352 
MR. C. GODFREY ON THE APPLICATION OF FOURIER’S 
Making this substitution, we have 
a 
00 
=-f 
2« J, 
sin 2ZwP 
P%-" 2p WP = 
hit 1 
TT _VV" 
V n = e TY = 
e .(viii.) 
§ 46. The result is now in a form which we can interpret. Lord Rayleigh* has 
worked out the width of the spectrum lines, taking into account the Doppler effect 
alone. The visibility function deduced from his work in accordance with Michelson’s 
definition of “ visibility”! is 
e - K *uH\*h .(i X .) 
The two functions (viii.) and (ix.) are of the same form, and differ only in the 
presence of /P in (viii.). Now Michelson’s experiments gave visibility-curves agree¬ 
ing in general character with (ix.) ; they would therefore agree equally well with the 
function (viii.) which has been found above. 
Numerical Estimates. 
§ 47. Miciielson has investigated the lines of several gases with his interferometer. 
He compares the “ half-widths ” (value of u for which visibility is 4 of maximum) of 
the visibility-curves with the values deduced by Lord Rayleigh from Doppler’s 
principle. Unfortunately Michelson misquotes Rayleigh’s result, and has dropped 
a 2 ; in Rayleigh’s formula the path-difference is 2A ; Michelson has taken it to 
he A. The last column of figures in jiage 294 of Michelson’s paper}; should be all 
doubled. This would give the observed “ half widths ” in every case much less than 
the calculated values. Furthermore, using the function which has been obtained in 
the present paper, 
V = 2 
4/ M -V 2 /i 
where l is the Napierian lo 
Hence for half-width 
of 
KU 
‘Z/My/lY/l* 
U = 
But v = 
Hence 
~ ; v being the average velocity of the molecules. 
2yU.\U Y 
u = \ . —— . - • 
7 r* v 
u/X = ‘33V/v, instead of Michelson’s '1 5 V/v 
Phil. Mag.,’ vol. 27, p. 304, 1889. 
t Michelson, ‘ Phil. Mag.,’ vols. 31 and 34. 
+ ‘Phil. Mag.,’ vol. 34, 1892. 
