A big part of what I do with the microscope comes directly out of books. I have no formal training with the microscope so books dealing with it usually contain something that I was totally unaware of, or just provide a solid footing. Occasionally they clear up misconceptions, which happed just this morning actually.

Microscope objectives are designated in many ways, but chief among them is by their magnification. Unfortunately for the beginner, there is more than one way to describe the magnification of an objective. For quite a long time objectives (and oculars) were described and marketed primarily by their focal length. They might also be described by the times they magnify an image, (as in 10x, 40x, 100x) or by the diameters of magnification they provide; a way that until recently I thought synonymous with the times designation.

The focal length of an objective (if you’ll forgive a generalization) is really just the distance from an object at which the objective is in primary focus. There are a few factors that can alter the distance for practical reasons, but in essence an objective with a focal length of 4mm needs to be 4mm from the object it is focused upon, an 8mm at 8mm, a 1/12in at one twelfth of an inch and so on.

An objective might also be described by the number of times it magnifies an image, the today ubiquitous “X” marked on nearly anything with a lens. The square root of the number of times magnified, provides the number of diameters of magnification. So that it may be said an objective that magnifies twenty five times, provides five diameters of magnification. Who knew?

I can say that I have seen articles and forums where the term “diameters” is used when speaking of “times,” I’ve even done it myself. Let us now turn to an old authority, Alfred Cheatham Stokes, in his book Microscopical Praxis:

A lens of any kind magnifying ten diameters is said to magnify one hundred times, or ten diameters in each direction, “times” representing the square of the “diameters,” and the diameters the square-root of the times.

It’s certainly odd that this does not appear to be more widely known, or Stokes more widely read. Microscopical Praxis is out of print and has been for years, so long in fact that it is in the public domain and one can find it nearly anywhere that handles or reprints public domain books.  Here’s a link to it at the Internet Archive.

In preparation for an upcoming effort I will need to mix up a solution. This solution needs to be of a particular concentration and to do that I’ll need to think back to chemistry class. One of the best parts of chemistry was mixing things together just to see what would happen, whatever the results. However, when one wishes to create something specific it’s important to know how to go about it.

It’s been my experience as an amateur microscopist that there are generally two types of guides out there; those made for children, and those made for professionals. I’m not saying there are no guides for the enthusiastic amateur, there are many very nice websites, periodicals, clubs, societies and forums out there which provide both advanced and accessible resources, I’m simply pointing out that if one picks up a book on the microscope or microscopic methods it’s apt to be either highly technical or exceedingly simplistic. Even the most technical of microscopy books can be wealths of information for the amateur, but such works often make certain assumptions concerning the knowledge of the reader in other fields, particularly chemistry.

Suppose one day in an effort to properly treat a specimen one follows a guide that calls for a 10% solution of something. At this point one has two options; purchase the solution, or purchase its components and prepare it ones self. If each of the components of the solution are liquids it’s a simple math problem. Computing the necessary ratio of components for any desired final volume is the work of a moment. However, when mixing a dry component and a liquid component things might get a bit tricky for people who have forgotten about mass.

To determine the ratio of two ingredients necessary when one is a solid and the other a liquid one must first measure them in a common unit, mass. When measuring each ingredient by grams it makes no difference if one or both is liquid or solid. To make things even simpler, one can look up the mass of a given volume of nearly any liquid and measure out the liquid component in milliliter and the solid component in grams.

The next time you see a recipe that calls for one part this and four parts that, just remember that the unit in which you measure is inconsequential so long as all ingredient are measured in the same unit, and consider buying a balance.