Now we have in this means of stating the ratio of aperture a means of performing a most useful operation, —namely, of testing not only whether one lens is less or more rapid than another, but by what precise amount it is less or more rapid. That this is a thing most useful to be able to know must be evident. We are continually using different kinds of lenses, and, as we explained before, we require at different times to use various sizes of stops. Now it is most useful to be able to say, when we are about to expose, "On such and such an occasion a subject just like this took so many seconds with such a lens and such a stop ; therefore, with the lens and stop which I am at present using I shall have to give so many seconds of exposure." The calculation necessary to make to be able to do this is a very easy one.
We have only to spare the denominator of the f ' fractions – f – f ' 10 — etc when we will have precisely the 4' 8 relative exposures. We would remind those who are rusty in their arithmetic that the denominator of a fraction is the lower figure, and that to square a number is to multiply it by itself. Thus 4 x 4 or 16 is 4 squared, S X S or 64 is S squared, 10 x 10 or 100 is 10 squared. And in the examples given of three lenses, one working at f another 10 and the third at the relative ex ' posures will be 16, 64, and 100,—that is to say, if the first required an exposure of 16 seconds, the others would require respectively 64 seconds and 100 seconds ; and if the first required a half or a quarter of 16 seconds—that is to say, S or 4 seconds—the others would require respectively a half and a quarter of 64 and 100 seconds—that is to say, 16 seconds and 25 seconds.
Possibly one more case will be useful. We have been working in an ordinary room using a lens of the " rapid landscape " type for portraits. We find that we have had to give 12 seconds. We want to discover what advantage we would gain by using a portrait lens.
We measure the aperture of our landscape lens, and find that it is 1 inch. The distance between the diaphragm and the ground glass we find to be 91 inches. We may disregard the fraction and say that the lens works at We We take a portrait lens and on measure ment find that the aperture of the front lens is 21-, inches, whilst the distance between the diaphragm and the ground glass or the focal length is 10 inches. This lens get 81 and H. The exposures with the two lenses will
be as 81 to 1G,—that is to say, with the portrait lens they will require a shade less than a fifth of what was required with the landscape lens. The landscape lens required 12 seconds, the portrait lens will require about seconds. The ability to make this simple calculation might be enough to determine us whether or not to purchase a lens of the last-mentioned description. A little further on is given a table where the average ex posures under various conditions are given for different apertures.
We now pass on to a description of the various forms of lenses which have been designed to suit different kinds of photographic work. We take first of all, as being the simplest, that known as The Single Lens, or at times the single achromatic or the single combination lens. The particular variety of this lens, which we illustrate, is known as the wide-angle landscape lens ; it differs from all other single lenses inasmuch as there go three pieces to make up the combination instead of two only, as is commonly the case. Certain advantages accrue from this.
The single lens is the most generally useful of all for landscape purposes. Its simplicity of form, there being only two reflecting surfaces, is a great advantage. The definition which it gives is exquisite; it is fairly rapid, its largest aperture being about • ' and it will, if it be 16 desired, include a fairly wide angle. In fact, it will take in far more than is necessary except in certain circum stances, which will be described in connection with land scape work. Its only drawback is that, as explained before, it will with some subjects give slight distortion.
We here illustrate the lens which hears the above title. It may be taken as typical of a class of lenses which are generally known as " rapid " landscape lenses. The different kinds vary slightly, but each consists essen tially of two lenses like single achromatic lenses fixed a little distance apart, and with the concave sides towards each other. The " rapid " lens is about the most useful of any, and is the one which the amateur should purchase if he wishes to work with one lens only. It will do for any kind of landscape work. It is specially adapted for instantaneous photography. It may be used for por traiture even in an ordinary room if the light be good and it gives no distortion.