A series of lines,.3 mm. wide, was viewed from a distance of 17 feet. Each line was made up of 10 mm. sections, separated by small intervals that were the same between the sections of each line, but differed for every line. It was found that a line, whose sections were.5 mm. apart, was visible as a discontinuous line. A line with the sections .25 mm. apart appeared continuous.
With the power usually used at Flagstaff, the first figures would correspond on the planet at opposition to a line five and a half miles wide visible as a discontinuous line, if the sections were eight miles apart. That the Martian markings should be composed of a series of dotted lines, separated by intervals never greater than eight miles, would seem far more wonderful than the canals themselves.
There is a wide-spread feeling that the double canals are due to diffractive effects in the telescope. The writer wishes to state, at soine length, why it appears to him that this can not be the case.
The writer has made many experiments, with various telescopes, on dark lines on a light field viewed by reflected light. In no ease has he been able to detect diffractive effects that in any way resemble the double canals of Mars, as seen in the Lowell refractor, while, on the other hand, parallel lines, close together, bear a striking similarity to the double canals.
In dealing with this subject, it is surprising to find how little is really known of diffractive effects caused by a dark line on a light field. This is the gist of the whole matter, and is a very different thing from the well-known effects of diffraction obtained when viewing a point, or a line, of light on a dark field.
In viewing a luminous point on a dark field through a given telescope the distance of the rings of diffraction from the center of the spurious disk may be easily found from the formula , where is the angle measured from the objective to the focus; c is a constant for each maximum or minimum; is a wave-length, and r is the radius of the objective. Now the second maximum, or the radius of the first bright ring, measures about 0″.31 in the Lowell refractor. If we extend this point to form a line, the ring will be transformed into
- Various observers have experimented at Flagstaff at different times with wires stretched against the sky, viewed at ever increasing distances. The distances at which a wire was distinctly visible varied with different individuals, and corresponded to an angular width for the wire varying from.69″ to.93″. Looking at Mars at opposition, with a power of 400, these angles would correspond on Mars to widths of from 0.31 to 0.42 miles. Making all possible allowance for loss of light, etc., in the telescope, it seems probable that, under favorable circumstances, a line less than a mile wide could be detected on the planet. By comparison with the finest micrometer threads, some of the single canals are estimated to be as much as 35 miles wide. The width of the various double canals, which remains constant for each canal, is estimated to range from 2° to 5° on the planet. This is found, by various terrestrial experiments at Flagstaff, to be far wider than lines that can be easily separated by the eye.