On the Propagation of Cusped Waves. 589 



tween the reduced pressure and temperature by substituting 

 this expression for x in the equation (8), 



It should be noted that we have confined ourselves to a 

 strictly mathematical treatment without taking physical con- 

 siderations into account. The equation (a) can "hardly be 

 considered to have any physical application when 6 is negative, 

 and ceases to represent viecessarily the relation between the 

 volume, pressure, and temperature of a substance when 

 #?<§, for then doubly central impacts between the molecules 

 become impossible (cf. Memoirs of Phys. Soc. of London, 

 vol. i. part 3, page 384). 

















Ref 



erences in the Figures. 















Reference 

 number... 



1 

 



2 



4 



3 



5 



4 



6 



5 

 6-75 



6 



7 



7 

 7-5 



8 



8 



9 

 9 



10 

 12 



11 



16 



12 

 24 



13 

 32 



14 



40 



15 



48 



16 

 56 



17 

 64 



18 



72 



19 

 80 



20 



-8 



All the curves in fig. 2 (except 8) should run up to the 

 asymptote x — 3; but, for the sake of clearness, they are dis- 

 continued before they approach each other so closely as to 

 be mutually indistinguishable. 



Figs. 1 and 2 are ruled into reference squares whose sides 

 are half the unit of length. 



Note. Since I wrote the above I have heard from Mr. R. 

 E. Baynes, M.A., Christchurch, Oxford, that he obtained an 

 identical result for the equation of the border-curve many 

 years ago. 



LVTI. On the Propagation of Cusped Waves and their Relation 

 to thj Primary and Secondary Focal Lines. By Prof 

 P. W. Wood *. 



IN a previous paper (Phil. Mag. July 1900, p. 148) I have 

 shown the forms of the wave- fronts reflected from 

 spherical surfaces, by means of geometrical constructions, 

 and photographs of the actual waves. In the present paper 

 I shall discuss somewhat more fully the case of the reflexion 

 of a plane wave by a hemispherical mirror, where we have a 

 reflected wave of a form which I have likened to a volcanic- 

 cone. A superficial examination of the forms might lead one 

 to imagine that the bowl of the crater collapsed to a point at 

 the principal focus of the mirror. This can of course only be 

 * Communicated by the Physical Society. 



