Chapter VI: Appendix (5)

8. Nor afterwards from the adjacent quiet _Medium_: These two Propositions are manifest _de Facto_ in Homogeneal Light, whose Colour and Refrangibility is not at all changeable, either by Refraction, or by the Contermination of a quiet _Medium_. And as for Heterogeneal Light, it is but an Aggregate of several sorts of Homogeneal Light, no one sort of which suffers any more alteration than if it were alone; because the Rays act not on one another, by _Prop._ 6. and therefore the Aggregate can suffer none. These two Propositions also might be further proved apart, by Experiments too long to be here described.

9. There can no Homogeneal Colours be reduced out of Light by Refraction, which were not commixt in it before. Because by _Prop._ 7. and 8. Refraction changeth not the Qualities of the Rays, but only separates those which have divers Qualities, by means of their different Refrangibility.

10. The Sun's Light is an Aggregate of an indefinite variety of Homogeneal Colours, by _Prop._ 1, 3, and 9. And hence it is, that I call Homogeneal Colours also Primitive or Original. And thus much concerning Colours.

_For a further Illustration of this Doctrine, Mr. _Newton_, in his Book
of Opticks lately published, has by undeniable Experiments explained
most of the Principal Phænomena of Light and Colours: To which we
refer the Reader._

_A Demonstration concerning the Motion of Light, communicated from
_Paris_._

Philosophers have been labouring for many Years to decide by some Experiment, whether the Action of Light be conveyed in an instant to distant Places, or whether it requireth time. M. _Romer_, of the _Royal Academy_ of Sciences, hath devised a way taken from the Observations of the first Satellit of _Jupiter_, by which he demonstrates, that for the distance of about 3000 Leagues, such as is very near the bigness of the Diameter of the Earth, Light needs not one Second of Time.

Let (in _Fig. 3. Plate 3._) _A_ be the _Sun_, _B_ _Jupiter_, _C_ the first Satellit of _Jupiter_, which enters into the shadow of _Jupiter_, to come out at _D_, and let _EFGHKL_ be the _Earth_, placed at divers distances from _Jupiter_.

Now suppose the _Earth_, being in _L_, towards the second Quadrature of _Jupiter_, hath seen the first Satellit, at the time of its emersion, or issuing out of the shadow at _D_, and that about 42½ Hours after (_viz._ after one Revolution of this _Satellit_) the _Earth_ being in _K_, do see it return'd in _D_: It is manifest, that if the Light require time to traverse the Interval _LK_, the _Satellit_ will be seen return'd later in _D_, than it would have been if the _Earth_ had remained in _L_. So that the Revolution of the _Satellit_ being thus observ'd by the Emersions, will be retarded by so much time, as the Light shall have taken in passing from _L_ to _K_; and that on the contrary, in the other Quadrature _FG_, where the _Earth_ by approaching goes to meet the Light, the Revolutions of the Emersions will appear to be shortned, by so much as those of the Emersions had appear'd to be lengthned. And because 42½ Hours, which this _Satellit_ very near takes to make one Revolution, the distance between the _Earth_ and _Jupiter_, in both the Quadratures, varies at least 210 Diameters of the _Earth_: It follows, that if for the Account of every Diameter of the _Earth_ there were required a Second of Time, the Light would take 3½ Minutes for each of the Intervals _GF_, _KL_; which would cause near half a quarter of an Hour between two Revolutions of the first _Satellit_, one observ'd in _FG_, and the other in _KL_, whereas there is not observed any sensible difference.

Yet doth it not follow hence, that Light demands no time. For after M. _Romer_ had examin'd the thing more nearly, he found that what was not sensible in two Revolutions, became very considerable in many being taken together; and that, for Example, forty Revolutions observed on the side _F_, might be sensibly shorter, than forty others observ'd in any place of the _Zodiack_ where _Jupiter_ may be met with; and that in proportion of Twenty two for the whole Interval of _HE_, which is the double of the Interval that is from hence to the Sun.

The necessity of this new Equation of the Retardment of Light, is establish'd by all the Observations that have been made in the _Royal Academy_, and in the _Observatory_, for the space of eight Years; and it hath been lately confirmed by the Emersion of the first _Satellit_ observ'd at _Paris_, the _9th_ of _November_ last, at 5 a-clock 35' 45" at Night, 10 Minutes later than it was to be expected, by deducting it from those that had been observ'd in the Month of _August_, when the _Earth_ was much nearer to _Jupiter_; which M. _Romer_ had predicted to the said Academy from the beginning of _September_.

But to remove all doubt, that this Inequality is caused by the Retardment of the Light, he demonstrates, that it cannot come from any Excentricity, or other Cause of those that are commonly alledged to explicate the Irregularities of the _Moon_, and the other Planets; though he be well aware, that the first _Satellit_ of _Jupiter_ was Excentrick; and that, besides his Revolutions were advanced or retarded, according as _Jupiter_ did approach to or recede from the Sun; as also, that the Revolutions of the _Primum Mobile_ were unequal: Yet, saith he, these three last Causes of Inequality do not hinder the first from being manifest.

_An introductory _Essay_ to the Doctrine of _Sounds_, containing some
Proposals for the improvement of _Acousticks_; As it was presented to
the _Dublin Society_, Nov. 12. 1683, by the Right Reverend Father in
God _Narcissus_ Lord Bishop of _Ferns_ and _Leighlin_._

Being to treat of the Doctrine of _Sounds_, I hold it convenient to premise something in the general, concerning this Theory; which may serve at once to ingage your Attention, and excuse my Pains, when I shall have recommended them, as bestow'd on a Subject not altogether useless and unfruitful.

And for this purpose I shall omit to speak any thing of the _Excellency_ of the Matter in Hand; though it might be celebrated by Arguments drawn from several Topicks, and particularly from this, that new Discoveries and Improvements may be made, both as to the _Generation_, _Propagation_ and _Reception_ of Sounds into the Sense; which, in a peculiar manner agrees to this, above the Object of any other Sense whatsoever. I shall, I say, omit these things, and apply my self wholly to the _Usefulness_ of the Theory, that we are now falling upon, which I think cannot better be discovered, than by making a comparison 'twixt the Senses of _Seeing_ and _Hearing_, as to their Improvements. I mean, by shewing, that this latter of _Hearing_ is capable of all those improvements which the Sense of _Seeing_ has receiv'd from Art, besides many more advantages that the _Ear_ may enjoy, by the help of our Doctrine, above the _Eye_; all which moreover will be of as great benefit to Mankind, as any thing that _Opticks_ have yet discover'd, if not of greater; which, with some other pre-eminencies that it has upon another Score, will happily render _Acousticks_ the nobler Science of the two.

In order to the making good what I but now premised of the Comparison of these two Faculties of _Seeing_ and _Hearing_, as to their Improvements, I observe;

That _Vision_ is threefold, _Direct_, _Refracted_, and _Reflex'd_; answerable whereunto we have _Opticks_, _Dioptricks_, and _Catoptricks_.

In like manner _Hearing_ may be divided into _Direct_, _Refracted_ and _Reflex'd_; whereto answer three parts of our Doctrine of _Acousticks_, which are yet nameless, unless we call them _Acousticks_, _Diacousticks_, and _Catacousticks_, or (in another Sense, but to as good Purpose) _Phonicks_, _Diaphonicks_, and _Cataphonicks_.

I. Direct Vision has been improv'd two ways, _ex parte_ Objecti, and _ex parte_ Organi _vel_ Medii.

1. _Ex parte Objecti_, Direct Vision has receiv'd advantages by the Arts of _Producing_, _Conserving_ and _Imitating Light_ and _Colours_, which are the Objects of Vision.

1. For the Art of _Producing Light_, we have the Frication of all hard Bodies that beget Fire; especially of the Flint and Steel; and instead of the Flint, most hard Stones (as well as the Cane) may be us'd to the same effect, as upon trial I have found. Add hereto the lately invented _Phosphorus_, which is a new and admirable way of producing a _Lucid Substance_ by Art, out of a Body in itself not _Lucid_; and therefore may not unfitly be term'd an _Artificial production_ of _Light_.

And then of the Art of _Conserving Light_, the _Lapis Bononiensis_ is a notable Instance; and so happily were the _Sepulchral Lamps_ of the Ancients.

2. As to _Colours_, 'tis the greatest part of the Art of _Dying_ to be able to make and fix (that is preserve) them; and the _Painters_ and _Limners_ will own it to be no small part of their Skill to be able well to _Mix_ (that is, in effect, to _Generate_) _Colours_.

3. For _Imitation of Light_ and _Colours_, 'tis well known how far _Perspective_ with the Art of _Limning_ and _Shadowing_ have gone therein, which all tend some way to the Advance or Improvement of _Direct Vision_.

Add to all these, That _a due Application of Light to the Object_ renders it Visible, if it were not so before; as appears from a dark Room illuminated; or else makes it better and more truly discernable by the Sense of _Seeing_, if before it might have been discern'd.

Hence the same _Colour_, in a diverse Light, will appear different, and no _Picture_ can well be discern'd or judg'd of but by its true Light. Besides, the _Limner_ will assure you, that he can hardly make true Work, or hit the Air of a Face exactly, unless he draw by a _North-Light_, by reason of the steadiness of that, and the uncertainty of all other Lights whatsoever. Which things shew, that the _Art of duly applying Light to the Object_ does very much help and improve Vision. So also does the due placing of the _Object_, as to _Height_ and _Distance_. But to enumerate all things that help _Direct Vision_, would be infinite.

2. _Ex parte Organi vel Medii_, Direct Vision has been improv'd by making use of a _Tube_, without Glasses, or a Man's clos'd Hand, to look thro'; which admitting into the _Eye_ only the principal Rays, that come directly from the Object, do very much strengthen and clear the Sight, by excluding all the Collateral Rays, that crouding into the Eye, together with the direct ones, would confound and disturb it, partly by mixing and interfering with the direct Rays, and partly (or rather chiefly) by too much enlightning the fund of the Eye, wherein Vision is truly (tho' then imperfectly) made.

On this is founded the Art of making _Spectacles_ without Glasses; (as well as _Tubes_) which is done by putting into the Glass-holes (instead of Glasses) two short _Tubes_ of between three and four Inches long (for their length is to be vary'd according to the Age or Eye of the Beholder, and so also is the Diameter of the extream ends) which _Tubes_ being made of _Spanish Leather_ (or Past-board, or some such like Matter) and black'd on the inside, are so to be placed, as that the visual Rays, receiv'd thro' them, may meet in one point (or rather issue out from one Point) of the Object standing at such a due distance, as the Person may clearly and distinctly see it, or according to his length of Sight (as ABC, in the 4th _Fig. Tab._ 3.)

And these _Spectacles_ may be suppos'd better for preserving the Sight, than the ordinary ones with Glasses, because they represent the Object more naturally, and withal more clearly and distinctly to the Eye, than the other, whose refracted Rays being collected together with the right ones in the Glasses, do somewhat confound good Vision, as before: Especially if the visive Power be strong enough to be sufficiently determin'd by the right Rays alone.

For I speak now of preserving a good Eye by these Spectacles, which holds in proportion true also of a bad one. Because those Rays (both right and refracted) being collected and brought so near the Eye (whether good or bad) as the Spectacles are usually plac'd, do too much affect it, both by their own brightness, and also by the brightness of the Colours of the Object (when they are bright) which is brought very near also; whereby the Eye is dazl'd and confounded, unless there be a strong attention and _conatus_ of the Spirits, whereto the bright Rays do certainly engage them, which of necessity weakens Vision, especially if these Glass-spectacles be much us'd.

Wherefore the now describ'd new Tube-spectacles, contributing so much to the help and preservation of Sight, may well be counted an improvement of _Direct Vision_, because they convey the Rays to the Eye without any kind of Refraction whatsoever. Seeing the same Object also through various holes, plac'd at certain distances, does somewhat alter Vision; but of this perhaps more hereafter.

Now as _Direct Vision_ has thus been improved, so likewise _Direct Hearing_ partly has already receiv'd, and partly may by the Doctrine whereof we are treating, (if well cultivated) farther receive as great and notable Improvements, both _ex parte_ Objecti, and _ex parte_ Organi _vel_ Medii.

1. As to the _Object_ of Hearing, which is Sound, improvement has been and may be made, both as to the _Begetting_, and as to the _Conveying_ and _Propagating_ (which is a kind of _Conserving_) of Sounds.

1. As to the _Begetting_ of Sounds. The Art of imitating any Sound, whether by _Speaking_ (that is pronouncing) any kind of Language, (which really is an Art, and the _Art of Speaking_, perhaps one of the greatest) or by _Whistling_, or by _Singing_ (which are allow'd Arts) or by _Hollowing_ or _Luring_ (which the Huntsman or Faulkner would have to be an Art also) or by imitating with the Mouth (or otherwise) the Voice of any Animal, as of _Quails_, _Cats_, and the like; or by _representing_ any Sound begotten by the Collision of Solid Bodies, or after any other manner; these are all _Improvements_ of _Direct Hearing_, and may be improv'd.

Moreover the Skill to make all sorts of _Musical Instruments_, both Ancient and Modern, whether _Wind_ Instruments or _String'd_, or of any other sort, whereof there are very many (as _Drums_, _Bells_, the _Systrum_ of the _Egyptians_, and the like) that beget (and not only propagate) Sounds; the Skill of making these, I say, is an Art, that has as much improv'd _Direct Hearing_, as an Harmonious Sound exceeds a single and rude one, that is, an immusical _Tone_; which Art is yet capable of farther improvement. And I do hope, that by the Rules, which may happily be laid down concerning the _Nature_, _Propagation_ and _Proportion_, or _Adapting_ of Sounds, a way may be found out, both to improve _Musical Instruments_ already in use, and to invent new ones, that shall be more sweet and luscious, than any yet known. Besides that, by the same means _Instruments_ may be made, that shall imitate any Sound in Nature, that is not Articulate, be it of Bird, Beast, or what thing else soever.

2. The _Conveying_ and _Propagating_ (which is a kind of _Conserving_) of Sounds, is much help'd by _duly placing the Sonorous Body_, and also by the _Medium_.

For if the Medium be _Thin_ and _Quiescent_, and the Sounding Body _plac'd conveniently_, the Sound will be easily and regularly propagated, and mightily conserv'd. I say,

1. If the _Medium be Thin and Quiescent_, because it otherwise causes a _Refracted Sound_, of which afterwards. Hence in a _still Evening_, or the _dead of the Night_ (when the Wind ceases) a Sound is better sent out, and to a greater distance than otherwise, tho' much of this may be ascrib'd to its _Refraction_ also.

2. I say, that the _Sonorous Body must be plac'd conveniently_, near a _Smooth Wall_, near _Water_, or _a Plain_, whose Surface is even.

1. Near a _Smooth Wall_, either Plain or Arch'd (Cycloidically or Elliptically, rather than otherwise, tho' a Circular or any Arch will do, but not so well.)

Hence in a Church, the nearer the Preacher stands to the Wall (and certainly 'tis much the best way to place Pulpits near the Wall) the better is he heard, especially by those who stand near the Wall also, though at a greater distance from the Pulpit; those at the remotest end of the Church, by laying their Ears somewhat close to the Wall, may hear him easier than those in the middle.

Hence also do arise _Whispering Places_. For the Voice being apply'd to one end of an Arch, easily rowls to the other. And indeed were the _Motion_ and _Propagation_ of Sounds but rightly understood, 'twould be no hard matter to contrive _Whispering Places_ of infinite variety and use. And perhaps there could be no better or more pleasant hearing a _Consort of Musick_ than at such a place as this, where the Sounds rowling along together, before they come to the Ear, must needs consolidate and imbody into one; which becomes a true composition of Sounds, and is the very Life and Soul of Consort.

2. If the Sonorous Body be plac'd near _Water_, the Sound will easily be convey'd, yet mollified; as Experience teacheth us from a Ring of _Bells_ near a River, and a great _Gun_ shot off at Sea, which yet differ much in the strength, and softness and continuance, or propagation of their Sounds, from the same at Land, where the Sound is more harsh and more perishing, or much sooner decays.

3. In a _Plain_ a Voice may be heard at a far greater distance than in uneven Ground.

The _Reason_ of all which last nam'd _Phænomena_ is the same; because the Sonorous Air meeting with little or no resistance upon a _Plane_ (much less upon an Arch'd) smooth Superficies, easily rowls along it, without being let or hinder'd in its Motion, and consequently without having its parts disfigured, and put into another kind of Revolution, than what they had at the first begetting of the Sound. Which is the true cause of its _Preservation_ or _Progression_, and fails much when the Air passes over an uneven Surface, according to the degrees of its inequality, and somewhat also, when it passes over the plain Superficies of a Body that is hard and resisting.

Wherefore the smooth Top of the Water (by reason of its yielding to the Arch'd Air, and gently arising again with a kind of Resurge, like to _Elasticity_, tho' it be not so, by which Resurge it quickens and hastens the motion of the Air rowling over it, and by its yielding preserves it in its Arch'd Cycloidical or Elliptical Figure) the smooth Top of the Water, I say, for these Reasons, and by these Means, conveys a Sound more entire, and to a greater distance than the plain Surface of a piece of Ground, a Wall, or any other Solid Body whatever, can do.

As for the _Speaking Trumpet_, by which a Voice may be convey'd to a considerable distance, I refer its consideration to that of _Refracted Sounds_, or _Refracted Audition_.

Thus much of the Improvements of Hearing, that respect its _Object_, which is _Sound_.

2. The _Organ_ and _Medium_ are to be consider'd. And, 1. The _Organ_, which is the _Ear_, is helpt much by placing it near a Wall (especially at one end of an Arch, the Sound being begotten at the other) or near the Surface of Water, or of the Earth, along which the Sounds are most easily and naturally convey'd, as was before declar'd. And 'tis incredible how far a Sound made upon the Earth (by the trampling of a Troop of Horses, for Example) may be heard in a still Night, if a Man lays his Ear close to the Ground in a large Plain.

_Otacousticks_ here come in for helping the _Ear_; which may be so contriv'd (by a right understanding the _Progression of Sounds_, which is the principal thing to be known for the due regulating all such kinds of Instruments) as that the Sound might enter the Ear without any Refraction, but as now they are generally made I refer them to _Refracted Audition_.

2. As to the _Medium_, I know not how that, by any contrivance of Art, can advantage _Direct Hearing_, otherwise than I have declar'd already in the propagation or conveyance of Sounds, though to the Refracting or Reflecting of them it may very much conduce; of which presently.

And so I have done with the first part of my present undertaking, which is the _Comparison of Direct Vision and Audition_, as to their Improvements from Art. The rest follow. Wherefore,

II. Concerning _Refracted Vision_ and its Comparison, I observe, That _Refracted Vision_ is always made _Ex parte Medii_, as _Reflected_ is _ex parte Objecti_. And therefore, though _Direct Vision_ may be help'd _ex parte Objecti, Medii vel Organi_, yet _Refracted_ can be improv'd only _ex parte Medii_, and _Reflected_ _ex parte Corporis oppositi_ alone. Unless it be in a mixt or compound Vision, that is _Refracto-Reflext_, when the reflext Rays pass to the Eye through a refracting Medium, such as the _Medium Internum_, contain'd in the Body of the Eye, always is. So that in truth, all Vision is _Refracted_ by an internal Refraction made in _ipso Oculo_.

And all that I have spoken of _Vision_ holds true of _Hearing_ also, both _Refracted_ and _Reflext_, and therefore need not be repeated.

_Refracted Vision_ arises from the different _Density_, _Figure_, and _Magnitude_ of the Medium, which is somewhat alter'd also by the diverse incidence of the visible Rays. And so it is in _Refracted Hearing_, all these Causes concur to its Production, and some others to be hereafter consider'd.

Now as any Object (a Man for example) seen through a thicken'd Air, by _Refraction_ appears greater than really he is: So likewise a _Sound_, heard through the same thicken'd part of the _Atmosphere_, will be considerably vary'd from what it would seem to be, if heard through a thinner Medium.

And this I call a _Refracted Sound_: But what this Refraction of Sound is, and how caus'd, may hereafter be discuss'd, when the Nature, and Motion, or Progression of Sounds are well stated.

For the Improvement of _Refracted Vision_ artificial Instruments have been made, by grinding or blowing Glasses, into a certain Figure, and placing them at due distances, whereby the Object may be (as 'twere) enabled to send forth its Rays more vigorously, and the Visive Faculty impower'd the better to receive them. And thus also Instruments may be contriv'd for the assisting both the _Sonorous Body_, to send forth its Sound more strongly, and the _Acoustick Faculty_, to receive and discern it more easily and clearly. _For_,

1. As a fine _Glass Bubble_, fill'd with clear Water, and placed before a burning Candle or Lamp, does help it to dart forth its Rays to a prodigious Length and Brightness: So an _Instrument_ may be invented, that apply'd to the Mouth (or any Sonorous Body) shall send forth the Voice distinctly to as prodigious a Distance and Loudness.

For if the _Stentoro-phonecon_ (which is but a rude and unartificial Instrument) does such great feats, what might be done with one compos'd according to the Rules of Art? whose make should comply with the Laws of _Sonorous Motion_ (which that does not) and therefore not so much _Refract_, as to alter and confound the _Tone_ of the _Voice_ and Words (as that somewhat does.)

Now of what use such an Instrument might be for speaking clearly and articulately at a distance (and that without altering the Tone of the Voice) whether it be at Sea or at Land (but especially at Sea in tempestuous Weather and in the Night) is obvious to any Man to conceive.

2. As Instruments have been invented to help the Eye, So likewise are there some, and more such there may be, for the Ear.

_For_,

1. As _Spectacles_ and other _Glasses_ are made to help the _Purblind_ and weak _Eyes_, to see at any competent distance: So there are _Otacousticks_ (and better may be made) to help weak _Ears_ to hear at a reasonable distance also. Which would be as great a help to the infirmity of Old Age, as the other invention of Spectacles is, and perhaps greater; forasmuch as the Hearing what's spoken is of more daily use and concern to such Men, then to be able to _read Books_ or to _view Pictures_.

2. As _Perspective-Glasses_ and Telescopes help the Eye to see Objects at a very great distance, which otherwise would not be discernable; in like manner may a sort of _Otacousticks_ be so contriv'd, as that they shall receive in _Sounds_ made at a very great distance also, but with so much advantage, that the Ear shall be able to hear them, which otherwise would have been _inaudible_.

And these _Otacousticks_ in some respects would be of greater use than _Perspectives_. For whereas at Land _Perspectives_ are many times render'd almost useless, by the interposition of Woods and Mountains, which hinder the Sight from reaching very far: Our _Otacousticks_ would, notwithstanding these Obstacles, take in a Sound made some Leagues off. Which might be of notable use in the time of War, for discovering the Enemy at a good distance, when he marches or lyes incamp'd behind a Mountain or Wood, or any such place of shelter.

Yea, even at Sea also, where _Perspectives_ are of most use, by reason of the plainess of the Surface of the Water; yet sometimes there _Otacousticks_ may be of more benefit, when in dark hazy Weather the Air is too thick, or in Stormy Tempestuous Weather the Waves arise too high for the _Perspective_ to be made use of.

But, whether at Sea or Land, _Perspectives_ become altogether insignificant in the Night-time (unless it be for viewing the Stars) which is the chief time for using _Otacousticks_; as it is generally, for Soldiers to take their March, when they would surprise their Enemies.

And therefore this sort of _Otacousticks_ have then their chief use, when _Perspectives_ are of no use at all; besides that they may be imploy'd in the Day-time, as well as _Perspectives_, whence they may (not unfitly) be term'd _the most useful Instrument_ of the two.

3. As _Microscopes_ or _Magnifying-Glasses_ help the Eye to see near Objects, that by reason of their smallness were _Invisible_ before; which Objects they Magnify to a strange greatness: So _Microphones_ or _Micracousticks_, that is Magnifying Ear Instruments, may be contriv'd after that manner, that they shall render the most minute Sound in nature distinctly audible, by Magnifying it to an unconceivable loudness.

By the help hereof we may hear the different Cries and Tones, as well as by _Microscopes_ see the divers Shapes and Figures of the smallest Animals.

4. As by _Polyscopes_ or _Multiplying-Glasses_, one thing is represented to the Eye as many, whether in the same or different Shapes (for so Multiplying-Glasses may be contriv'd:) So by a _Polyphone_ or _Polyacoustick_ well order'd, one _Sound_ may be heard as many, either of the same or a different Note. Insomuch, that who uses this Instrument, he shall, at the Sound of a single Viol, seem to hear a whole Consort and all true Harmony. By which means this Instrument has much the advantage of the _Polyscope_.

And thus much may suffice for comparing the Improvements made upon _Refracted Seeing and Hearing_; I call it _Refracted Hearing_, because made through a _Medium_, viz. thick Air, or an Instrument, through which the Sound passing is broken or refracted.

III. _Reflected Vision_ has been improv'd by the Invention of _Looking-glasses_ and _Polished Metals_, whether _Plane_, _Concave_, or _Convex_; and these two last, either _Spherical_, _Oval_, _Cylindrical_, _Conical_, _Hyperbolical_, or of several other shapes; all which cause a different Reflection, and vary the _Phænomena_.

Thus also _Reflext Audition_, made by _Ecchoes_, may be improv'd, by contriving several sorts of _Artificial Ecchoes_; as 'tis no hard matter to do in almost any place.

For (speaking in the general) _Any Sound, falling directly or obliquely upon any dense Body, of a smooth (whether Plane or Arch'd) Superficies, is beat back again and reflected, or does eccho more or less_.

I say (1.) _falling directly or obliquely_; because, if the Sound be sent out and propagated parallel to the Surface of the _Dense Body_, or be made so _far off_ and so _weak_, that it cannot reach it, there will be no Reflection of Sound, no _Eccho_.

I say (2.) _upon a Body of a smooth Superficies_; because if the Surface of the _Corpus Obstans_ be uneven, the Air by reverberation will be put out of its regular Motion, and the Sound thereby broken and extinguish'd: So that tho' in this case also the Air be beaten back again, yet Sound is not reflected, nor is there any Eccho.

I say (3.) _it does eccho more or less_, to shew, that when all things are, as is before describ'd, there is still an Ecchoing, though it be not always heard; either because the _direct Sound_ is too weak to be beaten quite back again to him that made it; or that it does return home to him, but so weak, that without the help of a good _Otacoustick_, it cannot be discern'd; or that he stands in a wrong place, to receive the reflected Sound, which passes over his head, under his Feet, or to one side of him; which therefore may be heard by a Man standing in that place, where the reflected Sound will come, provided no interpos'd Body does intercept it; but not by him, that first made it.

I shall further make out the comparison 'twixt _Reflex'd Vision_ and _Audition_, by these following _Propositions_.

1. As a _Plain Speculum_ reflects the _Object_ in its due _Dimensions_ and _Colours_; allowing for their difference of appearance, according to their distance: So a _Plane Corpus Obstans_ reflects the _Sound_ back in its due _Tone_ and _Loudness_; if allowance be likewise made for the proportionable decrease of the Sound, according to its distance.

2. As a _Convex Speculum_ reflects the _Object less_, but somewhat _brighter_ or clearer: So a _Convex Corpus Obstans_ repels the Sound (insensibly) _smaller_; but somewhat _quicker_ (though _weaker_) than otherwise it would be.

3. As a _Concave Speculum_ reflects the Object _bigger_, more obscure and _Inverted_: So a _Concave Corpus Obstans_ ecchoes back the Sound (insensibly) _bigger_, _slower_ (though _stronger_) and also _inverted_; but never according to the order of Words. Nor do I think it possible for the Art of Man to contrive a _Single Eccho_, that shall invert the Sound, and repeat backwards; because then the Words last spoken, that is, which do last occur to the _Corpus Obstans_, must first be repell'd; which cannot be: For where, in the mean time, should the first Words hang, and be conceal'd, or lie dormant? Or how, after such a pause, be reviv'd and animated again into Motion? Yet in complicated or _Compound Ecchoes_, where many receive from one another, I know not whether something that way may not be done.

From the determinate _Concavity_ or _Archedness_ of these reflecting Bodies, it comes to pass, that some of them, from a certain distance or posture, will eccho back but one determinate Note, and from no other place will they reverberate any; because of the undue Position of the sounding Body. Such an one (as I remember) is the Vault in _Merton_ College in _Oxford_.

4. As a _Speculum_ takes in and reflects more of its Object, when plac'd at a great distance from it, than when nearer; because it reflects according to the apparent Magnitude of the Body at such a distance, which is less: So also the _Ecchoing Body_, being remov'd farther off, reflects more of the Sound, than when nearer. And this is the reason, why some Ecchoes repeat but one Syllable, some one Word, and some many.

5. As _Specula's_ may be so plac'd, that reflecting one upon or into the other, either directly or obliquely, one Object shall appear many; as in Sir _Samuel Moreland_'s Glass-room: After the same manner _Ecchoing Bodies_ may be so contriv'd and plac'd, as that reflecting the Sound from one to the other, either directly and mutually, or obliquely and by Succession, out of one Sound shall many Ecchoes be begotten; which in the first case will be all together, and somewhat involv'd or swallow'd up of each other, and thereby confus'd (as a Face in Looking-glasses obverted) in the other they will be distinct, separate, and succeeding one another; as most _multiple Ecchoes_ do.

Moreover a _Multiple-Eccho_ may be made, by so placing the _Ecchoing Bodies_, at unequal distances, that they reflect all one way, and not one on the other; by which means a manifold successive Sound will be heard (not without astonishment) one Clap of the hands like many, one Ha, like a laughter, one single Word like many of the same Tone and Accent, and so one Viol like many of the same kind imitating each other.

Furthermore, as _Specula's_ may be so order'd, that by Reflection they shall make one single thing appear many different things; as one single Man to seem many Men, differing as to Shape and Complexion (or a company of Men) which I think Sir _Samuel Moreland_'s Contrivance does not: So may _Ecchoing Bodies_ also be order'd, that from any one Sound given, they shall produce many Ecchoes, different both as to their _Tone_ and _Intension_. (The ground whereof has elsewhere been laid down in a Treatise concerning the _Sympathy of Lute-strings_.)

By this means a _Musical Room_ may be so contriv'd, that not only one Instrument, play'd on in it shall seem many of the same _sort_ and _size_; but even a Consort of (somewhat) different ones; only by placing certain _Ecchoing Bodies_ so, as that any Note (play'd) shall be return'd by them in 3_ds_, 5_ths_, and 8_ths_, which is possible to be done otherwise than was mention'd before in _Refracted Audition_.

I have now done with my _Comparison_ of the two Noblest _Senses_, and _Sciences_, as to their _Improvements_; wherein I have been thus large, that I might give you a little prospect into the _Excellency_ and _Usefulness_ of _Acousticks_; and that thereby I might excite all that hear me, to bend their Thoughts towards the making of Experiments for the compleating this (yet very imperfect, tho' noble) Science; a _Specimen_ whereof I will give you in three _Problems_, and then present you with the _Semiplane_ of an _Acoustick or Phonical Sphere_, as an Attempt to explicate the great _Principle_ in this Science, which is _The Progression of Sounds_.

_The Problems are these:_

1. _Sonum intendere quousque velis_; or, _Datum sonum ad datum gradum intendere_.

2. _Sonum extendere quousque velis_; or, _Datum sonum ad datum distantiam extendere seu propagare_.

3. _Sonum transire ab extremo ad extremum_ & _non per Medium_.

1. The first is, _To make the least Sound_ (by the help of Instruments) _as loud as the greatest_; a whisper to become as loud as the shot of a Cannon.

By the help of this _Problem_, the most minute Sounds in Nature may be clearly and distinctly heard.

2. The second is, _To propagate any_ (the least) _Sound to the greatest distance_.

By the help hereof any Sound may be convey'd to any, and therefore heard at any distance, (I must add, within a certain, tho' very large Sphere.)

Moreover, by this means, a _Weather-cock_ may be so contriv'd, as that with an ordinary blast of Wind it shall cry (or whistle) loud enough to be heard many Leagues: Which happily may be found of some use, not only for _Pilots_ in mighty tempestuous Weather, when _light Houses_ are render'd almost useless, but also for the measuring the strength of Winds, if allowance be made for their different moisture. For I conceive, that the more dry any Wind is, the louder it will whistle _cæteris paribus_; I say, _cæteris paribus_, because, besides the strength and dryness of Winds or Breath, there are a great many other things (hereafter to be considered) that concur to the increase or magnifying of Sounds, begotten by them in an Instrument exposed to their Violence, or blown into.

3. The third _Problem_, is, _That a Sound may be convey'd from one extreme to the other_ (or from one distant place to another) _so as not to be heard in the middle_.

By the help of this _Problem_ a Man may talk to his Friend at a very considerable distance, so that those in the middle space shall hear nothing of what passed betwixt them.

FIG. V. TAB. III.

_Semiplanum Sphæræ Phonicæ seu Acousticæ._

You are to conceive that (rude) _Semiplane_, as parallel to the _Horizon_: For if it be perpendicular thereunto, I suppose the upper extremity will be no longer _Circular_, but _Hyperbolical_, and the lower part of it suited to a greater Circle of the Earth. So that the whole _Phonical_ Sphere (if I may so call it) will be a solid _Hyperbola_, standing upon a _Concave Spherical_ Base. I speak this concerning _Sounds_ made (as usually they are) nigh the Earth, and whose Sonorous _Medium_ has a free passage every way. For if they are generated high in the Air, or directed one way, the case will be different; which is partly design'd in the inequality of that Draught.

_A Discourse concerning the Modern _Theory_ of _Generation_, by Dr.
_George Garden_ of _Aberdeen_, being part of a Letter to Dr. _William
Musgrave_, L. L. D. Reg. Soc. S. and by him communicated the Royal
Society._

The Subject I pitch upon, is that of the Formation of Animals, You know how wide and unsatisfying Men's Conjectures were upon this Head, until this Age, in which first the deservedly Famous Dr. _Harvey_ discovered the proper place of the Formation of the Chick in the _Cicatricula_ of the Egg, and the Formation of the Parts so far as was discernable by the naked Eye; and after him _Malpighius_, by the help of exact Glasses, observ'd the first Rudiments of it there, both before and after Incubation: And _R. de Graef_, and others, having upon many Observations concluded, that the _Testes Fœminei_ were the Ovaries of Females, and consequently that all Animals were _ex ovo_; they began from hence to infer, that the Rudiments of each Animal were originally in the respective Females, and that the Male contributed only to give a new Ferment to the Mass of the Blood and Spirits, by which means a spirituous Liquor (which the Blood in its ordinary Ferment could not produce) did insinuate it self into the same Ducts and Pores of the Rudiments of those Animals, which were in greatest forwardness in the Ovary, and so extend and enlarge all their Parts, and at last bring them to perfection, as Mr. _Perrault_ does ingeniously discourse in the third Part of his _Essais de Physique_; till now at last _Leowenhoek_ has discover'd an infinite number of _Animalcula in semine marium_ of all kinds, which has made him condemn the former Opinions about the Propagation of all Animals _ex Ovo_.

Now upon comparing the Observations and Discoveries which have been made with one another, these three things seem to me very probable. 1. That Animals are _ex Animalculo_. 2. That these Animalcles are originally _in semine Marium_ & _non in Fœminis_. 3. That they can never come forward, nor be formed into Animals of the respective kind, without the _Ova in Fœminis_.

The first of these seems probable from these three Observations. 1. That some such thing has been so often observ'd by _Malpighius_, in the _Cicatricula_ of an Egg before Incubation, as the Rudiments of an Animal in the shape of a Tadpole, as may be seen in his first, and in his repeated Observations _de formatione Pulli in Ovo_. 2. The sudden appearance and displaying of all the Parts after Incubation, makes it probable, that they are not then actually formed out of a fluid, but that the _Stamina_ of them have been formerly there existent, and are now expanded. The first Part of the Chick which is discovered with the naked Eye, is, you know, the _Punctum saliens_, and that not till three days and nights of Incubation be past; and then, on the fifth day, the Rudiments of the Head and Body do appear. This made Dr. _Harvey_ conclude, that the Blood had a being before any other Part of the Body; and that from it, all the Organs of the _Fœtus_ were both form'd and nourished: But by _Malpighius_'s Observations we find that the Parts are then only so far extended, as to be made visible to the naked Eye, and that they were actually existent before, and discernable by Glasses. After an Incubation of thirty hours, are to be seen the Head, the Eyes, and the _Carina_ with the _Vertebræ_, distinct, and the Heart. After forty hours its Pulse is visible, and all the other Parts more distinct, which cannot be discerned by the naked Eye before the beginning of the fifth day; from whence it seems probable, that even the so early discovery of those Parts of the _Fœtus_ by the Microscope, is not the discerning of Parts newly formed, but only more dilated and extended by receiving of Nutriment from the _Colliquamentum_; so that they seem all to have been actually existent before the Incubation of the Hen. And what _Swammerdam_ has discovered in the transformation of Insects, gives no small light to this; whilst he makes appear in the Explanation of the 13th Table of the General History of Insects, that in those large _Eruca's_ which feed upon Cabbage, if they be taken about the time they retire to be transformed into _Aurelia's_, and plung'd often in warm Water to make a Rupture of the outer Skin, you will discern through the transparency of their second Membrane, all the Parts of the Butterfly, the Trunk, Wings, Feelers, _&c._ folded up. But that after the _Eruca_ is chang'd into an _Aurelia_, none of these Parts can be discern'd, they are so drencht with moisture, tho' they be there actually form'd. Another Consideration is from the Analogy, which we may suppose between Plants and Animals. All Vegetables we do see proceed _ex Plantula_, the Seeds of Vegetables being nothing else but little Plants of the same kind folded up in Coats and Membranes; and from hence we may probably conjecture, that so curiously an organized Creature as an Animal, is not the sudden Product of a Fluid or _Colliquamentum_, but does much rather proceed from an Animalcle of the same kind, and has all its little Members folded up according to their several Joints and Plicatures, which are afterwards enlarged and distended, as we see in Plants. Now tho' this Consideration alone may seem not to bear much weight; yet being join'd to the two former, they do mutually strengthen each other. And indeed all the Laws of Motion, which are as yet discovered, can give but a very lame account of the forming of a Plant or Animal. We see how wretchedly _Des Cartes_ came off when he began to apply them to this Subject; they are formed by Laws yet unknown to Mankind; and it seems most probable, that the _Stamina_ of all the Plants and Animals that have been, or ever shall be in the World, have been form'd, _ab Origine Mundi_, by the Almighty Creator within the first of each respective kind. And he who considers the Nature of Vision, that it does not give us the true magnitude, but the proportion of things; and that what seems to our naked Eye but a Point, may truly be made up of as many Parts as seem to us to be in the whole visible World, will not think this an absurd or impossible thing.

But the second thing which later Discoveries have made probable, is, that these Animalcles are originally _in Semine Marium_ & _non in Fœminis_. And this I collect from these Considerations: 1. That there are innumerable _Animalcula_ discover'd _in Semine Masculo omnium Animalium_. Mr. _Leewenhoeck_ has made this so evident by so many Observations, that I do not in the least question the truth of the thing. The reason of their Multitude, and some of the Difficulties which arise thereupon, he has cleared to very good Purpose, so that I shall not repeat them. 2. The observing the Rudiments of the _Fœtus_ in Eggs, which have been fecundated by the Male, and the seeing no such thing in those which are not fecundated, as appears from _Malpighius_ his Observations, make it very probable that these Rudiments proceed originally from the Male, and not from the Female. 3. The resemblance between the Rudiments of the _Fœtus in Ovo_, both before and after Incubation, and the _Animalcle_, makes it very probable, that they are one and the same. The same Shape and Figure which Mr. _Leewenhoeck_ gives us of the _Animalcle_, _Malpighius_ likewise gives of the Rudiments of the _Fœtus_, both before and after Incubation; yea, and even the _Fœtus's_ of Animals do appear so at first to the naked Eye, so that Dr. _Harvey_ does acknowledge that all Animals, even the most perfect, are begotten of a Worm, _De Gen. Anim. Ex._ 18. 4. This gives a rational account of many _Fœtus's_ at one Birth, especially that of the Countess of _Holland_, and how at least a whole Cluster of Eggs in a Hen are fecundated by one Coition of the Male. 5. This gives a new light, as it were, to the first Prophecy concerning the _Messiah_, that the Seed of the Woman shall bruise the Head of the Serpent, all the rest of Mankind being thus most properly and truly the Seed of the Man. 6. The Analogy I have already mentioned, which we may rationally suppose between the manner of the propagation of Plants and Animals, does likewise make this probable. Every Herb and Tree bears its Seed after its kind; which Seed is nothing else but a little Plant of the same kind, which being thrown into the Earth, as into its _Uterus_, spreads forth its Roots, and receives its Nourishment, but has its form within its self, and we may rationally conjecture some such Analogy in the Propagation of Animals.

The third Particular which later Discoveries make probable, is, that Animals cannot be formed of these _Animalcula_ without the _Ova in fœminis_, which are necessary for supplying of them with proper Nutriment: And this these Considerations seem to evince. 1. It is probable that an _Animalcle_ cannot come forward, if it do not fall into a proper _Nidus_. This we see is the _Cicatricula_ in Eggs; and tho' a Million of them should fall into an Egg, none of them would come forward, but what were in the Center of the _Cicatricula_; and perhaps the _Nidus_ necessary for their formation is so proportion'd to their bulk, that it can hardly contain more than one _Animalcle_; and this may be the reason why there are so few Monsters. This we see is absolutely necessary in _Oviparis_; and the only difference which seems to be between them and the _Vivipara_, in this matter, is in this, that in the latter the _Ova_ are properly nothing more but the _Cicatricula_, with its _Colliquamentum_, so that the _Fœtus_ must spread forth its Roots into the _Uterus_ to receive its nourishment; but the Eggs in _Oviparis_ may be properly term'd an _Uterus_, in relation to the _Fœtus_; for they contain not only the _Cicatricula_, with its _Amnion_ and the _Colliquamentum_, which is the immediate nourishment of the _Fœtus_, but also the materials which are to be converted into that _Colliquamentum_; so that the _Fœtus_ spreads forth its Roots no farther than into the White and Yolk of the Egg, from whence it derives all its nourishment. Now that an Animalcle cannot come forward without some such proper _Nidus_, Mr. _Leewenhoeck_ will not readily deny; for if there were nothing needful, but their being thrown into the _Uterus_, I do not see why many hundreds of them should not come forward at once; for as to what Mr. _Leewenhoeck_ says, that one of them would be-dwarf and choak the rest; this might fall out in process of time: But at first I do not see why many of them should not grow together, whilst scatter'd in so large a Field (and yet no such thing is observed) if there were not an absolute necessity of a _Cicatricula_ for their growth and thriving. Now, 2. That this _Cicatricula_ is not originally in _Utero_, seems evident from the frequent Conceptions which have been found _extra Uterum_: Such as the Child which continued Twenty six Years in the Woman of _Tholouse_'s Belly, mention'd _Numb._ 139. of the _Philos. Trans._ And the little _Fœtus_ found in the _Abdomen de St. Mere_, together with the Testicle torn and full of clotted Blood, recorded _Numb._ 150. both taken out of the Journals _des Savans_: Such also seem to be the _Fœtus_ in the _Abdomen_ of the Woman of _Copenhagen_, mention'd in the _Nouvelles des Lettres_, for _Sept._ 85. _pag._ 996. all the Members of which were easily to be felt through the Skin of the Belly, and which she had carried in her Belly for four Years; and the seven Years Gravidation, related by Dr. _Cole_, _Numb._ 172. of the _Transact._ That these two were undoubtedly _extra Uterum_, is uncertain, because the last was not open'd after her death, and the former may be yet still alive. Now granting once the necessity of a proper _Nidus_, for the formation of an Animalcle into the Animal of its respective kind; these Observations make it probable, that the _Testes_ are the _Ovaria_ appropriated for this use; for tho' the Animalcles coming thither in such Cases may seem to be extraordinary, and that usually the Impregnation is in _Utero_; yet it may be collected from hence, that the _Cicatriculæ_ or _Ova_ to be impregnated, are in _Testibus fœmineis_; for if it were not so, the accidental coming of Animalcles thither could not make them come forward more than in any other part of the Body, since they cannot be formed and nourished without a proper _Nidus_. But 3. It is acknowledg'd by all, that the _Fœtus in Utero_, for some considerable time after Conception, has no connexion with the Womb, that it sits wholly loose to it, and is perfectly a little round Egg with the _Fœtus_ in the midst, which sends forth its Umbilical Vessels by degrees, and at last lays hold on the _Uterus_. Now from hence it seems evident, that the _Cicatricula_, which is the Fountain of the Animalcles nourishment, does not sprout from the _Uterus_, but has its _Origin_ elsewhere, and falls in thither as into a fit Soil, from whence it may draw Nutriment for the growth of the _Fœtus_, else it cannot be easily imagin'd, how it should not have an immediate Connexion with the _Uterus_ from the time of Conception. If you join all these three Considerations together, _viz._ that an _Animalcle_ cannot come forward without a proper _Nidus_ or _Cicatricula_; that there have been frequent _Fœtus's extra Uterum_; and that they have no _Adhæsion_ to the _Uterus_, for a considerable time after Conception, they seem to make it evident, that Animals cannot be form'd _ex Animalculis_ without the _Ova in Fœminis_. To all these I shall subjoin the Proposal of an _Experimentum Crucis_, which may seem to determine, whether the _Testes Fœmineæ_ be truly the _Ovaria_, _viz._ Open the _Abdomen_ of the Females of some kinds, and cut out these Testicles, and this will determine, whether they be absolutely necessary for the formation of Animals.