434 Mr. S. R. Cook on the Distribution of 



and 



-^^=— ii^asm ^H-iw-i3 a sin 6 \ 1 + 3-cos 6 + 6— ^ 



oo c t c c z 



.a'7cos'^— 3cos^-) , a\ /ix fo^ • a 



-j-0-3— i. J- — ^it— (c — acos ^) S 3 -sin ^ 



+ 3 — cos ^ sin ^ + 10-3 ^ sm^^. . (27) 



The broken-line curve nn in Plate XVIII. fig. 11 exhibits 

 the distribution of pressure as given by equation (16), to the 

 approximation indicated, for two spheres moving with con- 

 stant velocity in the line of their centres. 



For two spheres whose direction of motion is perpendicular 

 to the line joining their centres (fig. 8) to the same degree of 

 approximation 



, , a^ /I . T ^^ zi r 1 , o '' . /I o^''^sin2^ — 1 



9=2^^-2 cos d-r^v^r cos 6 < 1 -!~o- sin ^ + 3^ x 



r c V c C z 



B<^ ^ , , fl' zjfi.Q^' • /] o«'5sin'(9-l 



-^-= — i^cos 6' + ii^^cos 6 { 1-i- 3— sm ^-r3-^ ;r 



or ^ c { c c" 2 



+ 5-, 



a^ 7sin^6>-3sin(9 



c' 2 



^ a- 5 sin-^ — 1 , 



C 1 



• /) 1 ^' • 



^ /I — ^^(i sm d — ^u ~a siLl ^ ^^ , ^ - 



Y + i?t— cos ^ <J 3 - sin 6 



c' 2 



and 



B</) 1 . /) 1 «' • /dJi . Q<^ • /I . .,a'5sin^^— 1 

 .-7^ = —iua sm O — ht- asmOi 1 + 3— sin^ + 3-^ ^ 



a-osm-0-1 _a'7 sin'^-3sin^^ ,^^, 



, .a' 7 siir^-3sm^l a^' /i/o « 



+ D—Y , r + iu -3 « cos 6\ 3 -cos ^ 



c z ' " c ^ c 



., or 5 sin'l9 - 1 , -, ^ «' 7 sin'^ - 1 sin 6'i 



The broken-line curve nn in fig. 12 exhibits the approxi- 

 mate distribution of pressure for two spheres in a perfect 

 fluid moving perpendicular to their line of centres. 



For each set of spheres observations were made when the 

 distance apart of the spheres was somewhat less than three 

 times their radius. The ratio of the radius to the distance 

 apart of the spheres used in computing the curves for the 

 distribution of pressure in a perfect fluid was 1/3. All terms 

 in the expansion of the second image will contain this ratio 

 to the sixth and higher powers, but all terms in the first 



