216 



THEORY OF MICROSCOPIC OBSERVATION. 



be determined from the above formulae for the optical constants of 

 the refracting media. If we denote the negative focal length 

 reckoned from the axis of the cylinder by F, the absolute refractive 

 index by n t and the radii as before, by R and r, we obtain, under 

 the suppositions given below, the following values : 



This table affords, of course, only a superficial criterion of the 

 position of the focal point in hollow cylinders, and is intended to 

 show, by means of examples, the influence which the ratio of the 

 radii and the surrounding media in general exercise upon the focal 

 length. It is easily understood that if r is very small as compared 

 with R, the curvature of the outer surface of the cylinder may be 

 neglected ; the optical effect is then approximately equivalent to 

 that produced by a hollow space of equal radius in a homogeneous 

 substance of the density of the cylinder, and with plane bounding 

 surfaces above and below. Similarly, it is evident that if the ratio 

 r : R approaches unity, the focal length will become greater, and at 

 last infinite. The virtual image here remains microscopically ob- 

 servable only up to a certain limit, with extremely small values 

 of r and R, although still perceptible in tubes with somewhat thin 

 walls. 



If the focal lengths are determined for the above cases experi- 

 mentally, by measuring the displacement of the body-tube with 

 a second Microscope placed horizontally, we obtain throughout 

 smaller values than those calculated, because the observed focal 

 lengths, as was above (p. 201) stated, always refer to marginal 

 rays only, which are inclined towards the axis more or less (c.y. y 

 about 15 or 20) according to the power and speciality of the 

 objective. 



Since the image of a hollow cylinder, as well as every real or 

 virtual image, may be regarded as a source of light, the focal 



