A convex lens added to another lens shortens its focus, and a concave lens lengthens its focus. To find the result of such a combination, multiply the two foci and divide the answer by their sum minus the distance of separation. Thus, with an 8-in. lens added to a G in. lens at a distanee of 2 in.,(8x6)/(8+6-2)=48/12 in. If it is desired in a fixed focus camera with lens of 5 1/2-in. focus and extension of 6in., se1 lor 8ft., to include objects at 1ft., it will be necessary to find the focus to which the present Lens must be reduced. To do this, divide the distance between the lens and a, near object by the extension (or the distance from the lens to the plate), which gives the ratio or proportionate size of the image. Multiply the whole distanee by the ratio and divide the answer by the ratio plus one squared. Thus 12/6 = 2, the ratio.

((12+6)x2)/(2+1)2 = 4 in .To find the focus of the lens that must be used to reduce the 5 1/2-in. lens to 4 in., let a equal the focus of the present lens, b equal the required focus, and c equal the difference between the two foci; then axb/c=(5 1/2x4)/1 1/2 = 14 2/3. In order to prove that this will give the focus desired, the first rule given above should be used, namely, (14 2/3 x 5 1/2)/(14 2/3+5 1/2) = 4. It will be noticed that the distance of separation is ignored. This is becaus it is found convenient to use the lens inserted close against the front combination, where the separation is practically nil. The above focus need not be exact; 14 in. would be sufficiently near. The supplementary lenses should be preferably achromatic, but it does no1 necessarily follow that they will form an achromatic combination with the existing lens. Simple uncorrected spectacle lenses of varying foci may be used. For, although in any case the achromatism is upset by tin-addition of another lens, the difference is in most cases of no great consequence practically, unless the alteration exceeds about one-fourth of the focus. It is advisable, however, to use a smaller stop.

A convenient method is to slip the lens (which should be shanked to fit with a pair of old scissors) into the hood and keep it in correct position with a ring of metal sprung in. But the most satisfactory method is to have the lenses mounted in a sliding frame made to pass through the tube against the diaphragm.