184 



Mr. A. M c Aulay on a Modification 



do not therefore conclude that on the present theory this 

 pressure of Maxwell's would not exist, but we do conclude 

 that it does not exist for eight minutes in the sether between 

 the sun and earth, that in fact at the instant when the earth 

 experiences the pressure the sun or some other body ex- 

 periences the reaction. This is. of course, because in the 

 present theory the conditions of equilibrium are always satis- 

 fied by the sether. 



13. Take 6 as the angle that a, makes with i. The solution 

 of § 12 with this meaning of is 



a = A (i cos 6 -\-j sin 0), 



(33) 



where A is a constant and 6 is any function of z—vt, for 

 instance 27r(z — vt)/\. I will now show that it is impossible 

 for two waves of this type inclined to one another to coexist. 



Fig. 5. 



Let i be drawD perpendicular to the plane of the paper up- 

 wards. Let j, k,j L , k^j 2 , k 2 be related as shown in fig. 5. 

 It is required to find whether with cr 1 zero the following 

 equations can be satisfied : — 



Eo = E m +Eo2i H n — H i+H 



01 



■02) 



« 1 = A 1 (icos0 1 + i ;'isin0 1 ), E i=ai, K 0l = k 1 u 1 } , .(34) 

 «2 = A 3 (^cos^ 2 + i / 2 sin^ 2 ), E 02 = «2j H 02 = & 2 a 2 



where A x and A 2 are constants, and ± and 2 are functions of 

 Zi and t and of z 2 and t respectively. 



Since <r' is zero these values of E and H satisfy equation 

 (17), and we know that in this case equation (18) is equivalent 

 to the equation YE H = a constant throughout time and 

 therefore throughout space. We have seen that VE 01 H 01 and 

 YE o2 H 02 are such constants, so that it only remains to make 

 if possible Y (E 01 H o2 + E 02 H 01 ) a constant. Now 



