'«40 



EXPERIMENTS AND CALCULATIONS. 



before tlie cavil, or a few inches behind it, 

 «o as either to throw tlie edge of its shadow 

 on the margin of the card, or to receive on 

 its own margin the extremity of the shadow 

 of the card, all the fringes which had be- 

 fore been observed in the shadow on the 

 wall immediately disappeared, although 

 vthe light inflected on the other side was 

 allowed to retain its course, and although 

 this light must have undergone any modi- 

 fication tliat the proximity of the other edge 

 of the slip of card might have been ca- 

 pable of occasioning. When the interposed 

 screen was at a greater distance behind the 

 narrow card, it was necessary to plunge it 

 more deeply into the shadow, in order to 

 extinguish the parallel lines; for here the 

 ligiit, diffracted from the edge of the object, 

 had entered further into the shadow, in its 

 way towards the fringes. Nor was it for 

 want of a sufficient intensity of light, that 

 one of the two portions was incapable of pro- 

 ducing the fringes alone; for, when t:hey 

 were both uninterrupted, the lines appeared, 

 ijvenif the intensity was reduced to one tenth 

 or one twentieth. 



iixjKr. 2. The crested fringes, described by 

 the ingenious and accurate Grimaldi, afford 

 an elegant variation of the preceding expe- 

 riment, and an interesting example of a 

 calculation grounded on it. When a sha- 

 dow is formed by an object which has a rec- 

 tangular terminiaion, besides the usual ex- 

 ternal fringes, there are two or three alterna- 

 .tions of colours, beginning from the line 

 which bisects the angle, disposed on each 

 side of it, in curves, which are convex to- 

 wards the bisecting line, and which converge 

 in some degree towards it, as they become 

 more remote liom the angular poini. These 



fringes are also the joint effect of the light 

 whigh is inflected directly towards the sha- 

 dow, from each of the two outlines of the 

 object. For, if a screen be placed within a 

 few inches of the object, so as to receive 

 only ene of the edges of the shadow, the 

 whole of the fringes will disappear. If, on 

 the contrary, the rectangular point of the 

 screen be opposed to the point of the sha- 

 dow, 60 as barely to receive the angle of the 

 shadow on its extremity, the fringes will re- 

 main undisturbed. 



II. COMPARISON OF MEASURES, DEDUCED 

 FROM VARIOUS EXPERIMENTS. 



If we now proceed to examine the dimen- 

 sions of the fringes, under different circum- 

 stances, we may calculate the differences of 

 the lengths. of the paths described by the 

 portions of light, which have thus been 

 proved to be concerned in producing those 

 fringes ; and we shall find, that where tlie 

 lengths are equal, the light always remains 

 white; but that, where either the brightest 

 light, or the light of any given colour, disap- 

 peiurs and reappears, a first, a second, or a 

 third time, the differences of thelengths of 

 the paths of the two portions are in arithme- 

 tical progression, as nearly as we can expect 

 experiments of this kirwl to agree with each 

 other. I shall compare, in this point of 

 view, the measures deduced from several ex- 

 periments of Newton, and from some of my 

 own. 



In the eighth and ninth observations of 

 the third book of Newton's Optics, some ex- 

 periments are related, which, together with 

 the third observation, will furnish us with 

 the data necessary for the calculation. Two 

 knives were placed, with their edges meeting 



