VELOCITY OF LIGHT IN WATER AND AIR. 125 



the light is moving from it to the spherical mirror E and back again ; and the 

 angular displacement of the returning ray around the centre M will, according 

 to the well-known law of reflection, be double the angular change of position of 

 the mirror. If the mirror makes n turns in a second, the time of one turn will 

 be the wth part of a second, and the time of making the change of position of 

 which the observation gives us the evidence, will be the same fraction of the n\\x 

 part of a second that half the angle subtended by RR' or RR", as the case 

 may be, at the centre M, is of SGO""; or as iRR' is of a whole circumference. 

 This distance' RR' or RR", being equal to SS' or SS", is directly measured 

 by the micrometer. Let it be put == o. The circumference of the circle whose 

 radius is RM, (which put = r,) is 2-r. Put the space ME;=5, or 2ME = 

 25, and the time of passing 2ME ;=:;{. Also let v represent the velocity of 

 light. Then — 



<5 ^ 2s 8-rns 



t=- ; andt' = — = ^--. 



'^-rn t 



J This expi-ession is, however, true only on the assumption that the returning 

 ray suflfers no deviation in passing the lens C. But since, if its original path 

 was, as we have assumed, the axis of the lens, it cannot, if sensibly deviated, 

 return through the axis, it will be bent at C, and the displacement RR' will be 

 less than we have assumed it to be. If D be the actually observed displacement, 

 and if RO be represented by r' and MC by s', then the value of our assumed 

 displacement in the above formula will become, as may easily be shown — 



sr' 



Substituting this value, we shall have for the velocity of light — 



With a distance * = 4 metres, and 800 turns of the mirror per second, Mr. 

 Foucault found a value of D = 6'"™, whence the value of v is found to be, in 

 English miles, 192,950.* 



13y placing a second fixed mirror, F, in any other convenient position, and 

 interposing a tube, as GH, filled with water or any other transparent medium, 

 the ends of the tube being closed with plate glass having parallel surfaces, the 

 velocities of light in air and such a medium may be compared. The mirrors E and 

 F will both give images of the wire at R; and if the value of v is the same for 

 both, the two images will be coincident, and appear as one; but if v have dif- 

 ferent values for the different media, one of the images will be more displaced 

 than the other. Mr. Foucault performed this experiment; and, in order to 

 identify the images, and to distinguish one from the other, he placed before the 

 mirror E a screen having a rectangular opening, such that one-third part of the 

 image from that mirror should be cut oft" from the top, and another third from 

 the bottom, the central third only being left unobstructed. In the image of the 

 aperture at R, as seen at O, the middle third had, very sensibly, greater bright- 

 ness than the top or the bottom, and the wire, as reflected fi'om E, was a^ipar- 

 ently but one-third as long as it appeared reflected from F. The image from F 

 was sensibly the most displaced, indicating lower velocity in water than in air; 

 the displacement, D, in the formula above, being a factor of the denominator. 



The next discovery of importance in the progress of optical science was made 

 near the close of the last century, by Dr. Wollaston, in his observations upon 

 the prismatic spectrum. He discovered that, by employing a pencil of light 



^- By Mr. Foucault's more recent experiments with this method, the velocity of light is 

 reduced to 190,249. IG miles. 



