Dioptrica nova, A treatise of dioptricks in two parts : wherein the various effects and appearances of spherick glasses, both convex and concave, single and combined, in telescopes and microscopes, together with their usefulness in many concerns of humane life, are explained / by William Molyneux of Dublin, Esq. ...

PROP. LV.

Concerning the Apertures of Object Glasses.

By the Aperture of a Glass I mean, that part of the Glass which is left open and uncovered. And this ought to be va∣rious

according as we would have more or less Light admitted. It also varies according to the various Focal lengths of the Ob∣ject-Glasses. For a ten Foot Object-Glass shall bear a greater Aperture than an Object-Glass of one Foot; and a twenty Foot Glass yet greater than a ten Foot Glass.

But at what Rate or Proportion the Apertures of Glasses alter in respect of their lengths, is not yet well setled.

Monsieur Auzout, (Phil. Transact. N. 4. P. 55.) Tells us, that he finds, That the Apertures, which Glasses can bear with Distinctness, are in (about) a Subduplicate Ratio to their lengths: Or as the Square Roots of their lengths. Whereof he intends to give the Reason and Demonstration in his Dioptrica (which we yet want.) But this Ingenious Person should have told us, when he speaks of the Apertures of Glasses, whether he de∣signs them for Objects on the Earth or in the Heavens. And if in this latter, whether for the Moon, Mars, Iupiter, or Venus. For each of these Objects will require a different Aperture of the same Glass. Because the Strength of their Light is diffe∣rent. For to view Venus there is requisite a much smaller Aperture, than to view the Moon, Saturn or Iupiter.

However till some better Rule can be found for settling the Apertures of Object-Glasses (which at present I shall not pre∣tend to) I shall here Present you with Mr. Auzout's Table, as 'tis to be found in the fore-cited Philosophical Transaction, Numb. 4. Noting only, that his Feet are Parisian Feet (which is to the London Foot as 1068: to 1000) and each Inch (which is the ¹ ₁₂ part of his Foot) is subdivided into twelve Lines. For it had not been worth our Pains to have reduced the whole Table to our English Measure. Vid. Tab. 36.

I have said before (Schol. 2. Prop. LIV.) That the Angle received, or Visible Area of an Object, is not Increased or Di∣minished by the greater or lesser Aperture of the Object-Glass; all that is effected thereby is the Admittance of more or less

[illustration]

A TABLE of the Apertures of Obiect-Glasses▪ The Points put to some of these Numbers denote Fractions.

Length of Glasses.	For Excellent ones.	For good ones.	For ordinary ones.
Feet. Inchs	Inch. Lines	Inch. Lines.	Inch. Lines.
4	4	4	3
6	5	5	4
9	7	6	5
0	8	7	6
1 6	9	8	7
2 0	11	10	8
2 6	1 0	11	9
3 0	1 1	1 0	10
3 0	1 2	1 1	11
4 0	1 4	1 2	1 0
4 6	1 5	1 3	1
5 0	1 6	1 4	1 1.
6	1 7	1 5	1 2
7	1 9	1 6	1 3
8	1 10	1 8	1 4
9	1 11.	1 9	1 5
10	2 1	1 10	1 6
12	2 4	2 0	1 8
14	2 6	2 2	1 9.
16	2 8	2 4	1 11.
18	2 10	2 6	2 1
20	3 0	2 7	2 2.
25	3 4	2 10	2 4.
30	3 8	3 2	2 7
35	4 0	3 4	2 10
40	4 3	3 7	3▪
45	4 6	3 10	3 2.
50	4 9	4 0	3 4.
55	5 0	4 3	3 6.
60	5 2	4 6	3 8.
65	5 4	4 8	3 10
70	5 7	4 10	3▪
75	5 9	5 0	4 2.
80	5 11	5 2	4 5
90	6 4	5 6	4 7.
100	6 8	5 9	4 10
120	7 5	6 5	5 3
150	8 0	7 0	5 11
200	9 6	8 0	6 9
250	10 6	9 2	7 8.
300	11 6	10 0	8 5
350	12 61	10 9	0 0
400	13 4	11 6	9 8

The feet here expres'd are Paris-feet, and a Line is the ¹ ₁₂ part thereof. The Paris-Foot is to the London-foot as 1068 to 1000

Tab. 36. pag. 170

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Rays; and consequently the more Bright or Obscure Appear∣ance of the Object. Tab. 35. f. 5. Let the greater Aperture of the Object-Glass x y z be x z; And the lesser Aperture m n. a b is a Remote Object Projected in the Distinct Base d e f. The Cone of Rays x a z is Projected in the Cone of Rays x d z; And consequently the Cone of Rays m a n (as be∣ing a part of the former x a z) shall be Collected at d in the Cone m d n. But then by this latter Aperture m n, all the Rays that fall on the outward Ring of the Glass, here expres∣sed by x a m, z a n, are excluded, and consequently the Point d shall not be illustrated with so much light as were the Aper∣ture as wide as z x. And therefore (supposing an Eye-Glass behind this Object-Glass, so as to constitute a Telescope) such a vigorous Light from each Radiating Point in the Object will not be brought into the Eye.

We have the exact Natural Resemblance hereof in the Eye it self: whose Pupil is contracted and dilated, according as the Light of an Object is more or less Intense.

Another Particular, wherein this Contraction or Dilatation of a Glasses Aperture is requisite, is this : An Object may be so nigh a Glass that the Rays from each single Point, falling upon the whole Breadth of the Glass, may Diverge so much that the Glass is not able to Correct the Divergence of those Rays that fall towards its outward Borders, so as to reduce them to Determine or Unite in the Distinct Base with those Rays, that fall nigher the middle of the Glass (as before is noted after Prop. III.) And then 'tis requisite to contract the Aperture of the Glass, so as to exclude these Exorbitant Rays. A notable Experiment of this we may make by holding a Minute Object very nigh the Pupil of the Eye, the Object shall appear very Confused. But by applying a Paper with a small Pin-hole before the Pupil, it shall reduce the Appearance to much more Distinctness than before.

Notes

• T. 35. F. 5