Double Refraction of Quartz. 103 



consequently only on the last term of this expression.* Now this is the 

 same that we should have had for the colours in Newton's scale depending 



on the thickness ^~ + r,r( °"~ -Jle» of a plate of air, if ^JH. be the 



same for all colours: or if the variations of "' ~^ be proportional to the 

 variations of X, the last term must be altered in a certain proportion, 

 and our statement will still be true. It appears therefore that the central 

 tint will be nearly that corresponding in Newton's scale to a plate of air 



2 Te 



whose thickness is ~- : and will be followed by the other orders of New- 

 ton's scale. This agrees sufficiently with the observations. 



7T0 



3. Unless — - 0, or = w, &c. the light is not = : therefore there 

 is no black cross. But the light is least when <p = 0, or = 90°, or = 180°. 

 or = 270°: and greatest when (p = 45", or = 135°, or = 225°, or = 315°. 

 This shews that there are dark brushes parallel and perpendicular to the 

 plane of reflexion, but not interrupting the rings. As k is nearly = 1 in 

 the neighbourhood of the axis (by hypothesis) they are not sensible near 

 the center: but as, on removing to a distance, k approaches to 1, they 

 become stronger. This is conformable to observation. 



* This is not strictly true: for though, in comparing this with one of Newton's rings, the 

 colours mixed may be the same, their intensities will not be equal except sin 2 — be the 

 same, and consequently the compound colour will not be the same. But it is plain that, if 

 we take the ring preceding and that followiug the point where the difference of — is the 



same as in the case before us, then at the points where sin 2 - — has the same value for the 



mean rays, we shall have mixtures differing in opposite ways from that under consideration. 

 In the same manner, in the rest of the paragraph, it must be understood that, if we take 

 those colours of Newton's scale between which the colours of these rings lie, we shall always 

 advance in the scale : but we may possibly have no ring intermediate between two of New- 

 ton's, or we may possibly have more than one. 



