CAMPANI'S EYE-PIECE : COMBINED ACTION WITH OBJECTIVE. 39 



If, then, p* is the distance of the image from the second principal 

 plane and / the focal length, the coefficient of amplification is 



p* 

 given by the formula, applicable for all cases, m = 1 , in 



which the negative sign indicates the inversion of the image. If 

 m is taken as positive, this expression becomes 



-,. 



T ~7~ 



from which latter formula the following relation may be directly 

 derived : If the eye is situated in the second focal point of the 

 Microscope, so that the distance of distinct vision is expressed 

 by p* /, the magnifying power is exactly proportional to this 

 distance. In other words, the virtual images which the Microscope 

 forms with different adjustments for short- and long-sighted eyes, 

 are seen at the same angle when viewed from the second focal 

 point, and must, therefore, exactly coincide. 



The combined action of the Microscope has been fully explained 

 above. We have still to trace the actual course of the rays of 

 light within the eye-piece and subsequent to their emergence from 

 the eye-lens. Since the objective-image, which serves as a virtual 

 object for the eye-piece, must be taken (with a vision of 200 mm.) 

 as 12'041 mm. from the plane surface of the eye-lens, the position 

 of the image formed by the field-lens can easily be calculated. 

 If its focal length is 40 mm., as above assumed, we obtain 

 from the given distance of the virtual object (= 49 12 '12041 

 = 35'959) a conjugate focus of 18'936 mm. This is the distance, 

 reckoned from the second principal point of the field-lens, at 

 which the true image actually appears, and where, therefore, the 

 diaphragm and the eye-piece micrometer must be applied in order 

 to be seen as distinctly as the image. 



The pencils of light which leave the objective have their base 

 upon its second principal plane ; their inclination to the axis is 

 determined by the rays of direction, which emanate from the corre- 

 sponding points of the object and may be regarded as the axes of 

 the pencils. Since these axes all emanate from one point, that 

 is, from the second principal point of the objective, they must also, 

 after refraction in the eye-piece, intersect in one point, and this latter 

 point is the image of the former. Its position is determined for the 



