An entire body of philosophy according to the principles of the famous Renate Des Cartes in three books, (I) the institution ... (II) the history of nature ... (III) a dissertation of the want of sense and knowledge in brute animals ... / written originally in Latin by the learned Anthony Le Grand ; now carefully translated from the last corrections, alterations, and large additions of the author, never yet published ... by Richard Blome.

CHAP. XIX. Concerning Reflexion and Refraction.

I. What Re∣flexion and Refraction is. FRom what hath been said, may be easily ga∣ther'd what it is for a Body to be Reflected or Refracted. For since in Compound Determination the Body moved, meeting with another Body, tho' it keeps the same motion, yet only retains one part of its Determination; it so happens that be∣cause it cannot go forwards, it suffers an Oblique Reflexion towards the opposite part; but if it can, then Refraction. Hence Reflexion may be de∣scrib'd, The Regress or Return that happens to a moved Body, because of the meeting of another Body, which it cannot penetrate. And Refraction, is the incurvation, or change of Determination in the Body moved, which happens to it, whilst it enters or penetrates the Medium.

II. Sometimes a Body is directly re∣flected. Thus if a Body moved directly, meets with ano∣ther that is unmoveable, it must be reflected by the same Line by which it is directly moved, there being no cause to oblige it, to describe any other. For example; if the Body G be mov'd directly by the Line GB, towards the Earth CE, which I * 1.1suppose unmoveable, it will not be reflected by the Lines BA, or BF, but by the Line BG. The Reason whereof is, because the Determination of the Lines BA and BF is compounded, and that no cause can be assigned, that should oblige the Body

G, which was moved with one only Determina∣tion toward the Earth CE, to retire from thence with two Determinations.

III. Sometimes obliquely. But if the Body A be mov'd obliquely by the line AB, and that it meet with the Earth CBE, which is suppos'd unmoveable, it will be reflected by the line BF, which is diverse from the line AB. To prove this, draw through the Points A and B, the lines AC and HB, perpendicular to CE. This done, consider in the first place that the Body A, moving towards B, doth at the same time ap∣proach to the lines CE and HB, that is to say, that its Determination from A to B, is compound∣ed of its Determination from A to C, and from A to H; or that which is the same thing, of its Determination from above to beneath, and from the left to the right. Consider in the second place, that the Earth CBE opposeth it self to the Determination from A to H, and by conse∣quence that the Body A, when it meets with the Earth, must take a quite contrary Determination to that which it had, by which in an equal space of time, it must advance equal quantities; that is to say, if within a Minute, the Body A, des∣cended by the line AB, to the line CBE, it must in another minute remount again from the line CBE by the line BF.

IV. The Angle of Reflecti∣on is equal to the An∣gle of In∣cidence. But that we may know more distinctly to what part the Body or Ball struck, must rebound, let us describe a Circle from the Center B, at the Interval BA: For all the Points which are distant the same Interval from B, as A is, do meet in this Circumference. Now to be able particularly to de∣termine this Point, let us with Des Cartes Chap. 2. Dioptr. erect three perpendicular lines AC, HB and FE, upon CE, so as there may be the same distance between AC and HB, as between HB and FE. Next let us say, that in the same space of time, in which the Ball hath been moved to∣wards the right from A, one of the Points of the line AC, into B, one of the Points of the line HB, it must move from the lines HB, to some point of the line FE. For all the Points of this line FE, have in this respect the same Distance from HB, as all the Points of the line AC, and it is also as much determined to move that way as it was before. Now so it is, that it cannot arrive at one and the same time to any point of the line FE, and to some point of the circumference of the Circle AFD, save only at the point D, or at F, because there are none but these two, where they intersect one another: So that the Earth hindring it from passing towards D, we must conclude that it must infallibly move towards F. And thus you may easily see how Reflection is made, to wit, according to an Angle, which is always equal to that which is call'd the Angle of Incidence. As if a Ray, coming from the point A, to fall up∣on the point B, on the surface of a flat Looking∣glass CBE, should so reflect toward F, that the Angle of Reflection FBE, be neither greater nor less, than the Angle of Incidence ABC.

V. The Angle of Reflecti∣on is some∣times less than the Angle of Incidence. Yet it is not necessary that the Angle of Re∣flection, should be always equal to the Angle of Incidence, forasmuch as sometimes it may be greater and sometimes less. For suppose the Body A, to descend by the line AC, towards the Body DE, and to reach the Center C, in the space of one Moment; and that the swiftness of this Motion; be diminished one half in the Point of Contact C; * 1.2it is evident that the Body A, being reflected from the opposite Body DE, in its Center C, cannot in one moment run through an equal line, since it is supposed to have lost one half of its swiftness, and therefore spending two Moments, in running through an oblique line, it will by Reflection arrive at the Point of the Circle B, and will there make the Angle of Reflexion BCE, less than the Angle of Incidence ACD. This Reflexion is commonly call'd from a Perpendicular, because the line of Reflection BC doth more deviate from a Perpen∣dicular, than the line of Incidence AC.

VI. When the Angle of Reflecti∣on is great∣er than the Angle of In∣cidence But if the Body B, be carried to the opposite Body DE by the oblique line BC, and arrive at the Center C, in the space of two Moments, and that its Motion be encreased in the point of Con∣tact, so as to become twofold swifter, it is evident that the Body B, rebounded by the opposite Bo∣dy DE, must in the space of one Moment, in its ascent run through ••an equal oblique line, and arrive at the point A of the Circumference of the Circle; and so the Angle of Reflection ACD, will be greater than the Angle of Incidence BCE. And this Reflection is call'd Reflection to a Perpen∣dicular, because the line of Reflection AC, doth less deviate from a Perpendicular than the line of Incidence BA.

VII. What Re∣fraction is, and how ••t is made. What has been said is sufficient to explain the nature of Reflection: We proceed now to Re∣fraction, which is when a Body passing from one Medium to another doth deflect from the straight line it described. So that by the Refracti∣on of Motion nothing else is understood, but the Deflection or turning aside, which a Body suffers in passing from one Medium into another. For the understanding of this Refraction, we are to consider, first, whether the second Medium re∣sists the Motion more or less than the first, and whether the Body moved do meet it directly, or obliquely; for if it meets it directly, whether it resist more or less, it is without doubt, that the Body moved must in no wise change the determi∣nation of its Motion, in penetrating of it.

VIII. A Body di∣rectly fall∣ing int•• •• medium ••••••∣fers no Re∣fraction. To prove this, let us suppose the Body L de∣scending in the Air by the Perpendicular line LB, and that it directly meet the Water which is under the surface CBE, which separates the two Me∣diums: This being so, I say that the Body L hav∣ing pierced the surface CBE, will tend directly * 1.3towards G, because the Water that is under that surface, doth resist it equally on all sides, and that there is nothing but the inequality of that resist∣ance, that can make it turn aside.

IX. But if it falls obli∣quely it i•• refracted. On the contrary, if the Body moved meets the second Medium obliquely, then of necessity it must deflect either to the right or left, according as the second Medium resists its Motion more or less than the first; as by example, let us imagine a Ball struck with a Racket from A, obliquely to B, to meet there not with the Earth, but with the Wa∣ter, whose surface is bounded with CBE, the Ball in this case doth not directly tend to D, but towards I, and this bending or deflection, which is measur'd by the Quantity of the Angle BDI, is call'd Refraction.

X. The cause of Refraction. The Cause of this Refraction is the Resistance it meets with: For seeing that every thing as much as in it lies continues always in the same state,

we can give no reason why any Body should de∣flect from the Straight way in which it began to move, but because it meets with some hindrance in that part from whence it rebounds. Thus when the Body A, after it is arriv'd to the Point B, is turn'd aside, and tends towards I, we must con∣clude that it meets with more resistance towards the left side of B, than on the right; and if it be turn'd aside towards D, that it finds a greater Re∣sistance from the right side of B, than from the left. And therefore if we perceive that the Water doth more hinder the motion of the Ball than the Air, we may easily judge that the Ball which in the Air is moved from the Point A to the Point B, that from thence it may pass into the Water, must pur∣sue its course towards I, and deflect from a Per∣pendicular.

XI. How a Body comes to be variously refracted. This may be apply'd to all Bodies and all the Mediums they pass through. Wherefore this may pass for a Maxim, that as often as a Body moved, passeth from one Medium into another, that doth resist it more, it must be refracted, by declining from a Perpendicular. And that on the contrary, when it passeth from one Medium to another where it finds less Resistance, there it must deflect towards a Perpendicular.

XII. It is requi∣ed to Re∣fraction that a Body fall oblique∣ly upon a∣nother Body I have already said that it is necessary to Re∣fraction that the Body fall obliquely upon the sur∣face that separates both Mediums, that so it may be deflected or turn'd aside. For if it should pro∣ceed Perpendicularly, without any Declination, seeing it would not be hindred on the one side more than on the other, from proceeding in a straight line, it could not suffer any Deflection, and consequently must continue its right motion, as hath been said.

XIII. Requisits to determin the quanti∣ties of Re∣fractions. To Determine the Quantity of Refractions, we must attend to the particular constitution of Bodies, whether they do more or less resist the passage of Bodies moved. For suppose we that the line CBE separates two Mediums, the upper whereof is Air and the undermost Water, and that the Water doth as much again as Air resist the motion of the Ball * 1.4A. Suppose we likewise that the Ball A, having past the oblique line AB in one moment, to meet with the Point B, there obliquely to enter the Wa∣ter: And that neither the Bigness, Weight, or Figure of the Ball do hinder it from so doing; Yea, and that its motion in the Air hath been always equal, and that having lost the one half of its swiftness, by meeting with the Water, it loseth now no more throughout its whole Course, how deep soever it may enter the Water; because this is nothing to the purpose, since the Deflection hap∣pens only in the Surface, and the Water, which resists equally on all sides, can only make the Ball to spend a greater or less space of time in its motion, but cannot make it to deflect from the Line, which it had begun to move in.

XIV. How much the Motion of a Ball is retarded by entring the Water. These things being observed, that we may know what way the Ball A must take, we are to consider that tho' the motion of the Ball, be lookt upon as simple, this doth not hinder but that its Determination in the line AB, with respect to the Surface of the Water, is compounded of two other motions, the one whereof presseth it from AF to CE, and the other at the same time presseth it from the left AC, to the right FE, so that both these together lead it to the Point B, by the right line AB.

XV. Where the variation is in the Body moved. Moreover we are to observe, that of both these Parts, whereof we understand that this Disposition consists, the one only is changed by the Surface of the Water, viz that which drives the Ball downwards, whereas that which pusheth the Bal l towards the right hand continues still the same.

XVI. How much the Balls motion is fore▪ slowed when it passeth through the Water. Having therefore described the Circle AFD from its Center B, and having describ'd upon CBE three Perpendicular Lines AC, HB, FE, so as that the space between them FE and HB, is the double of that which is between HB and AC, we shall find this Ball will go on to the Point I: for seeing that the Surface of the Water CBE, doth exactly take away one half of its swiftness, it must take up a double proportion of the time in which it passeth from A to B, in passing from B to any point of the Circumference AFD. And see∣ing nothing is lost of the Disposition whereby it was carried towards the right hand, in the double proportion of that time, wherein it proceeded from the line AC to HB, it must go twice the length towards the same part, and consequently approach to some point of FE at the same Moment in which it draws near to some point of the Circumfe∣rence of the Circle of AFD, which would be im∣possible if it did not advance to I.

XVII. The more obliquely a Ball falls on the Wa∣ter, the more is it destected. We are also to take notice that the more obli∣quely a Ball dasheth against the Surface of the VVater, the more it is turn'd aside by it; so that if it be directed to right Angles, as if it were struck from H to B, it proceeds in a right line without any Declination to G, as hath been said already. But if it be driven along by a right line, as AB is, and lie so obliquely on the Surface of the VVater CBE, that the drawn line FE, cannot intersect the line AD, then will it not penetrate the VVater, but will rebound from the Surface B into the Air to∣wards F, after the very same manner as if it had lighted on the Earth. As we see in those Stones wherewith Boys make Drakes in the Water; and as Bullets which (according to the Relation of those who have been in Sea fights) being oblique∣ly shot out of Cannons rebound from the VVater, and hit Men standing on the Decks.

Notes

• * 1.1

  Figure 12.
• * 1.2

  Figure 13.
• * 1.3

  Figure 14.
• * 1.4

  Figure 14.