246 THEORY OF MICROSCOPIC OBSERVATION, 



In addition to this difference of phase which depends upon the 

 inequality of the paths, we have under all circumstances to take 

 into account another half wave-length for the reflexion at the 

 denser medium. If we suppose the given layer to be wedge- 

 shaped, and illuminated by rays incident at right angles, it will 

 appear dark at all parts where its thickness is equal to an even 

 number of quarter wave-lengths, because then the difference in the 

 paths of the two systems of rays is expressed by an even multiple of 

 half wave-lengths, i.e. by whole wave-lengths, so that the difference 

 of phase caused by reflexion decides the matter. The intensity of 

 the light reaches its maximum in all places where the difference of 

 path is equal to an odd multiple of quarter wave-lengths. If, 

 therefore, the wave-length = X, and the thickness of the effective 

 layer = d, we get 



Bright lines if |, 3 . |, 5 . |, 7 . j 



Dark lines if d = , 2 . j , 4 . | , 6 . j 



Since the wave-lengths are in inverse ratio to the indices of 

 refraction, we can determine d for any substance whose refractive 

 power is known. It is only necessary to divide the known thickness 

 of the corresponding layer of air by the refractive index of the 

 substance the quotient is the desired thickness. A layer of 

 water with the refractive index f causes, therefore, exactly the same 

 effect as a layer of air one-third thicker. 



When white light is used, the maxima and minima of intensity 

 for rays of different refrangibility do not of course coincide. 

 Instead of the gradations from bright to dark, colours appear in 

 consequence of this, just as in the above-mentioned phenomena of 

 interference. They are the so-called Newton's colours, which, as is 

 well known, follow one another in a definite order according to the 

 increasing thickness of the layer. To each single colour there 

 corresponds a definite thickness of the layer of air, from which can 

 be calculated, in the same way as before, the thickness of any sub- 

 stance of known refractive power. 



According to the researches of Flcegel on Pleurosigma, we are met 

 by peculiar contradictions in these determinations if we compare 

 them with direct micrometric measurements. The calculated 

 thickness of the effective layer corresponds, as seems to result from 

 the data of Flcegel, to exactly half of the real value, so that we 



