ZOOLOGY AND BOTANY. MICROSCOPY, ETC. 819 



power of optical instruments as given in tlie latest discussions on the 



subject, and gives an experimental determination of the dioptric, and 



theuce the amplifying power of the Microscope by the methods used in 



the Laboratory of Medical Physics of the Faculty of Lyon. At the end 



of his paper he gives a table of the inverses of 1000 numbers from 



O'Ol to 10 •00, by which dioptrical calculations are much simplified. 



The conditions of visibility of an object seen by the naked eye and 



under constant illumination depend on the linear dimensions of the 



object, its distance from the eye, and on the acuteness of vision. If y 



is the absolute length of the object, and I its distance from the eye, the 



y 

 visual angle is proportional to y. The acuteness of vision is in the 



inverse ratio to the minimum visual angle under which two separated 

 luminous impressions are distinguished, so that if v denote the degree 

 of visibility of an object seen by an eye of acuteness V, we have 



V = \ J ' 



For an eye assisted by any optical apparatus, the four magnitudes 

 V, V, I, y will take new values v' , V, I' y', y' denoting the image of y. The 

 ratio of visibility of image and object W is then given by the equation 



w = -■ = ^', (1) 



V \ y I ^ '' 



which may be written 



V a 



W = ^.- (2) 



v' y 

 by replacing the ratio of the trigonometrical tangents -y- and -y by the 



angles a a under which image and object are seen, or by the arcs which 

 they intercept on the retina. For the same eye V = V and the ratio of 

 visibility becomes the amplifying power T, which M. Monoyer defines 

 as " the ratio in which an instrument increases the apparent magnitude 

 of objects," and we have 



a 



The object of a magnifying instrument is to increase the visibility 

 of objects. Formula (1) shows that this can be attained either by 

 diminishing l, as in the simple magnifier, or in augmenting y' as in the 

 projection-lens or solar Microscope, or, finally, in uniting both, as in 

 the compound Microscope. The degree of visibility, then, does not 

 depend solely on the magnification (grossissement), i. e. on the ratio of the 

 absolute dimensions of image and object, but also on the distances from 

 the eye ; and it is to a confusion between magnification and amplifying 

 power (joouvoir amplfiant) that many erroneous results are to be attri- 

 buted. Thus, the formula given by many authors, G = 1 + — , introduces 

 the distance of distinct vision D, but neglects the distance of the lens 

 from the eye. The older formula G = — in use up to the beginning of 



3 L 2 



