To measure the distance of an object from one station. This depends upon the increase of the focal distance of the telescope in the case of near objects. Look through a telescope at the object whose distance is required, and adjust the focus till it appear quite distinct; then slide in the drawer, till the object begins to be obscure, and mark that place of the tube precisely. Next draw out the tube till the object begins to be again obscured, and then make another mark as before. Then take the middle point between these two marks, and that will be the point where the image of the object is formed most distinctly; which is to be nicely measured from the object lens, and compared with the solar focus of the lens or telescope, so as to ascertain their difference. And the rule for finding the distance is,—‘As the difference between the focal distance of the object, and the solar focal distance : Is to the solar focal distance :: So is the focal distance of the object : To its true distance from the object lens.’ An example will render this matter more perspicuous.
figure 84.
Let AB (fig. 84.) be the object lens, EY the eye-glass, FC the radius, or focus of the lens AB, and Cf the focal distance of the object OB, whose distance is to be measured. Now suppose CF = 48 inches, or 4 feet, and that we find by the above method that Cf is 50 inches, then Ff is 2 inches; and the analogy is:—As Ff = 2, is to CF = 48, so is Cf = 50, to CQ = 1200 inches, or 100 feet. Again, suppose Cf = 49 inches, then will Ff = 1 inch; and the proportion is, 1 : 48 :: 49 : 2352 = QC, or 196 feet. A telescope of this focal length, however, will measure only small distances. But, suppose AB a lens whose solar focus is 12 feet, or 144 inches; and that we find, by the above method, that Cf, or the focal distance of the object, is 146 inches; then will Ff be 2 inches, and the proportion will be, as 2 : 144 :: 146 : 21024 inches, or 1752 feet = the distance QC. If with such a large telescope, we view an object OB, and find Ff but 1/10th of an inch, this will give the distance of the object as 17292 feet or nearly 3⅓ miles.
Since the difference between the radius of the object lens and the focal distance of the object is so considerable as 2 inches in a tube of 4 feet, and more than 12 inches in one of 12 feet, a method might be contrived for determining the distance of near objects by the former, and more distant objects by the latter, by inspection only. This may be done by adjusting or drawing a spiral line round the drawer or tube, through the two inch space in the small telescope, and by calculation, graduate it for every 100 feet, and the intermediate inches, and then, at the same time we view an object, we may see its distance on the tube. In making such experiments, a common object-glass of a long focal length, and a single eye-glass, are all that is requisite; since the inverted appearance of the object can cause no great inconveniency.
CHAPTER VII.
ON THE METHOD OF GRINDING AND POLISHING OPTICAL LENSES AND SPECULA.
I originally intended to enter into particular details on this subject, for the purpose of gratifying those mechanics and others who wish to amuse themselves by constructing telescopes and other optical instruments for their own use; but, having dwelt so long on the subject of telescopes, in the preceding pages, I am constrained to confine myself to a very general sketch.
1. To grind and polish lenses for eye-glasses, microscopes, &c.
First provide an upright spindle, at the bottom of which a pulley is fixed, which must be turned by a wheel by means of a cord and handle. At the top of the spindle make a screw the same as a lathe-spindle, on which you may screw chocks of different sizes, to which the brass tool in which the lens is to be ground, may be fixed. Having fixed upon the breadth and focal length of the lens, and whether it is to be a plano, or a double convex—take a piece of tin-plate or sheet copper, and, with a pair of compasses, draw an arch upon its surface, near one of its extremities, with a radius equal to the focal distance of the lens, if intended to be double convex, or with half that distance, if it is to be plano-convex. Remove with a file that part of the copper which is without the circular arch, and then a convex gage is formed. With the same radius strike another arch, and having removed that part of the copper which is within it, a concave gage will be obtained. The brass tool, in which the glass is to be ground, is then to be fixed upon a turning-lathe, and turned into a portion of a concave sphere, so as to correspond to the convex gage. In order to obtain an accurate figure to the concave tool, a convex tool of exactly the same radius is generally formed, and they are ground one upon another with flour emery; and when they exactly coincide, they are fit for use. The convex tool will serve for grinding concave glasses of the same radius—and it should be occasionally ground in the concave tool to prevent it from altering its figure.