Chapter V: Appendix (4)

_A Table shewing the Altitude, to given heights of the _Mercury_._

Inch. Feet.

30 0 29 915 28 1862 27 2844 26 3863 25 4922 20 10947 15 18715 10 29662 5 48378 1 91831 0.5 110547 0.25 129262 0.1 29 mil. or 154000 0.01 41 m. or 216169 0.001 53 m. 278338

_A Table shewing the heights of the _Mercury_, at given Altitudes._

Feet. Inch.

0 30 00
1000 28 91
2000 27 86
3000 26 85
4000 35 87
5000 feet 24 93
1 mile 24 67
2 20 29
3 16 68
4 13 72
5 11 28
10 4 24
15 1 60
20 0 95
25 0 23
30 0 08
40 0 012

Upon these Suppositions it appears, that at the height of 41 Miles the Air is so rarified, as to take up 3000 times the Space it occupies here, and at 53 Miles high it would be expanded above 30000 times; but it's probable that the utmost Power of its Spring cannot exert it self, to so great an Extension, and that no part of the _Atmosphere_ reaches above 45 Miles from the Surface of the Earth.

This seems confirm'd from the Observations of the _Crepusculum_, which is observ'd commonly to begin and end when the Sun is about 18 Degrees below the Horizon; for supposing the Air to reflect light from its most rarified Parts, and that as long as the Sun illuminates any of its _Atoms_, they are visible to an Eye not intercepted by the Curvity of the Earth, it will follow from _Fig. 5. Plate 1._ that the proportion of the height of the whole Air, to the Semi-diameter of the Earth, is much about, as 1 to 90, or as the excess of the _Secant_ of about 8½ Degrees to the _Radius_. For if _E_ be the Eye of the Observer, _S_ a Place where the Sun sets at the end of Twilight in _E_, and the Arch _ECS_, or _TCA_, be found 18 Degrees, the excess of the _Secant_ of half thereof _ECH_, would be the height of the Air, _viz._ _GH_: But the Beam of the Sun _ASH_, and the Visual Ray _EH_, do each of them suffer a Refraction of about 32 or 33 Minutes, whereby being bent inwards from _H_ towards _G_, the height of the Air need not be so great as if they went streight; and having from the Angle _ECS_ taken the double Refraction of the _Horizontal Ray_, the half of the Remainder will be 8½ Degrees _circiter_, whose _Secant_ being 10,111, it follows, that as 10000 to 111, so the Semi-diameter of the Earth supposed 4000 Miles, to 44,4 Miles; which will be the height of the whole Air, if the Places _E_, _S_, whose visible Portions of the _Atmosphere_ _ERZH_, and _SHKB_, just touch one the other, be 18 Degrees asunder.

At this height the Air is expanded into above 3000 times the space it occupies here, and we have seen the Experience of condensing it into the 60th part of the same Space, so that it should seem, that the Air is a Substance capable of being compressed into the 180000th part of the Space it would naturally take up, when free from pressure. Now what Texture or Composition of Parts shall be capable of this great Expansion and Contraction, seems a very hard Question; and which, I suppose, is scarce sufficiently accounted for, by comparing it to Wool, Cotten, and the like springy Bodies.

Hitherto I have only consider'd the _Air_ and _Atmosphere_, as one unalter'd Body, as having constantly at the Earth's Surface the 800th part of the weight of Water, and being capable of Rarifaction and Condensation _in infinitum_; neither of which _Hypotheses_ are rigidly true: For here in _England_ it is notoriously known, that the weight of the whole _Atmosphere_ is various, being counterpoised sometimes by 28½ Inches of _Mercury_, and at other times by no less than 30½; so that the under parts being pressed by about a 15th part, less weight, the _specifick_ Gravity of the Air upon that score will sometimes be a 15th part lighter than another; besides Heat and Cold, does very considerably dilate and contract the Air, and consequently alter its Gravity; to which add the mixture of _Effluvia_, or steams arising from almost all Bodies, which assimulating into the Form of Air, are kept suspended therein, as Salts dissolv'd in Liquors, or Metals in corroding _Menstrua_; which Bodies being all of them very much heavier than Air, their Particles by their Admixture must needs encrease the weight of that Air they lie incorporated withal, after the same manner as melted Salts do augment the specifick Gravity of Water. The other Consideration is, that the Rarifaction and Condensation of the Air is not precisely according to the proportion here laid down; for the Experiment very nearly agrees thereto, as may be seen in the 58th Chapter of Mr. _Hook's_ _Micrography_; yet are the Condensations not possible beyond certain degrees: For being compressed into an 800th part of the Space it takes up here, its consistence would be equally dense with that of Water; which yields not to any force whatsoever, as hath been found by several Experiments tried here, and at _Florence_, by the _Academia del Cimento_. Nor can the Rarifaction proceed _in infinitum_; for supposing the Spring whereby it dilates it self, occasion'd by what Texture of Parts you please, yet must there be a determinate Magnitude of the natural State of each Particle, as we see it is in Wool, and the like, whose Bodies being compressable into a very small Space, have yet a determinate bulk which they cannot exceed, when free'd from all manner of Pressure.

These Objections being true, do disturb the Geometrical Accuracy of these Conclusions, drawn from the specifick Gravity of the Air observ'd at any time; but the Method here shewn will compute by a like Calculation, the heights of the Quick-silver, and the Rarifactions of the Air from any assign'd height of the _Barometer_ at the Earth's Surface, and any specifick Gravity given. As to the Condensation and Rarifaction by Heat and Cold, and the various mixture of Aqueous and other Vapours, these two Objections seem generally to compensate each other; for when the Air is rarified by Heat, they are raised most copiously; so that though the Air properly so call'd, be expanded, and consequently lighter, yet the _Interstices_ thereof being crouded full of Vapours of much heavier Matters, bulk for bulk, the weight of the _Compositum_ may continue much the same, at least a most curious Experiment made by the Ingenious Mr. _John Caswell_, of _Oxford_, upon the top of _Snowdon_ Hill, in _Carnarvanshire_, seems to prove, that the first Inches of _Mercury_ have their Portions of Air near enough to what I now determine: For the height of the Hill being 1240 Yards, or very near it, he found the _Mercury_ to have subsided to 25,6 Inches, or 4 inches below the mean Altitude thereof at the Level of the Sea, (which is a greater difference than has been found in any of our former Experiments,) and the Space answering to 4 Inches, by my Calculation, should be 1288 Yards; and it agrees as well with the Observations in the Appendix to Mr. _Pascall_'s Book, _del Equilibre des Liqueurs_, made on the high Hill in _Auvergne_, call'd _le puy de Domme_. So that the Rarifaction and Vapours seem not to have alter'd considerably, the Gravity of the under Parts of the _Air_; and much above the height where these Experiments were made, do few Vapours ascend, and the Cold is such that the Snow lies continually, so that for the more elevated Parts of the Sphere of _Air_, there is much less Reason to doubt.

But now we have had occasion to mention the difference there is between the height of the _Mercury_ at one time, from the height thereof at another, it may not be unacceptable to offer at some Reasons for the said difference; which, at least to my self, seem to have some appearance of Truth. _First_, Then it's undoubtedly demonstrable, that the height of the Cylinder of _Mercury_ is equal to the weight of the whole incumbent Air, and consequently that that whole is sometimes a fifteenth more than at other times; which cannot otherwise be, but by the access of new Matter when 'tis heavy, and its diminution when 'tis light; that _Hypothesis_ therefore that shews how the Air shall be encreased or diminished, in any particular place, will give a Reason for the greater and lesser height of the _Mercury_ in the _Baroscope_: But to direct us in the choice of the several Causes, which may be assign'd for the Increase and Decrease of the Air, 'twill not be unnecessary to enumerate some of the principal Observations made upon the _Barometer_, most whereof are sufficiently known already to all those that are curious in these Matters.

The _First_ is, That in calm Weather, when the Air is inclin'd to Rain, the _Mercury_ is commonly low.

2. That in serene good settled Weather, the _Mercury_ is generally high.

3. That upon very great Winds, though they be not accompanied with Rain, the _Mercury_ sinks lowest of all, with relation to the Point of the Compass the Wind blows upon.

4. That _cæteris paribus_ the greatest heights of the _Mercury_ are found upon Easterly and North-Easterly Winds.

5. That in calm frosty Weather the _Mercury_ generally stands high.

6. That after very great Storms of Wind, when the _Quicksilver_ has been low, it generally rises again very fast.

7. That the more Northerly places have greater Alterations of the _Baroscope_, than the more Southerly.

8. That within the _Tropicks_ and near them, those Accounts I have had from others, and my own Observation at St. _Helena_, make very little or no Variation of the height of the _Mercury_ in all Weathers.

Now that Theory that can well account for all these appearances, will, in all probability, approach nearer the true cause of the _Barometers_ Variations, than any thing hitherto afforded; and such an one I am bound to believe, is that which I here lay down with submission to better Judgments.

I conceive that the principal Cause of the rise and fall of the _Mercury_, is from the variable Winds, which are found in the _Temperate Zones_, and whose great unconstancy here in _England_ is most notorious. I shall not at present inquire into the Cause of its uncertainty, but the Matter of Fact being most undoubted, the Legitimate Consequences thereof must be allow'd me, let it proceed from what it will.

A second Cause is the uncertain Exhalation and Præcipitation of the Vapours lodging in the Air, whereby it comes to be at one time much more crowded than at another, and consequently heavier; but this latter in a great measure depends upon the former. Now from these Principles I shall endeavour to explicate the several _Phænomena_ of the _Barometer_, taking them in the same order I laid them down.

1. _Why in calm Weather the Air being inclin'd to Rain, the _Mercury_ is commonly low?_ I Answer, That the _Mercury_'s being low, inclines it to Rain; for the Air being light, the Vapours are no longer supported thereby, being become specifically heavier than the Medium wherein they floated; so that they descend towards the Earth, and in their fall meeting with other aqueous Particles, they incorporate together, and form little drops of Rain; but the _Mercury_'s being at one time lower than another, is the effect of two contrary Winds blowing from the place whence the _Barometer_ stands; whereby the Air of that place is carried both ways from it, and consequently the incumbent Cylinder of Air is diminished, and accordingly the _Mercury_ sinks; as for Instance, if in the _German Ocean_ it should blow a Gale of Westerly Wind, and at the same time an Easterly Wind in the _Irish Sea_; or if in _France_ it should blow a Southerly Wind, and in _Scotland_ a Northern; it must be granted me, that That part of the _Atmosphere_ impendent over _England_, would thereby be exhausted and attenuated, and the _Mercury_ would subside, and the Vapours which before floated in those parts of the _Air_ of equal Gravity with themselves, would sink to the Earth.

2. _Why in serene good settled weather the _Mercury_ is generally high?_ To this I Answer, That the greater height of the _Barometer_, is occasion'd by two contrary Winds blowing towards the place of Observation, whereby the Air of other places is brought thither and accumulated; so that the incumbent Cylinder of Air being encreas'd both in height and weight, the _Mercury_ press'd thereby must needs rise and stand high, as long as the Winds continue so to blow; and then the Air being specifically heavier, the Vapours are better kept suspended, so that they have no inclination to Præcipitate and fall down in Drops, which is the reason of the serene good Weather, which attends the greater heights of the _Mercury_.

3. _Why upon very great Winds or Storms, tho' accompanied with no Rain, the _Mercury_ sinks lowest of all, with relation to the Point of the Compass upon which the Wind blows?_ This is caus'd by the very rapid Motion of the Air in these Storms; for the Tract or Region of the Earths Surface, wherein these Winds rage, not extending all round the Globe, that stagnant Air which is left behind, as likewise that on the sides, cannot come in so fast as to supply the Evacuation made by so swift a Current; so that the Air must necessarily be attenuated, when and where the said Winds continue to blow, and that more or less, according to their Violence; add to which, that the _Horizontal_ Motion of the Air being so quick as it is, may in all probability take off some part of the perpendicular pressure thereof; and the great Agitation of its Particles, is the Reason why the Vapours are dissipated, and do not condense into Drops, so as to form Rain, otherwise the natural Consequence of the Airs Rarifaction.

4. _Why _cæteris paribus_ the _Mercury_ stands highest upon an Easterly or North-Easterly Wind?_ This happens because that in the great _Atlantick Ocean_, on this side the thirty fifth Degree of North Latitude, the Westerly and South-Westerly Trade-Winds blow almost always; so that whenever here the Wind comes up at East and North-East, 'tis sure to be checked by a contrary Gale, as soon as it reaches the Ocean; wherefore, according to what is made out in our second Remark, the Air must needs be heaped over this Island; and consequently the _Mercury_ must stand high, as often as these Winds blow. This holds true in this Country, but is not a general Rule for others, where the Winds are under different Circumstances; and I have sometimes seen the _Mercury_ here as low as twenty nine Inches, upon an Easterly Wind, but then it blows exceeding hard, and so comes to be accounted for by what was observ'd upon the third Remark.

5. _Why in calm Weather the _Mercury_ generally stands high?_ The cause hereof is, as I conceive, that it seldom freezes but when the Winds come out of the Northern and North-Eastern Quarters, or at least unless those Winds blow at no great distance off; for the Northern Parts of _Germany_, _Denmark_, _Sweden_, _Norway_, and all that Tract from whence North-Eastern Winds come, are subject to almost continual Frost all the Winter; and thereby the lower Air is very much condens'd, and in that State is brought hitherwards by these Winds, and being accumulated by the opposition of the Westerly Wind blowing in the Ocean, the _Mercury_ must needs be prest to a more than ordinary height, and as a concurring Cause, the shrinking of the lower parts of the Air into lesser room by cold, must needs cause a descent of the upper parts of the Atmosphere, to reduce the Cavity made by this contraction to an _Æquilibrium_.

6. _Why after very great Storms of Wind, when the _Mercury_ has been very low, it generally rises again very fast?_ This I have frequently observed, and once found it risen an Inch and a half in less than six Hours, after a long continu'd Storm of South-West Wind. This seems to be occasion'd by the sudden Accession of new Air to supply the great Evacuation which such continu'd Storms make thereof, in those places whence they happen (as in the third Remark) and by the Recoile of the Air, after the force ceases that impelled it; and the Reason why the _Mercury_ rises so fast, is because the Air being very much rarify'd beyond its mean density, the Neighbouring Air runs in the more swiftly to bring it to an _Æquilibration_, as we see Water runs the faster for having a great declivity.

7. _Why in more Northerly places the Variations of the _Baroscope_ are greater than in the Southerly?_ The truth of the Matter of Fact is prov'd from Observations made at _Clermont_ and _Paris_, compar'd with others, made at _Stockholm_, as may be seen in the Appendix to Mr. _Pascal_'s Book before-cited. The Reason I conjecture to be, that the more Northerly Parts have usually greater Storms of Wind than the more Southerly, whereby the _Mercury_ should sink lower in that Extream; and then the Northerly Winds bringing the condens'd and ponderous Air from the Neighbourhood of the Pole, and that again being check'd by a Southerly Wind, at no great distance, and so heaped, must of necessity make the _Mercury_ in such case stand higher in the other Extream.

8. And Lastly, _Why near the _Æquinoctial_, as at _Barbadoes_ and St. _Helena_, there is very little or no Variation of the height of the Barometer?_ This Remark, above all others, confirms the Hypothesis of the variable Winds, being the cause of these Variations of the height of the _Mercury_; for in the Places above-named, there is always an easie Gale of Wind blowing nearly upon the same Point, _viz._ E. N. E. at _Barbadoes_, and E. S. E. at St. _Helena_; so that there being no contrary Currents of the Air, to exhaust or accumulate it, the Atmosphere continues much in the same State. However, upon Hurricanes, the most violent of Storms, the _Mercury_ has been observ'd very low, but this is but for once in two or three Years, and it soon recovers its settled state of about 29½ Inches. I doubt not but the same thing is in the East Coast of _Africa_, and in _India_, where the Monsoons or Trade-Winds are for half the Year one way, and half the Year another; only it's probable, that there may something worth noting happen, about the times of the change or shifting of the Winds, which might be obtain'd, if any Body had the Curiosity to keep the _Barometer_ at our Factories in _India_.

I doubt not but this Doctrine will find some Opposers, and that one principal Objection will be, that I suppose the Air sometimes to move from those Parts where it is already evacuated below the _Æquilibrium_, and sometimes again towards those parts, where it is condens'd and crouded above the mean State, which may be thought contradictory to the Laws of Staticks and the Rules of the _Æquilibrium_ of Fluids. But those that shall consider how, when once an impetus is given to a Fluid Body, it is capable of mounting above its Level, and checking others that have a contrary tendency to descent by their own Gravity, will no longer regard this as a material Obstacle, but will rather conclude, that the great _Analogy_ there is between the rising and falling of the Water upon the Flux and Reflux of the Sea, and this of the accumulating and extenuating the Air, is a great Argument for the Truth of this Hypothesis: For as the Sea over against the Coast of _Essex_, rises and swells by the meeting of the two contrary Tides of Flood, (whereof the one comes from the S. W. along the Channel of _England_, and the other from the North); and on the contrary sinks below its Level upon the retreat of the Water both ways in the Tide of Ebb; so it is very probable that the Air may Ebb and Flow, after the same manner; but by reason of the diversity of Causes, whereby the Air may be set in moving, the times of these Fluxes and Refluxes thereof, are purely Casual, and not reducible to any Rule, as are the Motions of the Sea, depending wholly upon the regular Course of the Moon.

_A Letter of Mr. _Isaac Newton_, Professor of the Mathematicks in the
University of _Cambridge_; containing his New Theory about _Light_
and _Colours_: Sent by the Author to the Publisher from _Cambridge_,
Feb. 6. 1671/2; in order to be communicated to the _Royal Society_._

_SIR_,

To perform my late promise to you, I shall without further Ceremony acquaint you, That in the beginning of the Year 1666 (at which time I apply'd my self to the grinding of Optick-glasses of other Figures than _Spherical_,) I procur'd me a Triangular Glass-Prism, to try therewith the celebrated _Phænomena_ of _Colours_. And in order thereto, having darken'd my Chamber, and made a small hole in my Window-shuts, to let in a convenient quantity of the Sun's Light, I plac'd my Prism at his entrance, that it might be thereby refracted to the opposite Wall. It was at first a very pleasing Divertisement, to view the vivid and intense Colours produced thereby; but after a while applying my self to consider them more circumspectly, I became surpriz'd to see them in an _oblong_ Form; which, according to the received Laws of Rarefraction, I expected should have been _Circular_.

They were terminated at the sides with streight Lines, but at the ends, the decay of Light was so gradual, that it was difficult to determine justly, what was their Figure; yet they seem'd _Semicircular_.

Comparing the length of this colour'd _Spectrum_ with its breadth, I found it about five times greater; a disproportion so extravagant, that it excited me to a more than ordinary Curiosity of examining, from whence it might proceed. I could scarce think, that the various thickness of the Glass, or the termination with shadow or darkness, could have any Influence on Light to produce such an effect; yet I thought it not amiss, first to examine those Circumstances, and so try'd what would happen by transmitting Light through parts of the Glass of divers thicknesses, or through holes in the Window of divers bignesses, or by setting the Prism without, so that the Light might pass through it, and be refracted before it was terminated by the hole: But I found none of those Circumstances material. The fashion of the Colours was, in all these Cases, the same.

Then I suspected, whether by any unevenness in the Glass, or other contingent Irregularity, these Colours might be thus dilated. And to try this, I took another Prism like the former, and so plac'd it, that the Light passing through them both, might be refracted contrary ways, and so by the latter return'd into that Course, from which the former had diverted it. For, by this means, I thought the _regular_ effects of the first Prism would be destroy'd by the second Prism, but the _irregular_ ones more augmented by the multiplicity of Refractions. The Event was, that the Light, which by the first Prism was diffused into an _oblong_ Form, was, by the second, reduc'd into an _orbicular_ one, with as much regularity, as when it did not at all pass through them. So that whatever was the cause of that length, 'twas not any contingent Irregularity.

I then proceeded to examine more critically, what might be effected by the difference of the incidence of Rays coming from divers parts of the Sun; and to that end, measur'd the several Lines and Angles belonging to the Image. Its distance from the Hole or Prism was twenty two Foot; its utmost length 13¼ Inches; its breadth 2⅝; the Diameter of the Hole ¼ of an Inch; the Angle, with the Rays, tending towards the middle of the Image, made with those Lines, in which they would have proceeded without Refraction, was 44° 56'. And the Vertical Angle of the Prism, 63° 12'. Also the Refractions on both sides the Prism, that is, of the Incident, and Emergent Rays, were as near, as I could make them, equal, and consequently about 54° 4'. And the Rays fell perpendicularly upon the Wall. Now subducting the Diameter of the Hole from the length and breadth of the Image, there remains 13 Inches the length, and 2⅜ the breadth, comprehended by those Rays, which passed thro' the Center of the said Hole, and consequently the Angle of the Hole, which that breadth subtended, was about 31', answerable to the Sun's Diameter; but the Angle, which its length subtended, was more than five such Diameters, namely 2° 49'.

Having made these Observations, I first computed from them the refractive Power of that Glass, and found it measur'd by the _ratio_ of the Sines, twenty to thirty one. And then, by that _ratio_, I computed the Refractions of two Rays flowing from opposite parts of the Sun's _discus_, so as to differ 31' in their obliquity of Incidence, and found that the emergent Rays should have comprehended an Angle of about 31', as they did, before they were incident.

But because this Computation was founded on the Hypothesis of the proportionality of the Sines of Incidence and Refraction, which, tho' by my own Experience I could not imagine to be so erroneous as to make that Angle but 31', which in reality was 2° 49'; yet my Curiosity caus'd me again to take my Prism. And having plac'd it at my Window, as before, I observ'd, that by turning it a little about its _Axis_ to and fro, so as to vary its obliquity to the light, more than an Angle of four or five Degrees, the Colours were not thereby sensibly translated from their place on the Wall, and consequently by that Variation of Incidence, the quantity of Refraction was not sensibly varied. By this Experiment therefore, as well as by the former Computation, it was evident, that the difference of the Incidence of Rays, flowing from divers parts of the Sun could not make them, after decussation, diverge at a sensibly greater Angle, than that at which they before converged; which being, at most, but about thirty one or thirty two Minutes, there still remain'd some other cause to be found out, from whence it could be two Deg. 49 Min.

Then I began to suspect, whether the Rays, after their Trajection through the Prism, did not move in curve Lines, and according to their more or less Curvity, tend to divers parts of the Wall. And it increas'd my suspicion, when I remember'd that I had often seen a Tennis-Ball, struck with an oblique Racket, describe such a curve Line. For a Circular as well as a Progressive Motion being communicated to it by that stroak, its parts on that side, where the Motions conspire, must press and beat the contiguous Air more violently than on the other, and there excite a Reluctancy and Reaction of the Air proportionably greater. And for the same Reason, if the Rays of Light should possibly be globular Bodies, and by their oblique Passage out of one Medium into another, acquire a circulating Motion, they ought to feel the greater resistance from the ambient Æther, on that side, where this Motion conspires, and thence be continually bowed to the other. But notwithstanding this plausible ground of suspicion, when I came to examine it, I could observe no such Curvity in them. And besides (which was enough for my purpose) I observ'd, that the difference 'twixt the length of the Image, and Diameter of the Hole, through which the Light was transmitted, was proportionable to their distance.

The gradual removal of these suspicions, at length led me to the _Experimentum Crucis_, which was this; I took two Boards, and plac'd one of them close behind the Prism at the Window, so that the light might pass through a small hole, made in it for the purpose, and fall on the other Board, which I plac'd at about twelve Feet distance, having first made a small hole in it also, for some of that incident Light to pass through. Then I plac'd another Prism behind this second Board, so that the Light, trajected through both the Boards, might pass thro' that also, and be again refracted before it arrived at the Wall. This done, I took the first Prism in my Hand, and turn'd it to and fro slowly about its _Axis_, so much as to make the several parts of the Image, cast on the second Board, successively pass through the hole in it, that I might observe to what places on the Wall the second Prism would refract them. And I saw by the Variation of those places, that the Light, tending to that end of the Image, towards which the Refraction of the first Prism was made, did, in the second Prism, suffer a Refraction considerably greater than the Light tending to the other end. And so the true cause of the length of that Image was detected to be no other, than that _Light_ consists of _Rays differently refrangible_, which, without any respect to a difference in their incidence, were, according to their degrees of Refrangibility, transmitted towards divers parts of the Wall.

When I understood this, I left off my aforesaid Glass Works; for I saw, that the perfection of Telescopes was hitherto limited, not so much for want of Glasses truly figur'd, according to the prescriptions of Optick Authors (which all Men have hitherto imagin'd), as because that Light it self is a _Heterogeneous mixture of differently refrangible Rays_. So that, were a Glass so exactly figur'd, so as to collect any one sort of Rays into one Point, it could not collect those also into the same Point, which having the same Incidence upon the same Medium, are apt to suffer a different Refraction. Nay, I wonder'd, that seeing the difference of Refrangibility was so great, as I found it, Telescopes should arrive to that perfection they are now at. For, measuring the Refractions in one of my Prisms, I found, that, supposing the common Sine of Incidence upon one of its plains, was forty four Parts, the Sine of Refraction of the utmost Rays on the red end of the Colours, made out of the Glass into the Air, would be sixty eight parts, and the Sine of Refraction of the utmost Rays on the other end, sixty nine parts; so that the difference is about a twenty fourth or twenty fifth part of the whole Refraction. And consequently the Object glass of any Telescope cannot collect all the Rays, which come from one point of an Object, so as to make them convene at its _Focus_ in less room than in a Circular space, whose Diameter is the fiftieth part of the Diameter of its Aperture; which is an irregularity, some hundred of times greater, than a circularly figur'd _Lens_, of so small a section as the Object-glasses of long Telescopes are, would cause by the unfitness of its Figure, were Light _uniform_.

This made me take _Reflections_ into Consideration, and finding them regular, so that the Angle of Reflection of all sorts of Rays was equal to their Angle of Incidence; I understood, that by their mediation, Optick Instruments might be brought to any degree of Perfection imaginable, provided a _Reflecting_ Substance could be found, which would polish as finely as Glass, and _reflect_ as much Light as Glass _transmits_; and the art of communicating to it a _Parabolick_ Figure be also attain'd. But there seem'd very great Difficulties, and I have almost thought them insuperable, when I further consider'd, that every Irregularity in a reflecting Superficies makes the Rays stray five or six times more out of their due course, than the like Irregularities in a refracting one; So that a much greater Curiosity would be here requisite, than in Figuring Glasses for Refraction.

Amidst these Thoughts I was forc'd from _Cambridge_ by the Intervening Plague, and it was more than two Years before I proceeded further. But then having thought on a tender way of polishing, proper for Metal, whereby, as I imagin'd, the Figure also would be corrected to the last; I began to try what might be effected in this kind, and by degrees so far perfected an Instrument (in the essential parts of it like that I sent to _London_,) by which I could discern _Jupiter_'s four Concomitants, and shew'd them divers times to two others of my Acquaintance. I could also discern the Moon-like Phase of _Venus_, but not very distinctly, nor without some niceness in disposing the Instrument.

From that time I was interrupted, till this last Autumn, when I made the other. And as that was sensibly better than the first (especially for Day-Objects,) so I doubt not but they will be still brought to a much greater perfection by their Endeavours, who, as you inform me, are taking care about it at _London_.

I have sometimes thought to make a _Microscope_, which in like manner should have, instead of an Object-glass, a reflecting piece of Metal. And this I hope they will also take into Consideration: For those Instruments seem as capable of improvement as _Telescopes_, and perhaps more, because but one reflective piece of Metal is requisite in them, as you may perceive in _Plate 3. Fig. 1._ where _AB_ representeth the Object Metal, _CD_ the Eye-glass, _F_ their common Focus, and _O_ the other Focus of the Metal, in which the Object is placed.

But to return from this digression, I told you, that Light is not similar, or homogeneal, but consists of _difform_ Rays, some of which are more refrangible than others: So that of those, which are alike incident on the same Medium, some shall be more refracted than others, and that not by any virtue of the Glass, or other external Cause, but from a predisposition, which every particular Ray hath to suffer a particular degree of Refraction.

I shall now proceed to acquaint you with another more notable deformity in its Rays, wherein the _Origin of Colours_ is unfolded: Concerning which I shall lay down the _Doctrine_ first, and then, for its Examination, give you an Instance or two of the _Experiments_, as a Specimen of the rest.

The Doctrine you will find comprehended and illustrated in the following Propositions.

1. As the Rays of Light differ in degrees of Refrangibility, so they also differ in their disposition to exhibit this or that particular Colour. Colours are not _Qualifications of Light_, derived from Refractions, or Reflections of natural Bodies, (as 'tis generally believed) but _Original_ and _connate Properties_, which in divers Rays are divers. Some Rays are disposed to exhibit a red Colour and no other; some a yellow and no other, some a green and no other, and so of the rest. Nor are there only Rays proper and particular to the more eminent Colours, but even to all their intermediate Gradations.

2. To the same degree of Refrangibility ever belongs the same Colour, and to the same Colour ever belongs the same degree of Refrangibility. The _least Refrangible_ Rays are all disposed to exhibit a _Red_ Colour, and contrarily those Rays, which are disposed to exhibit a _Red_ Colour, are all the least Refrangible: So the _most Refrangible_ Rays are all disposed to exhibit a deep _Violet Colour_, and contrarily those which are apt to exhibit such a _Violet Colour_, are all the most Refrangible. And so to all the intermediate Colours in a continued Series belong intermediate degrees of Refrangibility. And this Analogy 'twixt Colours, and Refrangibility, is very precise and strict; the Rays always either exactly agreeing in both, or proportionally disagreeing in both.

3. The Species of Colour, and Degree of Refrangibility proper to any particular sort of Rays, is not mutable by Refraction, nor by Reflection from Natural Bodies, nor by any other Cause, that I could yet observe. When any one sort of Rays hath been well parted from those of other kinds, it hath afterwards obstinately retain'd its Colour, notwithstanding my utmost Endeavours to change it. I have refracted it with Prisms, and reflected it with Bodies, which in Day-light were of other Colours; I have intercepted it with the colour'd Film of Air interceding two compressed Plates of Glass; transmitted it through colour'd Mediums, and through Mediums irradiated with other sorts of Rays, and diversly terminated it, and yet could never produce any new Colour out of it. It would by contracting and dilating become more brisk, or faint, and by the loss of many Rays in some Cases very obscure and dark; but I could never see it chang'd _in specie_.

4. Yet seeming Transmutations of Colours may be made, where there is any mixture of divers sorts of Rays. For in such mixtures, the component Colours appear not, but by their mutual allaying each other, constitute a midling Colour. And therefore, if by Refraction, or any other of the aforesaid Causes, the difform Rays, latent in such a mixture, be separated, there shall emerge Colours different from the colour of the Composition. Which Colours are not new generated, but only made apparent by being parted; for if they be again intirely mix'd and blended together, they will again compose that Colour, which they did before separation. And for the same reason, Transmutations made by the convening of divers Colours are not real; for when the difform Rays are again severed, they will exhibit the very same Colours, which they did before they entered the Composition; as you see, _Blue_ and _Yellow_ Powders, when finely mixed, appear to the naked Eye _Green_, and yet the Colours of the component Corpuscles are not thereby really transmuted, but only blended. For, when viewed with a good Microscope, they still appear _Blue_ and _Yellow_ interspersedly.

5. There are therefore two sorts of Colours. The one Original and Simple, the other compounded of these. The Original or Primary Colours are, _Red_, _Yellow_, _Green_, _Blue_, and a _Violet-purple_, together with Orange, Indico, and an indefinite variety of intermediate Gradations.

6. The same Colours in _Specie_ with these primary Ones, may be also produced by Composition: For, a mixture of _Yellow_ and _Blue_ makes _Green_; of _Red_ and _Yellow_, makes _Orange_; of _Orange_ and _Yellowish Green_, makes _Yellow_. And in general, if any two Colours be mix'd, which in the Series of those, generated by the Prism, are not too far distant one from another, they by their mutual Alloy compound that Colour, which in the said Series appeareth in the mid-way between them. But those, which are situated at too great a distance, do not so. _Orange_ and _Indico_ produce not the intermediate _Green_, nor _Scarlet_ and _Green_ the intermediate _Yellow_.

7. But the most surprizing and wonderful Composition was that of _Whiteness_. There is no one sort of Rays which alone can exhibit this. 'Tis ever compounded, and to its Composition are requisite all the aforesaid primary Colours, mix'd in a due proportion. I have often with admiration beheld, that all the Colours of the Prism being made to converge, and thereby to be again mixed as they were in the light before it was incident upon the Prism, reproduced light, intirely and perfectly white, and not at all sensibly differing from a _direct_ light of the Sun, unless when the Glasses, I used, were not sufficiently clear; for then they would a little incline it to _their_ Colour.

8. Hence therefore it comes to pass, that _Whiteness_ is the usual Colour of _Light_; for Light is a confused aggregate of Rays, indued with all sorts of Colours, as they are promiscuously darted from the various parts of luminous Bodies. And of such a confused aggregate, as I said, is generated Whiteness, if there be a due proportion of the Ingredients; but if any one predominate, the Light must incline to that Colour; as it happens in the blue Flame of Brimstone, the yellow Flame of a Candle, and the various Colours of the fixed Stars.

9. These things consider'd, the _manner_, how Colours are produced by the Prism, is evident. For, of the Rays, constituting the incident Light, since those which differ in Colour proportionally differ in Refrangibility, _they_ by their unequal Refractions must be severed and dispersed into an oblong Form, in an orderly succession, from the least refracted Scarlet to the most refracted Violet. And for the same reason it is, that Objects, when look'd upon through a Prism, appear coloured. For the difform Rays, by their unequal Refractions, are made to diverge towards several parts of the _Retina_, and there express the Images of things coloured, as in the former case they did the Sun's Image upon a Wall. And by this inequality of Refractions, they become not only coloured, but also very confused and indistinct.

10. Why the Colours of the _Rainbow_ appear in falling drops of Rain, is also from hence evident. For those drops, which refract the Rays, disposed to appear Purple, in greatest quantity to the Spectator's Eye, refract the Rays of other sorts so much less, as to make them pass beside it; and such are the drops on the inside of the _Primary_ Bow, and on the outside of the _Secondary_ or Exteriour one. So those drops, which refract in greatest plenty the Rays, apt to appear red, toward the Spectator's Eye, refract those of other sorts so much more, as to make them pass beside it; and such are the drops on the Exteriour part of the _Primary_, and Interiour part of the _Secondary_ Bow.

11. The odd Phænomena of an infusion of _Lignum Nephriticum_, _Leaf-gold_, _Fragments of colour'd Glass_, and some other transparently coloured Bodies, appearing in one Position of one Colour, and of another in another, are on these grounds no longer Riddles. For those are Substances apt to reflect one sort of Light, and transmit another; as may be seen in a dark Room, by illuminating them with similar or uncompounded Light. For then they appear of that Colour only, with which they are illuminated; but yet in one Position more vivid and luminous than in another, accordingly as they are disposed more or less to reflect or transmit the incident Colour.

12. From hence also is manifest the reason of an unexpected Experiment, which Mr. _Hook_, somewhere in his _Micrography_, relates to have made with two wedge-like transparent Vessels fill'd, the one with a red, the other with a blue Liquor; namely, that though they were severally transparent enough, yet both together became opake: For, if one transmitted only red, and the other only blue, no Rays could pass through both.

13. I might add more Instances of this Nature; but I shall conclude with this general one, that the Colours of all natural Bodies have no other Origin than this, that they are variously qualified to reflect one sort of Light in greater plenty than another. And this I have experimented in a dark Room, by illuminating those Bodies with uncompounded Light of divers Colours. For by that means any body may be made to appear of any Colour. They have there no appropriate Colour, but ever appear of the Colour of the Light cast upon them; but yet with this difference, that they are most brisk and vivid in the Light of their own day-light-colour. _Minium_ appeareth there of any Colour indifferently, with which 'tis illustrated, but yet most luminous in red; and so _Bise_ appeareth indifferently of any Colour with which 'tis illustrated, but yet most luminous in blue. And therefore _Minium_ reflecteth Rays of any Colour, but most copiously those endu'd with red, and consequently when illustrated with day-light, that is, with all sorts of Rays promiscuously blended, those qualified with red, shall abound most in the reflected Light, and by their prevalence cause it to appear of that Colour. And for the same reason _Bise_, reflecting blue most copiously, shall appear blue by the excess of those Rays in its reflected Light; and the like of other Bodies. And that this is the intire and adequate cause of their Colours, is manifest, because they have no power to change or alter the Colours of any sort of Rays incident apart, but put on all Colours indifferently, with which they are enlightned.

These things being so, it can be no longer disputed, whether there be Colours in the dark, nor whether they be the Qualities of the Objects we see, no nor perhaps, whether Light be a Body. For, since Colours are the _Qualities_ of Light, having its Rays for their intire and immediate Subject, how can we think those Rays _Qualities_ also, unless one Quality may be the Subject of and sustain another; which in effect is to call it _Substance_? We should not know Bodies for Substances, were it not for their sensible Qualities; and the principal of those being now found due to something else, we have as good reason to believe that to be a Substance also.

Besides, whoever thought any Quality to be a _heterogeneous_ Aggregate, such as Light is discovered to be? But to determine more absolutely, what Light is, after what manner refracted, and by what Modes or Actions it produceth in our Minds the Phantasms of Colours, is not so easie. And I shall not mingle Conjectures with Certainties.

Reviewing what I have written, I see the Discourse it self will lead to divers Experiments sufficient for its Examination; and therefore I shall not trouble you farther, than to describe one of those, which I have already insinuated.

In a darkned Room, make a hole in the shut of a Window, whose Diameter may conveniently be about a third part of an Inch, to admit a convenient quantity of the Sun's Light. And there place a clear and colourless Prism, to refract the entring Light towards the farther part of the Room; which, as I said, will thereby be diffused into an oblong coloured Image. Then place a _Lens_ of about three Foot Radius (suppose a broad Object-glass of a three Foot Telescope,) at the distance of about four or five Foot from thence, through which all those Colours may at once be transmitted, and made by its Refraction to convene at a farther distance of about ten or twelve Feet. If at that distance you intercept this Light with a Sheet of white Paper, you will see the Colours converted into whiteness again by being mingled. But it is requisite, that the _Prism_ and _Lens_ be placed steady, and that the Paper, on which the Colours are cast, be moved to and fro; for, by such motion, you will not only find at what distance the whiteness is most perfect, but also see how the Colours gradually convene, and vanish into whiteness; and afterwards, having crossed one another in that place where they compound whiteness, are again dissipated and severed, and in an inverted order retain the same Colours, which they had before they entred the Composition. You may also see, that, if any of the Colours at the _Lens_ be intercepted, the whiteness will be changed into the other Colours. And therefore, that the Composition of whiteness be perfect, care must be taken that none of the Colours fall besides the _Lens_.

In the annexed Design, _Tab. 3. Fig. 2._ of this Experiment, _ABC_ expresseth the Prism set end-wise to sight, close by the hole _F_ of the Window _EG_. Its vertical Angle _ABC_ may conveniently be about 60 Degrees: _MN_ designeth the _Lens_. Its breadth 2½ or 3 Inches. _SF_ one of the streight Lines, in which difform Rays may be conceived to flow successively from the Sun. _FP_, and _FR_ two of those Rays unequally refracted, which the _Lens_ makes to converge towards _Q_, and after decussation to diverge again. And _HI_ the Paper, at divers distances, on which the Colours are projected, which in _Q_ constitute _Whiteness_, but are _Red_ and _Yellow_ in _R_, _r_, and ρ, and _Blue_ and _Purple_ in _P_, _p_, and π.

If you proceed further to try the impossibility of changing any uncompounded Colour (which I have asserted in the third and thirteenth Propositions,) 'tis requisite that the Room may be very dark, lest any scattering light, mixing with the Colour, disturb and allay it, and render it compound, contrary to the design of the Experiment. 'Tis also requisite, that there be a perfecter separation of the Colours, than, after the manner above described, can be made by the Refraction of one single Prism; and how to make such farther separations, will scarce be difficult to them, that consider the discovered Laws of Refractions. But if trial shall be made with Colours not throughly separated, there must be allowed changes proportionable to the mixture. Thus if compound Yellow Light fall upon blue _Bise_, the Bise will not appear perfectly yellow, but rather green, because there are in the yellow mixture many Rays indued with green, and green being less remote from the usual blue Colour of Bise than yellow, is the more copiously reflected by it.

In like manner, if any one of the Prismatick Colours, suppose red, be intercepted, on design to try the asserted impossibility of reproducing that Colour out of the others which are pretermitted; 'tis necessary, either that the Colours be very well parted before the red be intercepted; or that, together with the red, the neighbouring Colours, into which any red is secretly dispersed, (that is, the yellow, and perhaps green too) be intercepted; or else, that allowance be made for the emerging of so much red out of the yellow green, as may possibly have been diffused, and scatteringly blended in those Colours. And if these things be observed, the new Production of red, or any intercepted Colour, will be found impossible.

This, I conceive, is enough for an Introduction to Experiments of this kind; which if any of the _Royal Society_ shall be so curious as to prosecute, I should be very glad to be informed with what success: That, if any thing seem to be defective, or to thwart this Relation, I may have an opportunity of giving farther Direction about it, or of acknowledging my Errors, if I have committed any.

_Since the Publication of this Theory, some Misunderstandings happening
between a _French_ Philosopher at _Paris_ and Mr. _Newton_, he has
endeavour'd to explain himself a little further in these Things,
according to the following Method._

_DEFINITIONS._

1. I call that Light Homogeneal, Similar, or Uniform, whose Rays are equally refrangible.

2. And that Heterogeneal, whose Rays are unequally refrangible.

_Note_, There are but three Affections of Light in which I have observ'd its Rays to differ; _viz._ Refrangibility, Reflexibility, and Colour; and those Rays which agree in Refrangibility, agree also in the other two, and therefore may well be defined Homogeneal; especially since Men usually call those things Homogeneal, which are so in all Qualities that come under their Knowledge, tho' in other Qualities, that their Knowledge extends not to, there may possibly be some Heterogeneity.

3. Those Colours I call Simple or Homogeneal, which are exhibited by Homogeneal Light.

4. And those Compound or Heterogeneal, which are exhibited by Heterogeneal Light.

5. Different Colours, I call, not only the more eminent Species, Red, Yellow, Green, Blue, Purple, but all other the minutest Gradations; much after the same manner, that not only the more eminent Degrees in Musick, but all the lead Gradations, are esteem'd different Sounds.

_PROPOSITIONS._

1. The Sun's Light consists of Rays differing by indefinite Degrees of Refrangibility.

2. Rays which differ in Refrangibility, when parted from one another, do proportionally differ in the Colours which they exhibit. These Two Propositions are Matter of Fact.

3. There are as many Simple or Homogeneal Colours, as Degrees of Refrangibility. For to every Degree of Refrangibility belongs a different Colour, by _Prop._ 2. and that Colour is Simple, by _Def._ 1, and 3.

4. Whiteness, in all respects like that of the Sun's immediate Light, and of all the usual Objects of our Senses, cannot be compounded of two Simple Colours alone. For such a Composition must be made by Rays that have only two Degrees of Refrangibility, by _Def._ 1 and 3. and therefore it cannot be like that of the Sun's Light. by _Prop._ 1. nor, for the same Reason, like that of ordinary white Objects.

5. Whiteness, in all respects, like that of the Sun's immediate Light, cannot be compounded of Simple Colours without an indefinite Variety of them. For to such a Composition, there are requisite Rays endu'd with all the indefinite Degrees of Refrangibility, by _Prop._ 1. And those infer as many Simple Colours, by _Def._ 1 and 3. and _Prop._ 2 and 3.

To make these a little plainer, I have added also the Propositions that follow.

6. The Rays of Light do not act on one another, in passing through the same Medium.

7. The Rays of Light suffer not any change of their Qualities from Refraction.