Dr. Pearson mentions that an old Dollond’s telescope of 63 inches focal length, and 3¾ inches aperture, supposed to be an excellent one, was brought to Mr. Tulley, when he was present, and the result of the examination was that its achromatism was not perfect. The imperfection was thus determined by experiment. A small glass globe was placed at 40 yards distance from the object-end of the telescope when the sun was shining, and the speck of light seen reflected from this globe formed a good substitute for a large star, as an object to be viewed. When the focal length of the object-glass was adjusted to this luminous object, no judgment could be formed of its prismatic aberrations, till the eye-piece had been pushed in beyond the place of correct vision; but when the telescope was shortened a little, the luminous disk occasioned by such shortening was strongly tinged with red rays at its circumference. On the contrary, when the eye-piece was drawn out, so as to lengthen the telescope too much, the disk thus produced was tinged with a small circle of red at its centre, thereby denoting that the convex lens had too short a focal length; and Mr. Tulley observed, that if one or both of the curves of the convex lens were flattened till the total focal length should be about 4 inches increased, it would render the telescope quite achromatic, provided in doing this the aberration should not be increased.
The following general remarks may be added. 1. To make anything like an accurate comparison of telescopes, they must be tried not only at the same place, but as nearly as possible at the same time, and, if the instruments are of the same length and construction, if possible, with the same eye-piece. 2. A difference of 8 or 10 times in the magnifying power, will sometimes, on certain objects, give quite a different character to a telescope. It has been found by various experiments that object-glasses of two or three inches longer focus will produce different vision with the same eye-piece. 3. Care must be taken to ascertain that the eye-glasses are perfectly clean and free from defects. The defects of glass are either from veins—specks—scratches—colour, or an incorrect figure. To discover veins in an eye or an object-glass, place a candle at the distance of 4 or 5 yards; then look through the glass, and move it from your eye till it appear full of light—you will then see every vein, or other imperfection in it which may distort the objects and render vision imperfect. Specks or scratches, especially in object-glasses, are not so injurious as veins, for they do not distort the object, but only intercept a portion of the light. 4. We cannot judge accurately of the excellence of any telescope by observing objects with which we are not familiarly acquainted. Opticians generally try an instrument at their own marks, such as the dial-plate of a watch, a finely engraved card, a weather-cock, or the moon and the planet Jupiter, when near the meridian. Of several telescopes of the same length, aperture and magnifying power, that one is generally considered the best with which we can read a given print at the greatest distance, especially if the print consists of figures, such as a table of logarithms, where the eye is not apt to be deceived by the imagination, in guessing at the sense of a passage, when two or three words are distinguished.
There is a circumstance which I have frequently noticed, in reference to achromatic telescopes, particularly those of a small size, and which I have never seen noticed by any optical writer. It is this,—if the telescope, when we are viewing objects, be gradually turned round its axis, there is a certain position in which the objects will appear distinct and accurately defined; and if it be turned round exactly a semicircle from this point, the same degree of distinctness is perceived; but in all other positions, there is an evident want of clearness and defining power. This I find to be the case in more than ten 1 foot and 2 feet telescopes now in my possession; and therefore I have put marks upon the object-end of each of them, to indicate the positions in which they should be used for distinct observation.—This is a circumstance which requires, in many cases, to be attended to in the choice and the use of telescopical instruments, and in fixing and adjusting them on their pedestals. In some telescopes this defect is very striking, but it is in some measure perceptible in the great majority of instruments which I have had occasion to inspect. Even in large and expensive achromatic telescopes this defect is sometimes observable. I have an achromatic whose object-glass is 41/10 inches diameter, which was much improved in its defining power, by being unscrewed from its original position, or turned round its axis—about one-eighth part of its circumference. This defect is best detected by looking at a large printed bill, or a sign-post at a distance, when, on turning round the telescope or object-glass, the letters will appear much better defined in one position than in another. The position in which the object appears least distinct is when the upper part of the telescope is a quadrant of a circle different from the two positions above-stated, or at an equal distance from each of them.
7. On the mode of determining the magnifying power of Telescopes.
In regard to refracting telescopes, we have already shown that, when a single eye-glass is used, the magnifying power may be found by dividing the focal distance of the object-glass by that of the eye-glass. But when a Huygenian eye-piece, or a four-glass terrestrial eye-piece such as is now common in achromatic telescopes, is used, the magnifying power cannot be ascertained in this manner; and in some of the delicate observations of practical astronomy, it is of the utmost importance to know the exact magnifying power of the instrument with which the observations are made, particularly when micrometrical measurements are employed to obtain the desired results.—The following is a general method of finding the magnifying powers of telescopes when the instrument called a dynameter is not employed; and it answers for refracting and reflecting telescopes of every description.
Having put up a small circle of paper, an inch or two in diameter, at the distance of about 100 yards, draw upon a card 2 black parallel lines, whose distance from each other is equal to the diameter of the paper circle. Then view through the telescope the paper circle with one eye, and the parallel lines with the other; and let the parallel lines be moved nearer to or further from, the eye, till they seem exactly to cover the small circle viewed through the telescope. The quotient obtained by dividing the distance of the paper circle by the distance of the parallel lines from the eye, will be the magnifying power of the telescope. It requires a little practice before this experiment can be performed with accuracy. The one eye must be accustomed to look at an object near at hand, while the other is looking at a more distant object through the telescope. Both eyes must be open at the same time, and the image of the object seen through the telescope must be brought into apparent contact with the real object near at hand. But a little practice will soon enable any observer to perform the experiment with ease and correctness, if the telescope be mounted on a firm stand, and its elevation or depression produced by rack-work.
The following is another method, founded on the same principle:—Measure the space occupied by a number of the courses, or rows of bricks in a modern building—which, upon an average, is found to have 8 courses in 2 feet, so that each course or row, is 3 inches. Then cut a piece of paper 3 inches in height, and of the length of a brick—which is about 9 inches—so that it may represent a brick, and fixing the paper against the brick wall, place the telescope to be examined at the distance of about 80 or 100 yards from it. Now, looking through the telescope at the paper with one eye, and at the same time, with the other eye, looking past the telescope, observe what extent of wall the magnified image of the paper appears to cover, then count the courses of bricks in that extent, and it will give the magnifying power of the telescope. It is to be observed, however, that the magnifying power determined in this way, will be a fraction greater than for very distant objects, as the focal distance of the telescope is necessarily lengthened in order to obtain distinct vision of near objects.
In comparing the magnifying powers of two telescopes, or of the same telescope, when different magnifying powers are employed, I generally use the following simple method. The telescopes are placed at 8 or 10 feet distant from a window, with their eye-ends parallel to each other, or at the same distance from the window. Looking at a distant object, I fix upon a portion of it whose magnified image will appear to fill exactly two or three panes of the window. Then putting on a different power, or looking through another telescope, I observe the same object, and mark exactly the extent of its image on the window-panes, and compare the extent of the one image with the other. Suppose for example, that the one telescope has been previously found to magnify 90 times, and that the image of the object fixed upon exactly fills three panes of the window, and that with the other power or the other telescope, the image fills exactly two panes, then the magnifying power is equal to two thirds of the former, or 60 times; and were it to fill only one pane, the power would be about 30 times. A more correct method is to place at one side of the window, a narrow board, two or three feet long, divided into 15 or 20 equal parts, and observe how many of these parts appear to be covered by the respective images, of the different telescopes. Suppose, in the one case, 10 divisions to be covered by the image, in a telescope magnifying 90 times, and that the image of the same object in another telescope, measures 6 divisions, then its power is found by the following proportion, 10 : 90 : 6 : 54 : that is, this telescope magnifies 54 times.
Another mode which I have used for determining, to a near approximation, the powers of telescopes, is as follows:—Endeavour to find the focus of a single lens which is exactly equivalent to the magnifying power of the eye-piece, whether the Huygenian or the common terrestrial eye-piece. This may be done by taking a small lens, and using it as an object-glass to the eye-piece. Looking through the eye-piece to a window and holding the lens at a proper distance, observe whether the image of one of the panes exactly coincides with the pane, as seen by the naked eye; if it does, then the magnifying power of the eye-piece is equal to that of the lens. If the lens be ½ inch focal length, the eye-piece will produce the same magnifying power, as a single lens when used as an eye-glass to the telescope, and the magnifying power will then be found by dividing the focal distance of the object-glass by that of the eye-glass. But if the image of the pane of glass does not exactly coincide with the pane as seen by the other eye, then proportional parts may be taken by observing the divisions of such a board as described above, or we may try lenses of different focal distances. Suppose, for example, that a lens 2 inches focal length had been used, and that the image of a pane covered exactly the space of two panes, the power of the eye-piece is then equal to that of a single lens 1 inch focal distance.
The following is another mode depending on the same general principle. If a slip of writing-paper one inch long, or a disk of the same material of one inch diameter, be placed on a black ground at from 30 to 50 yards distance from the object-end of the telescope, and a staff painted white, and divided into inches and parts by strong black lines, be placed vertically near the said paper or disk; the eye that is directed through the telescope when adjusted for vision, will see the magnified disk, and the other eye, looking along the outside of the telescope, will observe the number of inches and parts that the disk projected on it will just cover, and as many inches as are thus covered will indicate the magnifying power of the telescope—at the distance for which it is adjusted for distinct vision. The solar power, or powers for very distant objects, may be obtained by the following proportion:—As the terrestrial focal length, at the given distance: is to the solar focal length :: so is the terrestrial power, to the solar power. For example, a disk of white paper one inch in diameter, was placed on a black board, and suspended on a wall contiguous to a vertical black staff that was graduated into inches by strong white lines, at a distance of 33 yards 2½ feet, and when the adjustment for vision was made with a 42 inch telescope, the left eye of the observer viewed the disk projected on the staff, while the right eye observed that the enlarged image of the disk covered just 58½ inches on the staff, which number was the measure of the magnifying power, at the distance answering to 33 yards 2½ feet—which in this case exceeded the solar focus by an inch and a half. Then according to the above analogy, we have, as 43.5 : 42 :: 58.5 : 56.5 nearly. Hence the magnifying power due to the solar focal length of the telescope in question is 56.5, and the distance 33 yards 2½ feet, is that which corresponds to an elongation of the solar focal distance an inch and a half.[31] If we multiply the terrestrial and the solar focal distances together, and divide the product by their difference, we shall again obtain the distance of the terrestrial object from the telescope. Thus, (43.5 + 42)/1.5 = 1218 inches = 101.5 feet, or 33 yards 2½ feet.