132 COLOURS or THIN PLATLS. 



air at the points where these rings are formed, #a, If3, cy, 

 &c., are as the squares of the distances 0#, 0&, Oc, &c., or as 

 the squares of the diameters of the rings. To determine the 

 law of the thicknesses, therefore, we have only to measure 

 these diameters. This was done by Newton with great ac- 

 curacy, and it was found that the squares of the diameters 

 were in arithmetical progression; consequently, the thick- 

 nesses corresponding to the successive rings formed a similar 

 progression. 



(145) But Newton did not stop here : he ascertained 

 further the absolute thickness of the plate of air at which each 

 ring was formed. It is manifest that if the thickness of the 

 plate be determined for any one ring, that corresponding to 

 the others will be given by the law just stated. Newton, 

 accordingly proceeded to ascertain this thickness for the dark 

 ring of the fifth order. This was done by measuring its 

 diameter accurately, and determining the radius of the spheri- 

 cal surface from the focal length of the lens and its refractive 

 index. The thickness is thence immediately deduced ; for it 

 is equal to the square of the radius of the ring divided by 

 the diameter of the spherical surface. The value thus de- 

 duced being suitably corrected, it was found that the thick- 

 ness of the plate of air was the yy^o o ^ an i ncn > a ^ the 

 dark ring of the fifth order ; and this thickness being decuple 

 of that corresponding to the first bright ring, it followed 

 that the thickness of the plate of air, at the place of the 

 first bright ring, was the iWooo f an i ncn - Thus the 

 bright rings of the successive orders are formed at the thick- 

 nesses 



* 3 5 _7 &c 

 1.78000' 178000' 178000, 178000 



-and the intermediate dark rings at the thicknesses 



2 4 6 i 



_ __ __ ___ 



178000 1 USuuO 1 178000' 178000 



&c . 



