of the lignites about Lough 

 Neagh, which contain 51 to 58 per cent. (Sir R. Kane). Com- 

 pared with other lignites its percentage of ash is high; but 

 though it also contains a large quantity of hygroscopic water, 

 yet in this respect it does not contrast so unfavourably with them. 



(/3) Moderately brittle, of a brilliant black lustre, sp. gravity 

 1*29 to 1-305, hygroscopic water 7 to 8 per cent., burns rapidly, 

 caking but little, and leaving a light porous coke; a slight ad- 

 mixture of iron pyrites in thin scales ; ash light, and of a dull 

 reddish colour. From the large amount of carbon present, and 

 the small amount of ash, this makes a very good burning coal. 

 It is as rich in carbon as many of the English and most of the 

 Scotch coals. 



(7) Hard, compact, difficult to pulverize, of a dull black colour, 

 powder brownish black, burns brightly, tumesces little, cakes 

 but slightly, ash greyish white; sp. gravity 1*275 to 1*37, 

 hygroscopic water 1*5 to 1*9 per cent., coke about 50 per cent. 

 There is a considerable admixture of iron pyrites, which occurs in 

 thin layers. This coal yields a large quantity of gas of high illu- 

 minating quality ; and were it not for the large percentage of ash 

 it contains, it would be equal to any of the English Cannel-coals. 



XXVII. On the Nodal Lines of a Square Plate. 

 By Lord Raylejgh, F.R.S. 

 To the Editors of the Philosophical Magazine and Journal. 

 Gentlemen, 

 REGRET to find that the investigation of one of the nodal 

 lines of a square plate, published in your August Number, 

 is to a great extent vitiated by the erroneous assumption that it is 

 possible for a square plate to vibrate after the manner of a 

 simple bar. The function representing such a motion satisfies 

 the general differential equation, as well as the two necessary 

 boundary conditions along the pair of edges for which the mo- 

 tion is constant ; but on the other pair of edges one of the con- 

 ditions is in general violated. This corresponds to the fact 

 that if a plate is bent by couples acting along one pair of oppo- 

 site edges, it will in general take a contrary curvature in the 

 perpendicular direction. 



Several too confident assertions in the paper referred to must 

 now be retracted; and the deviation of Dr. Strehlke's measure- 

 ments from my calculations are no greater than are fairly attri- 

 butable to the imperfections of the latter. It appears that the 



