ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 491 



TT 7 



favourable as possible, we get P = — : - ; H being tbe size of tbe image 



and D its distance from the nodal point. Putting d = 1, that is, choosing 

 for unit length the distance of distinct vision of the eye under consideration, 



we may write P = =-— • Now if S = distance between the second prin- 

 cipal plane of the instrument and the nodal point, / = distance between 

 the second principal focus and the second principal plane — = — ^^^—. 



1/8 

 Hence P = -(^l.|. - 



This is the formula which in different shapes appears as the expression 

 for the magnifying power; but an unjustifiable limitation is generally 

 imposed upon it by rejecting negative values of 8 and D. As a matter of 

 fact 8 is generally negative. (Supposing the eye at the left-hand side of the 

 page and looking towards the right, the positive direction is here taken as 

 from left to right, negative from right to left, the nodal point being origin.) 

 If 8 and D were always positive P would be increased by increasing 8 and 

 diminishing D, i. e. by bringing the eye as close as possible to the eye- 

 piece, so that the image is produced at the pundum proximum. The fact 

 that this is not done in practice is generally explained on physiological 

 grounds. The eye is withdrawn from the lens, it is said, so as to avoid the 

 prolonged effort of accommodation. M. Guebhard, on the other hand, 

 maintains that accommodation is relaxed simjdy because in most cases 

 nothing is gained by it. It will be seen that D may have any value between 

 the punctum proximum and the punctum remotum, i. e. between the greatest 

 and least distances of distinct vision, and the former may be equal to co 

 for emmetrojjy and even negative for hypermetropy. As regards 8, it is 

 in general physically impossible to bring the nodal point nearer to the 

 instrument than 12 mm., and few instruments have a longer focal length 

 than this, so that 8 is generally negative. 



The author then discusses the interpretation of the formula in the 

 different cases which may arise according as D is -(- o^ ~ > ^^(^ greater or 

 less than 8. With the Microscope, for example, where 8 is negative, D 

 positive, and 8 numerically less than D, 8 must be as small and D as large 

 as possible, that is to say, the eye must be brought close to the eye-piece, 

 but accommodation must be relaxed, so that vision takes place at the greatest, 

 and not, as is generally stated, at the least distance of distinct vision. 



D positive, 8 negative, and 8 greater than D is the case of the camera 

 obscura, or projection on a screen. 



The case of hypermetropy (D negative) is curious ; here 8 if -|- must 

 be small, but if negative must be as large as possible, and the instrument 

 will have its greatest power when the eye is withdrawn as far as possible 

 and has the image formed behind it at the greatest distance of distinct 

 vision ; the magnifying power continues to increase as the eye is moved 

 farther from the lens, and in this respect hypermetropy is attended 

 with a considerable advantage over every other peculiarity of vision. 



The author finally expresses a desire that opticians shoiild determine 

 not only the focal lengths of their instruments, but also the focal positions, 

 so that the actual magnifying power attainable could be calculated from 

 these data and from the i^hysical constants of the eye, instead of assuming, 

 as is generally done, that 250 or 300 mm. represents universally the 

 distance of distinct vision. 



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