Virtual Images & Initial Magnifying Power. By E. M. Nelson. 1 83 
of accommodation of 8 in., if the eye is held close to the lens, the 
power will be, as in table, 6^ (formula i.) ; but if the eye is held 
] }, in. from the lens, at the back principal focus, the power will be one 
less than that given in the table, or 5J (formula ii.). 
The real image formed by the lens on a screen, distant 8 in. from 
the lens, will be amplified two diameters less than that in the table, 
or 4J times (formula iii.). 
The expression, “ The reciprocal of the focus is the power of the 
lens” was introduced by Herscliel (Art. Light, Eucy. Metrop.). In 
the paper referred to above, Abbe recommends microscopists to sub- 
stitute this expression of Herschel’s for the usual formula 
m = 
_ /• 
•01 
If Herschel’s formula were adopted, the power of a 4-in. lens would 
be 1/4, that of an inch 1, and a 1/2-in. 2. For my own part, while 
fully admitting the usefulness of “ the reciprocal of the focus ” for 
optical formulae, I cannot see how the powers of the above lenses are 
more intelligibly rendered by the figures 1/4, 1, and 2 than by the 
old notation of 2|, 10, 20. 
It must be understood that microscopists are not necessarily 
either opticians or mathematicians ; so, if this new nomenclature were 
adopted, a note must be appended to explain that when an image 
produced by a 1-in. lens is viewed, either when virtual or on a screen, 
it will not be of the same size as the object, a meaning which the 
new nomenclature would seem to convey. It will be said that 
the figures given by the new nomenclature are only proportional to 
the power, a statement which gives us this highly interesting fact, 
that “ the power of a lens ” is proportional to its power ! It will be 
noticed that, whether the old or new nomenclature is adopted, it will 
only hold true in the one case (formula ii.) of a virtual image, where 
the eye is held at the back principal focus of the lens. In each of 
the other cases neither nomenclature gives a correct answer, or even 
one proportional to it, but I think none will deny that the old nomen- 
clature conveys a better general impression in these cases than the 
other is likely to do. 
We now come to another point in Abbe’s paper, where he states 
that the magnification is the same in the case ot virtual images what- 
ever the accommodation may be, because the images are viewed under 
the same visual angle. In order to discuss this often argued and 
much misunderstood subject it will be advisable to dispense with 
everything that is likely to cause confusion or ambiguity. I therefore 
propose to deal with the images on the retina, as the size of these 
under varying conditions can be exactly calculated. It will be neces- 
sary first to reduce the phrase “ magnifying power ” to its simplest 
terms. Magnifying power is the amount of the enlargement of the 
retinal image. The advantage of this definition lies in the fact that 
the retinal image is a real or screen image, and therefore we may dis- 
pense with all consideration of the ghostly virtual images and the 
