ON THE THEORY OF LIGHT ANp COIOURS. 



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lours. The undulations which are now to be 

 compared are those of equal frequency. 

 When the two series coincide exactly in 

 point of time, it is obvious that the united 

 velocity of the particular motions must be 

 greatest; and also, that it must be smallest, 

 and, if the undulations are of equal strength, 

 totally destroyed, when the time of the 

 greatest direct motion, belonging to one un- 

 dulation, coincides with that of the greatest 

 retrogtade motion of the other. In inter- 

 mediate states, the joint undulation will be 

 of intermediate strength ; but by what laws 

 this interinediate strength must vary, cannot 

 be determined without furthej- ,data. It is 

 well known that a similar cause produces, 

 inbound, that effect which is called a beat; 

 two series of undulations of nearly equal 

 magnitude cooperating and destroying each 

 other alterijaitely, as they coincide more or 

 less perfectly in the limes of performing 

 their respective motions. 



CoRouhATiy i, Qf t/ie iJolours afUriattd 

 Surfaces. 



J3oyle appears to hav<2 beien the first that 

 observed the colours of scratches on po- 

 lislred surfaces. Nicwton lias not noticed 

 them. Mazieas and Mr. Brougham have 

 •Blade some psperinients on the subject, yet 

 .yrjthout deriving any satisfactory conclusion. 

 liM »|l the vsriiejies of these jjolours are 

 very easily deduced from this proposition. 



JL^t there be, in a given plane, two reflect- 

 ing points very near each other, and let the 

 ■plane be so situated that the reflected iuiage 

 i)f a luminous object seen in it may appcaj- 

 ^ocojjncide with the points; then it is obvious 

 that the ler^ih of the incident and irefltict^d 

 jay, taken together, is equal with respect 

 to both points, considering them a:j capable 



vol.. IJ. 



of reflecting in all directions. Let one of the 

 points be now depressed below the given plane ; 

 tten the whole path of the light, reflected 

 from it, will be lengthened by a line which is 

 to tiie depression of the point as twice the 

 cosine of incidence to the radius. (Plate 14. 

 Fig. tOG.) 



If, therefore, equal undulations of given 

 dimensions be reflected from two points, 

 situated near enough to appear to the eye 

 but as one, wherever -this line is equal to 

 half the breadth of a whole undulation, tiifc 

 reflection ftom the depressed point will so 

 interfere with the reflection from the fixed 

 point, that the progressive motion of the one 

 will coincide with the retrograde motion of the 

 other, and they will both be destroyed ; but, 

 when this line is equal to the whole breadth 

 of an undulation, the eflecc will be doubled- 

 and when to a breadth and a half, again de- 

 stroyed ; and thus for a considerable number 

 of alternations ; and, if the reflected undu- 

 lations be oi" dilfereijt kinds, they will be va-f 

 riously aftected, according to their propori- 

 tions to the various lengths of the line which 

 is the difference between the lengths of their 

 two paths, and which may b denominated 

 ihe interval of retardation. 



In order that the effect may be the more 

 perceptible, a numlier of pairs of points must 

 be united into two parallel lines ; and, if 

 several such pairs of lines be placed near 

 each other, they will facilitate the observa- 

 tion. If one of the Jines be made to revolve 

 lound the other, ?w an .axi^, t\ie djepressioa 

 below the given plane will be as the sine of 

 the iuclina.,tiou ; and wijila thp eye and lu- 

 piinous object remain £,xed, the difference of 

 thelengthsof the paths will vary iis this sine. 



The i)cst subjects for the experiment aj:e 

 4l 



