CAMPANl'S EYE-PIECE: COMBINED ACTION WITH OBJECTIVE. 37 



quantity for tlie same observer, since the eye is, within certain 

 limits, capable of accommodation. The magnifying power of the 

 eye-piece, in particular, undergoes considerable fluctuations ; for 

 instance, the number 4'01, which corresponds to a vision of 

 200 mm., decreases to 1*93 for short-sighted persons whose limit 

 of distinct vision is 100 mm. Neither does the magnifying power 

 of the objective remain constant, as the position of the real image 

 also varies with the range of vision, and consequently the ratio 

 of the anterior to the posterior focus. Short-sighted persons bring 

 the objective -image nearer to the eye-lens and thus move the final 

 virtual image closer also ; this lengthens the posterior focus of the 

 objective, and shortens the anterior. The magnifying power of the 

 objective is consequently increased, while that of the eye-piece is 

 decreased. Since, however, the latter takes place in a far greater 

 degree, the final virtual image is so much the smaller, and the 

 combined amplification is consequently so much the less, the 

 shorter the distance of distinct vision. For comparison the mag- 

 nifying powers are given below for different ranges of sight. The 

 tube-length from the first to the last refracting surface is taken at 

 200 mm., and the objective amplification, when p* is equal to 

 200 mm., at 88-0096 (vide table on p. 34). 



From this comparison we see, in the first place, that the eye- 

 piece amplification is approximately proportional to the range of 

 vision, while the objective amplification shows small fluctuations 

 in the opposite direction; whence it follows that the combined 

 amplification also varies with the range of vision. But the mathe- 

 matical relation is not given by it, and a glance at the last column 

 is sufficient to show that the ratio of the magnifying powers differs 

 by several units from that of the distances of distinct vision. It 

 would be a matter of calculation to find out whether, and to what 

 degree, these differences continue, when, instead of the last surface 

 of the eye-piece, an adjacent point in the axis, which nearly 

 corresponds to the position of the eye during observation, is 



