The following table contains a statement of the apertures and magnifying powers of Newtonian Telescopes, and the focal distances of their eye-glasses. The first column contains the focal length of the great speculum in feet; the second, its linear aperture in inches; the third, the focal distance of the single glass in decimals, or in 1000ths of an inch, and the fourth column, contains the magnifying power. This portion of the table was constructed by using the dimensions of Mr. Hadley’s Newtonian Telescope, formerly referred to, as a standard—the focal distance of the great mirror being 62½ inches, its medium aperture 5 inches, and power 208. The fifth, sixth, and seventh columns contains the apertures of the concave speculum, the focal lengths of the eye-glasses and the magnifying powers, as calculated by Sir D. Brewster, from a telescope of Mr. Hauksbee, taken as a standard; whose focal length was 3 feet 3 inches, its aperture about 4 inches, and magnifying power 226 times.

INDEX:
A: Focal distance of concave metal.
B: Aperture of concave metal.
C: Focal distance of single eye-glass.
D: Magnifying power.
E: Aperture of the concave speculum.
F: Focal length of the eye-glass.
G: Magnifying power.

Sir D. Brewster’s Numbers.
A.B.C.D.E.F.G.
Feet.Inch.Dec.In.Dec.Inch.Dec.In.Dec.
0.860.167361.340.10756
11.440.199602.230.12993
22.450.2361023.790.152158
33.310.2611385.140.168214
44.100.2811716.360.181265
54.850.2972027.510.192313
65.570.3112328.640.200=1/5360
76.240.3232609.670.209403
86.890.33428710.440.218445
97.540.34431411.690.222487
108.160.35334012.650.228527
118.760.36236513.580.233566
129.360.36739014.500.238604
139.940.37741415.410.243642
1410.490.38443716.250.248677
1511.040.39146017.110.252713
1611.590.39748317.980.256749
1712.140.40350618.820.260784
1812.670.40952819.630.264818
19 13.200.414 55020.450.268852
2013.710.42057121.240.271885

One great advantage of reflecting telescopes above common refractors, is, that they will admit of eye glasses of a much shorter focal distance, and consequently, will magnify so much the more, for the rays are not coloured by reflection from a concave mirror, if it be ground to a true figure, as they are by passing through a convex glass though figured and polished with the utmost exactness. It will be perceived from the above table, that the focal length of the eye glasses is very small, the lowest there stated being only about 1/10 of an inch, and the highest little more than ¼ of an inch focal distance. Sir W. Herschel obtained the high powers which he sometimes put upon his telescopes, by using small double convex lenses for eye glasses, some of which did not exceed the one fiftieth of an inch in focal length. When the focal length of the concave speculum, and that of the eye glass are given, the magnifying power is found by dividing the former by the latter, after having reduced the focal length of the concave speculum to inches. Thus the 6 feet speculum, multiplied by 12, produces 72 inches, which, divided by Brewster’s number for the focus of the eye glass = 200, or 1/5 of an inch, produces a quotient of 360 as the magnifying power. It has been calculated that, if the metals of a Newtonian telescope be worked as exquisitely as those in Sir W. Herschel’s 7 feet reflector, the highest power that such a telescope should bear with perfect distinctness, will be found by multiplying the diameter of the great speculum in inches, by 74, and the focal distance of the single eye glass may be found by dividing the focal distance of the great mirror by the magnifying power. Thus 6.25—the aperture in inches of Herschel’s 7 feet Newtonian—multiplied by 74 is 462½, the magnifying power; and 7 multiplied by 12, and divided by 462.5 is 0.182 of an inch, the focal distance of the single eye glass required. But it is seldom that more than one half of this power can be applied with effect to any of the planetary bodies. For general purposes the power produced by multiplying the diameter of the speculum by 30, or 40, will be found most satisfactory.

The following are the general prices of reflecting telescopes as made by the London opticians.

£s.
A four feet, seven inch aperture, Gregorian Reflector; with the vertical motions upon a new invented principle, as well as apparatus to render the tube more steady in observation; according to the additional apparatus of small speculums, eye-pieces, micrometers, &c. from80 to 1200
Three feet long, mounted on a plain brass stand232
Ditto, with rack-work motions, improved mounting, and metals3918
Two feet long without rack-work, and with 4 magnifying powers, improved1515
Ditto with rack-work motion221
Eighteen inch on a plain stand99
Twelve inch Ditto66

The above are the prices stated in Messrs. W. and S. Joneses catalogue.

The following list of prices of the various kinds of reflecting telescopes is from Messrs. Tulley’s (of Islington) catalogue.

£s.
1 foot Gregorian reflector, on pillar and claw stand, metal 2½ inches diameter, packed in a mahogany box66
1½ foot ditto, on pillar and claw stand, metal 3 inches diameter, packed in mahogany box1111
2 feet ditto, metal 4 inches diameter1616
Ditto, ditto, with rack-work motions254
3 feet ditto, metal 5 inches diameter, with rack-work motions420
Ditto, metal 6 inches diameter, on a tripod stand, with centre of gravity motion685
4 feet ditto, metal 7 inches diameter, as above1050
6 feet ditto, metal 9 inches diameter, on an improved iron stand2100
7 feet Newtonian reflectors, 6 inches aperture, mounted on a new and improved stand1050
Ditto, ditto, metal 7 inches diameter1260
9 feet ditto, metal 9 inches diameter2100
10 feet ditto, metal 10 inches diameter3150
12 feet ditto, metal 12 inches diameter5250

Comparative brightness of achromatic and reflecting telescopes. The late astronomer royal, Dr. Maskelyne, from a comparison of a variety of telescopes, was led to the following conclusion,—‘that the aperture of a common reflecting telescope, in order to show objects as bright as the achromatic must be to that of an achromatic telescope as 8 to 5,’—in other words, an achromatic whose object glass is 5 inches diameter, will show objects with as great a degree of brightness as a reflector whose large speculum is 8 inches in diameter. This result, if correct, must be owing to the small number of rays reflected from a speculum compared with the number transmitted through an achromatic object glass.