that Matter takes up no Room in the ^Ether. 851 



given velocity-components U, V is proportional to the mass 

 and density of the plate conjointly, and the advantage o£ using 

 a material of high density is thus evident. 



19. In the application o£ the formula (5) to the apparatus 

 used, the axis of z is vertically upward, x parallel to the 

 breadth of the plate, and y parallel to its thickness. Let «■ 

 be the angle, reckoned in the sense NESW, which the 

 normal to the face ab makes with the meridian. While the 

 other factors of (5) remain constant, UV will vary with 

 the time, and will necessarily involve the unknown velocity 

 of the sun with respect to the aether. As axes fixed in space 

 take 



z' in the direction (S to N) of the earth's axis, 

 y' „ „ of the first point of Aries, 



x'° forming a right-handed system with y', z' ; 



(thus at the vernal equinox the axis of x makes an acute 

 angle with the earth's way) . The velocity-terms due to the 

 earth's rotation will here be neglected. Let (A, B, 0) be 

 the velocity of the earth's centre through the aether, referred 

 to the axes of a?', y' ', z f . Let <f> be the angle through which 

 the earth has turned since a certain transit of the first point 

 of Aries, and the co-latitude of the place of observation. 

 We then find 



U V = {-i(A 2 - B 2 ) sin 2*7(1 + cos 2 0)+AB cos 2w cos 0} cos 2</> 

 + {JAB sin 2w(l + cos 2 0) + * (B 2 - A 2 )cos 2vrcos0} sin2(/> 

 + { —AC cos 2m sin + \ BC sin 2-sr sin 20} cos <£ 

 + { — BC cos 2-57 sin — ^-AC sin 2s7sin 20)} sin <£ 

 + i(A 2 + B 2 )sin2*7sin 2 6>-iC 2 sin2*7sin2(9. . . (6) 



20. In the actual case, -57 = 71-/ 4 approximately, and (6) 

 becomes 



UV =i(A 2 -B 2 )(l + cos 2 0) cos 2</> + ^AB(l -f cos 2 0) sin 2</> 

 + iBC sin 20 cos <£-i AC sin 20 sin 

 + i(A 2 + B 2 )sin 2 6>-lC 2 sin20 (6 a) 



Here each of the components A, B, of the earth's velocity 

 through the aether may be regarded as made up of two terms, 

 one due to the sun's unknown velocity through the aether, 

 the other to the earth's orbital motion. Now the sun's 

 velocity, it may be supposed, does not vary perceptibly in 

 direction or magnitude during the period covered by any 

 practicable observations, and over an interval not exceeding 



