the Colours of Mixed Plates. 683 



in front of the eye then corresponds to a thickness for which 

 (fi—l)t is an integral number of wave-lengths. The angular 

 width of the dark rings in the halo may be determined by 

 making them coincide in succession with a movable faint 

 luminous reference mark placed in the same plane as the 

 source. The actual value of (/x— l)t may be determined in 

 one or other of two ways. The first method is to observe 

 the spectrum of white light transmitted through the portion 

 of the film under consideration, and by noting the wave- 

 lengths of the light freely transmitted through the film 

 without interference to determine the value of (/£ — \)t 

 by calculation, The second method utilizes the fact that 

 the number of wave-lengths, say w, comprised in (fi — l)t is 

 the same as the total number of dark rings visible in the 

 halo, provided the latter is not too large ; for the outermost 

 dark ring in the halo then corresponds to interference under 



a path-difference — , and the innermost dark ring to a path- 

 difference ?ik— -x. The results of both methods agree. 

 2 



Table I. shows the results ot a few determinations of the 

 angular diameter of the dark rings in the halo. 



Table I. 



(l<-l)t. 





A 



ngular diameter of dark rings. 





Remarks. 



{ calc. 



0° 

 



0' 



6° 45' 

 6 15 



14° 12' 

 13 40 



22° 42' 

 22 13 



32° 40' 

 33 10 



[measured 

 Outer rings not 



6 \ ... i ob f- 

 { calc. 













7 3(3 

 6 42 



18 10 



15 40 



28 40 

 27 30 



45 

 44 



Ditto. 



A ... < i 

 calc. 













10 30 

 9 27' 



10 (» 



20 27 



35 24 

 30 50 





Ditto. 



In the cases under consideration, where (jh — l)t is an 

 integral number of wave-lengths, formulas (1) and (2) 

 agree in making the first dark ring coincide with the 

 centre of the halo. Elsewhere the intensity of the halo 

 given by formula (2) is too small appreciably to influence 

 the positions of any of the observable dark rings, though it- 

 may result in partial blurring of one or two rings nearest 

 the centre. The theoretical values of the angular dia- 

 meters of: the dark rings may therefore be taken as given 

 by formula (1) exclusively, and have accordingly been 

 calculated and shown in Table I. The agreement between 

 theory an 1 observation is seen to be satisfactory. 



2Z2 



