536 Prof. Arthur Schuster on 



The excess of energy according to (5) will be proportional to 



I. 



Vtt 



2\ 



/eV ffl2 * 2 cos 2kt dK= ^-e-^ a \^ + 3a^-12a 2 T-) 



If we call E dx the energy supplied to a strip of width dx 

 and unit length by each source separately, then for r=0 the 

 energy should be 4tE dx. Hence the excess of energy 

 (E — 2E ) due to the double source will be determined by 



E-2E =§E 6-* 2 (4^ + 3-12e 2 ), ... (6) 



where z is written for r/a. 



The retardation t may be expressed in the usual way in 

 terms of the distance of the two sources from each other and 

 from the screen. If 



D = distance of screen from source of light ; 

 2d = distance of the two sources of light from each other ; 

 Y = velocity of light ; 



x == distance of any point of the screen from the central 

 line, i. e. that line on the screen for which t = ; 



we have the following relations : — 



z = xd/(VDa), 



The quantity a can be determined if we know the wave-length 

 for which the energy is a maximum in a spectrum formed by 

 a grating, the condition for the maximum being 



or kcl= v 3. 



2_ 

 4/3 



As we are now dealing with the only interference-effect 

 which can properly be said to take place with white light 

 when the source is only doubled, and not multiplied more 

 frequently as in the case of thin fUms, it seems worth while to 

 discuss the energy-curve as given by (6) a little more closely. 



In fig. 7 (page 541) the line A gives the assumed illumination 

 of the screen due to the source only. The source being doubled 

 by the introduction of the mirror, the straight line B gives on 

 the same scale the illumination of the screen calculated on 

 the assumption that there is no interference ; the intensity in 

 that case being simply doubled. The curve C gives the actual 

 illumination obtained by Lloyd's mirror-arrangement, cal- 

 culated on the hypothesis that Michelson's formula for the 



Hence \xazx.) = tt= ira V. 



