THEORY OF LIGHT AND COLOURS. 171 



rent planes, the interval will vanifli, and all the undulation? 

 will confpire. At other inclinations, the interval will be the 

 difference of the fecants from the fecant of the inclination or 

 angle of refraction of the principal beam. From thefe caufes, 

 all the colours of concave mirrors obferved by Newton and 

 others are neceffary confequences : and it appears that their 

 production, though fomewhat fimilar, is by no means, as 

 Newton imagined, identical with the production of thole of 

 thin plates. 



Corollary 4. Of Blacknefs. 



In the three preceding corollaries, we have confidered the Bhcknefs pro- 

 refracting and reflecting fubftances as limited by a mathema- ^"y^J"^ 

 tical furface; but this is perhaps never phyiically true. The tions at the con- 

 ethereal atmofpheres may extend on each fide the furface as £ ne of ^ fu £ 

 far as the breadth of one or more undulations ; and, if they be ether gradually 

 fuppofed to vary equally in denfity at every part, the partial var ' es «« den r 

 reftedions from each of the infinite number of i'urfaces, jw^gtofwhkhit.that 

 the denfity changes, will very much interfere with each other, the undulations 

 and deflroy a confiderable portion of the reflected light, fo^ r o" n ea ch 

 that the fubftance may become pofitively black ; and this ef- other, and con- 

 fed may take place in a greater or lefs degree, as the denfity [*JJJ2oa of 

 of the ethereal atmofphcre varies more or lefs equably ; and, light. 

 in fome cafes, particular undulations being more affected than 

 others, a tinge of colour may be produced. Accordingly, 

 M. Bouguer has obferved a confiderable lofs of light, and in 

 fome inftances a tinge of colour, in total reflections at the fur- 

 face of a rarer medium. 



Corollary 5. Of Colon rs by Jnflcchon . 



Whatever may be the caufe of the inflection of light pailing Colours by inn 

 through a (mall aperture, the light near e It its centre mud be fle< ?' an8X * 

 thc leaf! diverted, and the neareft to its fides the mod ; aff-dklVipBi length* 

 other portion of light falling very obliquely on the margin of °f the bended 

 the aperture, will be copioully reflected in various directions ; aftemacSnsIn 118 

 fome of which will either perfectly or \'Qry nearly coincide in the compound 

 direction with the unrefle&ed light, and, having taken a cir- j^Coota ?. 

 cuitous route, will fo interfere with it, as to caufe an appear- 

 ance of colours. The length of the two tracks will differ the 

 lefs, as the direction of the reflected light has been lefc 

 changed by its reflection, that is, in the light palling neareft 



to 



