Explication

of the Re

when they confpire together, and in their mean Distances from the Earth, is to the Force (G) of Gravity as 5,4815X1 to 4,4815X2871400, or as I to 2347565, and the Sum of the greatest Forces of the Luminaries, or at their leaft Distance from the Earth, is to the Force of Gravity, as I to 2032890. From whence it appears, that thofe Forces united, cannot deflect the Direction of Gravity, nor confequently the Pendulum, from the true Vertical the 10th Part of a Second, nor caufe a Variation in the Length of the Pendulum beating Seconds, which would exceed the of a Line, &c.

T

THEORY of the REFRACTION of LIGHT.

I.

HE Effects which Bodies exert on each other by their Attraction, become fenfible only when it is not abforbed by the Attraction of fraction of the Earth, and it appears that this mutual Attraction of Bodies becomes Light deriv ed from the fenfible only when they are almoft contiguous, and that then it Principle of acts in a Ratio greater than the inverse Triplicate of the Distances. Attraction. Now the Atmosphere, or the Mafs of Air encompaffing the Earth, acting on Light in a very fenfible Manner, it is certain, that if Attraction be the Caufe, it fhould follow this Ratio.

The Sine of

Incidence

and Refrac

tion are al

ways in a conftant Ratio.

The Advantage of the Principle of Attraction confifts in having no Need of any Suppofition but only the Knowledge of the Phenomena, and the more accurate are the Obfervations and Experiments, the easier it is to apply this Principle to their Explication.

II.

It is well known, that Light traverfing Mediums of different Denfities, changes its Direction. Snellius, and after him Defcartes, found from Experiment, that the Sine of Incidence and that of Refraction are always in a conftant Ratio; and Newton employs the 14th and laft Section of the first Book of the Principia in explaining the Reason why thofe Sines fhould be in a conftant Ratio, and proving that this Ratio depends on the Principle of Attraction. It is in this Explication we fhall follow Newton.

Every Ray of Light which enters obliquely into any Medium, is to be confidered as a Body acted on at the fame Time by two Forces, in order to apply to the Explication of their Effects the Principles of Mechanicks. Defcartes and Fermat confidered Light as a Body of a sensible Magnitude on which the Mediums act after the fame Manner as they appear to do on other Bodies: and finding that the Mediums which Light traverses, produce in them Effects quite contrary to those which fhould refult from the Principles of Mechanicks, they invented each an Hypothefis in order to reconcile, in this Cafe, the Laws of Mechanicks, which are inconteftable, and the phificial Effects which are almost as certain.

III.

of Refracti

It is well known, that the denfer the Mediums are, the greater Refistance Bodies which penetrate them meet with in feparating their Parts. Now, in this Cafe, the Angle of Refraction is greater than the Angle of Incidence, because the vertical Velocity of the Body being diminished by the Refistance of the Mediums, the horizontal Velocity influences The Laws more the Direction of the Diagonal which the Body in obeying the on of Bodies two Forces into which its Motion is refolved, defcribes; hence it is, that of a fenfible when the Resistance of the Medium is infurmountable, the Body, instead Magnitude. of penetrating the Medium, returns back by its Elafticity, and the Proportion between this Refiftance and the vertical Velocity of the Body may be fuch, that the Body would lofe all its vertical Velocity, and would flide on the Surface of the Medium if it had no Elafticity, and if the Surface of the Medium was a perfectly smooth Plane.

IV.

is

of

The Laws

of Refraction of Light

different" from that

of Bodics

of a fenfible

Now quite the contrary happens to the Rays of Light, the denfer the Medium is which they traverse, the more the Sine of Incidence exceeds that of Refraction; therefore the vertical Velocity of the Rays increased in this Cafe, which is quite the Reverse of what the Laws Mechanicks feem to indicate. Defcartes, in order to reconcile them with Experiment, which he Magnitude. could not evade, maintained, that the denfer the Mediums were, the eafier Paffage they opened to Light; but this Manner of accounting for this Phenomenon was rather rendering it doubtful than explaining it. Fermat, finding the Explication of Defcartes impoffible, thought it more advisable to have Recourse to Metaphificks, and the final Causes. Hypothefes

He afferted, that fince Light does not arrive to us by the fhorteft Paf- of Defeartes fage, which is the straight Line, it was becoming the Divine Wisdom, and Fermat. it should arrive in the shortest Time; this Principle, once allowed, it followed, that the Sines of Incidence and Refraction are to each other as the Facilities of the Medium to be penetrated.

V.

It is easy to see how Attraction solves this Difficulty; for this Principle evinces, that the progreffive Motion of Light, not only is not lefs retarded in the more denfe Medium, as Defcartes pretended, but is really accelerated, and that by the Attraction of the more dense Medium when it penetrates it. It is not only when the Ray has arrived at the refracting Medium and at the Point of Incidence that it acts on it; the Incurvation of the Ray commences fome Time before, and it increases in proportion as it approaches the refracting Medium, and even within this Medium to a certain Depth.

Attraction accounts for every Circumftance attending Light in its Paffage through one Medium into another; for the vertical Velocity of

Attraction accounts

for every

Circumftance at

tending the Refraction of Light.

Experiments of Newton

which prove

that the Re

fraction of

Light depend on

the Density of the Mediums thro' which

it paffes.

The Rays of Light have not all the fame

Degree of Refrangibility.

the Ray is increased in the more dense Medium, which it traverses until it arrives at the Point where the fuperior and inferior Parts of this Medium act with equal Force on it, then it continues to advance with the acquired Velocity until being on the Point of quitting it, the fuperior Parts of this Medium attract it with a greater Force than the inferior Parts. The vertical Velocity of the Ray is diminished thereby, and the Curve it defcribes at its Emerfion, is perfectly equal and fimilar to the one it defcribed at its Incidence, (the Surfaces which bound the refra&ing Medium being fuppofed parallel) and the Position of this Curve is directly oppofite to that of the first. In fine, the Ray passes through Degrees of Retardation which are in the fame Ratio, and in the fame inverse Order as the Degrees of Acceleration which it passed through at its Incidence.

VI.

Newton, who was as fuperior in the Art of making Experiments as in that of employing them, found on examining the Deviation of the Rays of Light in different Mediums, that the Attraction exerted on the Particles of Light follows the Ratio of the Density of those Mediums, if we except those which are greasy and fulphurous. Since then the different Denfities of those Mediums is the Caufe of the Refraction of Light, the more homogeneous Bodies are, the more tranfparent they will be; and those which are most heterogeneous will be least fo, for the Light in traverfing them, being perpetually reflected in different Directions within thofe Bodies, the Quantity of Light which arrives to us is thereby diminished; hence it is, that when the Sky is clear, the Stars are fo diftinctly perceived, but when clouded, the Řays are intercepted, and cannot reach the Earth.

VII.

Newton alfo found, that every Ray of Light, however fmall, is compofed of feven Rays, which as long as they are united continue white, but resume their natural Colour when they are feparated, and that those Rays have not all the fame Degree of Refrangibility, that is, in paffing through one Medium into another of different Denfity, are inflected fome more and others lefs; fo that when they pass through a Lens, those Rays do not all meet the Axe at the fame Distance, but some nearer and others farther off, and thus form as many diftin&t Pictures of the Object as there are Colours. The Eye only perceives the most vivid, but as the Pictures are not equal, the greatest form round those, feveral coloured Circles, which is called the Crown of Aberration. This Aberration is quite diftin&t from that which arifes from the Defect of Reunion of the Rays caufed by the spherical Figure of the Lenfes.

The Aberration of Refrangibility in the Rays of Light is not fenfible when their Refraction is inconfiderable; now the Rays parallel to the

optic Axe of a Lens, and thofe at a fmall Distance from this Axe, are very little inflected, and the Picture they form may be confidered as fimple, as not being furrounded by any coloured Circles. Hence it is, that Artists are under the Neceffity of giving to the objective Glafs an Aperture of a very small Number of Degrees of the Sphere of which this Glass forms a Part, and confequently of increafing the focal Diftance of this Glafs, and the Length of the Telescope, as often as they change the Proportion of the objective and ocular Glaffes, in order to increase its magnifying Power. Thofe Obftacles to the Perfection of refracting Telescopes arifing from the Nature of Light, and the Laws of Refraction, Newton was on the Point of removing; an Experiment he made opened the Way which leads to this Difcovery, but he did not purfue it: the Experiment is as follows: As often as Light, tra- Method for verfing different Mediums, is fo corrected by contrary Refractions, that it correcting emergeth in Lines parallel to thofe in which it was Incident, continues ration ever after white. OPTICS, First B. Part II. Exp. 8.

How the

the Aber

arifing from Euler in 1747, meditating on this Subject, demonftrated, that this Affer- the different. Refrangibition was false, and confequently that the Experiment was ill made. Mr. Do- lity of the lond, an eminent English Optician, well versed in the Theory and Practice Rays was of his Art, repeated this Experiment after the fame Manner that Newton difcovered. defcribed it; he conftructed for this Purpose, with two Plates of Glafs, a Kind of Port-folio, which being filled with Water, formed a Prism of Water, that by clofing or opening the Glaffes, was fufceptible of all Kinds of Angles; he plunged into the Water of this Prifm, whofe Angle was turned downwards, another Prism of Chrystal, whofe Angle was turned upwards,, and by moving the Plates of Glafs, he found that Inclination which was neceffary to make the Objects obferved through the two Prisms of Water and Glafs appear exactly at the fame Height as they did to the naked Eye; it was then manifeft, that the Refraction of one Prifm was destroyed by the Refraction of the other, yet the Objects were tinged with various Colours, which was quite contrary to what Newton had afferted. Mr. Dolond afterwards tried, by moving the Plates of his Prism of Water, whether there was not fome poffible Proportion between the Angles of the two Prisms capable of deftroying the Colours, and found that there was such a Proportion, which widely differed from that which destroys the abfolute Refraction. The Objects not coloured viewed through the Prifms thus combined, not appearing at the fame Height as when viewed by the naked Eye. From whence it was eafy to conclude, that the Aberration of the Rays arifing from their different Degrees of Refrangibility, might be corrected by employing transparent Mediums of different Denfities, and that the Rays would be refracted, but in a different Manner from what they would be in paffing through one Medium. Mr. Dolond in 1759, difcovered a Method

The Principle of Attraction

ferves to explain how Refraction

is changed

tion.

answering this Purpofe, which he has employed with Success in the Construction of achromatic Telescopes, and the most eminent Mathematicians have fince exerted all their Skill in investigating the different Combinations for the focal Distances, and the Quantity of Curviture requifite to correct at once, the Aberration arising as well from the different Degrees of Refrangibility of the Rays, as from the circular Figure of the Lenfes. Those Researches fhall be explained hereafter.

VIII.

The Principle of Attraction ferves to explain why the Refraction is changed into Reflection at a certain Obliquity of Incidence, when the Rays of Light pafs through a more dense Medium into a less dense one; for in the Paffage of a Ray through a more denfe Medium into another that is lefs, the Curve it defcribes is inflected towards the more dense into Reflec- Medium it has paffed through; now the Proportion between its Obliquity and the Force which draws it towards this more dense Medium may be fuch, that its Direction may become parallel to the Surface of the Medium which it quits, before it has paffed the Limits within which the Attraction of this Medium is confined; and in this Cafe, it is very easy to fee, that it should return toward the refracting Medium it had quitted, defcribing a Branch of a Curve equal and fimilar, to the Curve which it described in paffing through this Medium, and reaffume after having again entered this Medium the fame Inclination it had before it quitted it.

The Action of the Medium which Light traverses, may give the Rays the Obliquity they require in order to be reflected, and as the more the Mediums differ in Denfity the lefs is the Obliquity of Incidence requifite that the Rays may be reflected, the Rays will be reflected at the leaft Obliquity of Incidence when the contiguous Space or refracting Medium will be purged of Air, and when the Vacuum will be most perfect. And fo it happens in the Air-Pump, in which the more the Vacuum is increased, the quicker a Ray is reflected at the fuperior Surface of a Prifm placed therein. The Refraction is therefore changed into Reflection at different Incidences, according to the Denfity of the different Mediums, Diamond which is the most brilliant Body known, operates an entire Reflection when the Angle of Incidence is only 30 Degrees, and it is according to this Angle Jewellers cut their Diamonds, that they may lose the leaft Quantity of the Light they receive.

IX.

It is eafy to perceive, that when a Ray of Light paffes through a lefs denfe Medium into a more compact one, the Refraction cannot be changed into Reflection let the Obliquity of Incidence be ever fo great, for when the Ray is on the Point of quitting the lefs denfe Medium, the other Medium which is contiguous to it, begins to act on it, and