Three at least will be required, and they can be obtained second-hand for about $2.50 or so. The most convenient power to start with are about 7, 15, and 30 to the inch of aperture, giving 63, 135, 270 on the 9 in. When experience is gained a fourth of about

55 to the inch will be useful for double stars and faint details on planets; and if a still higher power is required the field lens of this may be removed, the eye-lenses alone giving 75 to the inch, or 675 on the 9 in.; it will seldom or never be advisable or necessary to go so high. For general work it will probably be found that about 30 to the inch (270) is the most useful. If the focal length of the mirror is stated when buying, the optician will supply the correct powers. Eyepieces by Zeiss and Steinheil are listed at $3 or so, with their focal lengths in millimetres marked on them. One millimetre =.04 in. nearly, and the magnifying power is equal to

Focal length of mirror Focal length of eyepiece

A Zollner star spectroscope to fit the 135 power will give good views of the spectra of stars down to the 3d or 4th magnitude. This merely requires fitting like a cap on to the flange of the previously focussed eyepiece.

For observation of the sun I recommend the method of projection on a sheet of paper or a card with a low eyepiece. If the expense of a diagonal solar reflector is allowable, the sun may be examined directly, with a dark glass cap, but under no circumstances should any attempt be made to examine the sun directly without some such aid. The heat concentrated by a 9 in. mirror or, indeed, by any size over 2 1/2 in. or 3 in. is enough to instantly melt or crack any dark glass on the eyepiece, unless, indeed, the mirror is used unsil-vered. If it is wished to examine the sun directly and no " solar diagonal " is at hand, the aperture should be reduced to 2 1/2 in., or at the most 3 in., by an "eccentric " stop, so that one side of the mirror only is used. This should not be placed in contact with the mirror, but a few inches away.

A cap with a very light neutral-tinted glass to fit the lowest power eyepiece is very useful for observing the moon. Of course, if caps, spectroscopes, etc., will fit all the eyepieces, so much the better; and all the eye pieces should, of course, be fitted with the standard screw.

A dew-cap, or short cylinder of tin or paper, blackened inside, to fit over the object-glass of the finder is most useful, and saves a lot of trouble due to dewing of the object-glass.

Before concluding, there is one piece of apparatus I should like to mention - the Barlow lens. This is an achromatic concave lens which, placed in front of the eyepiece at a few inches distance, at the same time enlarges the image and throws it further ont from the main tube. It is almost a necessity if a solar diagonal reflector is to be used. A very efficient substitute is an ordinary concave eyeglass of about 10 in. (negative) focus, which may be mounted in a wood or brass cylinder and placed inside the eyepiece tube. I used this plan for a considerable time for all purposes, as the concave lens has the effect, in my case, at least, of improving eatly the performance of an under-corrected mirror. Of course, with high powers a certain amount of color is introduced into the image, but much less than might be thought, while with low powers, for example, the prismatic effect was quite unnoticeable at or near the center of the field. I merely give this as a hint. A good mirror requires no such help.

I have now made as clear as I can how I was able to provide myself with a telescope which has proved of good quality at a very small cost. Throughout the articles I have recommended nothing that I have not myself tried and found successful; and even if the method I have adopted is imperfect, I think I may claim that it will for a given (small) sum of money provide a very much better instrument than could possibly be bought for the same sum. The cost of the 9 in. reflector I have described is, roughly, about $95, and I doubt if even a first-class 3 in. refractor could be bought secondhand for that sum. As from time to time queries are asked with regard to non-achromatic telescopes, perhaps I may conclude with a word of advice to the authors of those queries and others. It is this:

Do not attempt to make anything of the sort. Any non-achromatic telescope will be most unsatisfactory and not worth the trouble of fitting up. Make a reflector. If you are frightened at the details and difficulties of the work, get two 4 in. or 4 1/2 in. discs 3/1 or 1/2 in. thick. Grind the mirror to a good long focus5 or 6 ft. Never mind the testing of the curve, and polish on fine cloth instead of pitch, if you are afraid of pitch. Get a bit of plate glass 1 in. in diameter to serve as a flat. Get an eyepiece giving about a hundred diameters, and mount the whole thing roughly on a post. You will not have, a first-class instrument, but it will be as easy to make as a non-achromatic refractor, quite as cheap and immeasurably superior. This to the beginner who does not want to go to the trouble of testing, etc.; but there is no doubt whatever that he will sooner or later take up the work seriously and turn out a good instrument.

I trust that these articles may have been of some use to some beginner or other; and I must apologize for having taken so long to complete them.