Astronomical and Nautical Collections, 447 



dulations performed in the thickness of the glass ; and thd 

 proportion of these two numbers will be that of the veloci- 

 ties of light in the different mediums. Now this proportion 

 is found by experiment the same with that of the sines of 

 incidence and of refraction between air and glass ; which 

 agrees with the theory of the refraction of undulations, as 

 will be seen hereafter. 



The same experiment maybe employed, on the other hand, 

 for determining with extreme precision the thickness of a 

 thin plate of a substance of known refractive density; placing 

 it in the way of one of the two pencils of light, and measuring 

 the displacement of the fringes which it occasions. 



This method of determining: refractive densities is hoW*" 

 ever liable to some difficulties, when we wish to apply it to 

 a body much more dense than air, such as water, or glass, for 

 example ; since it is necessary to employ a very thin plate 

 only, in order that the fringes may not be too much dis- 

 placed for observation ; and then it becomes difficult 16 

 measure the thickness of such a plate with sufficient accu- 

 racy. We may, indeed, place in the way of the other pencil 

 a thick plate of a transparent substance, of which the refrac- 

 tive density has been ascertained by the ordinary methods, 

 and we can then employ as thick a plate of the new sub- 

 stance. But then it becomes simpler to measure its refrac- 

 tive density by the common method : [unless we choose to 

 immerse the whole apparatus in a fluid very nearly approach- 

 ing to it in refractive density, which may sometimes be done 

 without inconvenience. Tr.] 



The case, in which Mr. Arago''s experiment has a decided 

 advantage over the direct method, is when we desire to 

 determine very slight differences of velocity in mediums of 

 nearly equal refractive density : for by lengthening the pas- 

 sage of the light in the two mediums of which we wish to 

 compare the refractive density, we can increase the accuracy 

 of the results almost without limit. In order to form an ided 

 of tlie extreme precision that may be attained by these mea- 

 surements, it is sufficient to observe that the length of the 

 yellow undulations in air being about .000021 E.I., there are 



two millions of them in the length of about 42 inches. Now 



2 G 2 ■ -^ 



