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presented to the earth being who ly concealed Or Wholly illuminate d. At other times the illuminat ed sui face is represented by the Spacet est be tween the intersections of two great Circles, the potnts of intersectiora be ing at the extremi ty of a lunar diameter. Regarding theSe potnis as the lunar potes, the in ner boundary of the illumina ted part may be regni ded as a meridian circle. A cirCle dra n throughthe lunar potes So as to divide the lunar Sursace visibi e to us in totiuo equat paris may be called the lunar Coliare. The innstr boundaryof the luminous portion hecome S identicat with the colure on thesevenit, and twenty-frst Jay, and appearS to u S as a Straight line. Besore the foui ieentli Jay this Circle present S iis Convex fide to the Sun, after that day it S concave side. In the lalter half of the monili the phases are Seen reverSed illi Complete OCCuliation returnS. So too by a reaSoning procesS we be come Convinced that thoughthe henVen appenrS to us as a plane sursace, it must in reali ty be Spheri Cal, or at lea St polyhedral, go as to be unctis tinguis habie Doma Sphere. Vere it plane, the Stai S would ali di sappear below theliori Zon or rise above it at the sanae moment .... 108-li4
As distance is appreciated only through a reasoning proceSS. So itis With magnitude. The mere magnitude of the angle subtended by the object cloeS not sum Ce, sor objects of the Same magnitude atdifferent distances appear of different magnitude, and Con VerSely. AS in the case of distance, there muSt be intermediate objecis familiarto the eye with whicli mental Comparison Can be made. Extremedi Stance osten renderS Such a comparison impos Sible . . 1 DL II 6
apprehended by a Change in the position os a body relatively to
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produced. Again, While we are Walhing at night in any direction, a Star to the right of us Will seem to move with us, Since it holdsvery nearly the Same poSition relatively to us at the eno of our passage as at the beginning : the star being far of the differencemade by our Change of place is impercepti ble. When the sun ison the meridian, a long line of men extending Dona east to west xv illati see him directly in front and the shadorus of their bodies willappear parallel; the divergen Ce of the Shadows is too smali to bepercepti ble. The motion of the planeis is imperceptibi e by directinspection. Rapio motion in a circle, follo ed by rest, gives the
One of the most dissiculi problenis is that of the scintillation of the
fixeo stars. Aristolle rem artis their contrast in this respect with the planeis, and attributes it to their greater distance ; the eye, being more stra ined, is tremul Ous. Scintillation is different Dona the tremor Sometimes Seen in the Stin and other planeis at rising and setting. Is distance were the sole explanation, we Should expe et Saturn to scintillate, whicli it cloes not. Further, it is only the larger of the fixed stars that do So. Therefore strength of light must be a condition. And yet, Sin Ce the sun at noon does not Scintillate, the light must not be too Strong. One of the Causes would Seem to be the internat Strain of the eye at very di Stant objecis. The planetarybodies are ea Sily perceived to be near, and with them there is nostra in . Moreo ver, the faCt of extreme distance of itSelf wealiens the visual rays. It may be objected that the strain is greater in the caseos sinali stars than os large : but here the condition of sumciently Strong light is wanting. Again, it is objected that is ocular stratiabe one of the factors, this dependS upon each observer's Choice and will. But this is not So. It is one of those actions whi Ch havebecome involuntary through habit. Eut how is this differen eos distance bet ween the plane is and the stars to be knownῖ Iis quantity doubiless is not known. But the faci that there is adimerenCe is a matter of Sensation. Has the densi ty, or has themotion of the medium, an 'thing to do with scintillation 8 Perhaps both contribute, as Averroes has suggested ; and perhaps also atthese immense distances the visual power is exhausted, and actingon ly intermittent ly, produces the tremulo us impression. By motionos the medium Ke are to understand here, not violent motions of the
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lower air like wind, but subile motions caused by the revolutions of the heavens and of the exhalations whicli pervade them. A Combination of the foregoing Cata Ses may sufficient ly expla in this
Complicated problem . . . . . . . . . t 20-126
VO may now sum up the re Suits of Our stud y of direct vision. We have spoken of vi Sion aS Opera ting by sensation, by re ColleCtion, and by a Syllogistic proces S. Is these two last are to be interpreted as in the schoOis, they would imply the intervention os Reason. But it is evident that brutes have the power os recogni ging and distinguishingboth universals and particularS. A d Og recogniZeS a particular mala, and also reCogniges men in generat frona clog S, trees Or other ObjeCt S. There re this faculty must be a function of Sensitive lis , and cannoti mply reason in the Strici sense of that wOrd. Further, animal S PASSthrough a train of mental processes analogo uS to syllogi Sti C reasoning, though they cannot put it into a logical figure. They have a store-house of mental impressionS. They Can genera lige, and they Candraw conclusi OnS ; though they a re not ConSCi OuS of do ing So, and cannot give an account of what is passing within them . . 126 129
FIR ST DISTINCTION : ON REFLECTED UISION . . . 130-l46
It i S unne Ces Sary to repeat what has been at ready sa id of the structure of the eye and the sunctions of sensation. Bodies thatim pede the passage of visual radiations may be ei ther whollyopaque, AS a Sione Wall ; or partialty opaque, aS Water, glaSS, crystal. Opaque bodies clo not de Stroy the radiation they merelyalter iis path. An opaque body may be rough or smOoth. Whenthe Surface i S rough, the paris being un symmetrical scat ter theradiations irregularly, and there is no image. With smooth SurlaCesthe paris ali act alilae, and the radiation comes bach to the eyeun injured, though Debler than in direct vision Proos is subjoinedof the equali ty of the angi es of inciden ce and reflexion, and this proos vili hold, whether the sui face be plane or spherical: for the Tay maybe regarded as falling on the tangent plane .... 130-132
The mirror contains nothing. What is seen is the real objeci, only the radiation froni it has followed an angular CourSe. The eje
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must be siluated at the extremi ty of that Course, whether it has been straight or angular, in order to receive the impression. It follows that the radiation produces no durable esseCt on the reflectingsui face. From this again it folio ius that ille Inoon and the Stars shine with their own light, not with light reflected Dom the sun :other i Se we should See the Sun's image reflected in them. Nei ther, again, is a Comet the reflexion os solar light Do in the furface of n Star. The Case of the rainbow will be considered asterward S. The
position in which we juclge the reflected object to be is, in planem irrors, at the intersection bellino the mirror of the prolongation of the reflected rny with that of the perpendicular let fati on the mirrorisona the objeci. But in mirrors other than plane the apparentPΟSition VarieS Very greatly ....... 132-134CHAPTER III.
There are Seven hinds of mirrors, spherical, Conicat, Cylindrical, or plane. of the first three classes each may be ei ther ConVeX or Concave. Geometri Cal proos i S gi ven that in plane mirrors the image and the objeci appear equi distant frona the plane of the mirror Onopposite Si de S. Nothing reatly takes place et ther in the mirror orbe hinci it. The effect produceo is a mental impression CauSed by the peculiar path taken by the radiation frona the objeci. In spheri-Cal Convex mirrors, the intersection of the visual ray with a line trawn Dom the object to the Centre of the sphere fixes the apparent position of the objeci. This intersection may be beyond the mirror,
in the mirror, or on the Same si de as the objeci. Usualty the image appears leSs than the reali ty, be cause the rays Come DOm n Smaller rea than in the case of the plane mirror : in the spheri Cal most Ofthem are dispersed. The image is erect but distorieo: the outerrays of the Cone touChing potnis more di Stant from the eye than themedian rays. Ora ly when the image of a right line crosses the Centre of the sphere is that image rectilinear. Moreover, in ConVex mirTOTSthe image is nearer to the mirror than the object is, hecause the intersection of the visual ray with the perpendicular occurs SoOner in spherical than in plane mirrors. In Cylindrical mirrors the errorSare even grenter than in Spherical, excepi in the one CaSe wherea line in the object is equi distant horn the axis of the Cylinder. Only lf this line has any breadth, iis transverse magnitude wili be
The greatest illusions are tho se that occur in concave mirrorS, bothas to the Sige of the image, and the number of iis repetitionS; Some
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Is a mirror be placed in a vesset of water and the image of the sun reflected stom it, a second image will appear beside the firsi, whichwas held to be that os a star. Is it were, the sun 's light would hi deit. Moreo ver, the Same effect is produced by the moon or bya Candie. There are in faci here two mirrors, the sursace of the water and that of the mirror. That frona the mirror is more peri Ct, the other being wenkened by the loss of Some of the rab S throughTODRCtion. Fracture os a mirror does not necessari ly reguli in multiplication Os images, uni ess the pie Ces are remoVed hom eaCh
other . . . . . . . . . . . . t 44-J46
SECOND DISTINCTION : ON RETRACTION . . . . t 46-159
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whicli is denser than the air, towards the normal; with the exceptionos such rays as fali verti Cally on the Cornea. The Same pol ni may emit a vertical rny anct also an infinite number of oblique rays, thesel alter Co- opera ting in the act of Vision ..... 146- 148CHAPTER II.
The intersection of the perpendicular directed hom a poliat in the object with the visual ray determines the apparent position of that poliat. I f the eye be in the rarer medium and the object be in thedenSer the potnt appears nearer than it reatly is ; and conversely 148-149
Examples of the foregoing. The submerged part os an oarillustrates case I of Ch. 2. Is the eye were under water the upperpart would illustrate Case 2. I f an object be placed in a basin, and the observer step backwards tili it beComes invisibie, the object will againbecome visibi e by pouring water in to the basin. This again illustrates
os intervening objecis makes judgement of distance dissiculi. A crystallens is consisting of a sinali portion of a Sphere, with the convexi tyturned to the eye, Will magni ου Smali objecis placed beneath it, in
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accordance with the fifth rule. Is it be the half of a sphere or morethan the half, then the Centre of the sphere u ill be bet ween the eyeand the objeci and the magnifying effect will be less. A cantile however held at a moderate distance will appear larger than is
placed nearer, beCause the refracted rays frona the extremi ty of the object are talien for direCt rayS. MoreOVer, TayS from the nearer position are apt to daggle a weali vision and thus are neutralige d. Frona a Some hat more distant position they are better apprecia ted. These are a sew illustrations os ille effecis os refraction. They arenot intended as an exhaustive treaiment of the subjeci. . . 153-l59THIRD AND LAST DISTINCTION 159 166
Ait these scientific trullis have a spiritual Signification. The prayer, Guard us as the pupil of thine eye, Cannot be uncterstood without knowledge of the structure of the eye and the pupil. Each of the Structures by whicli the pupit is defended has an allegorical
AS in vision we should ne ither be too sar frona the object nor toonear, so for spiritual vision we should net ther be too far hom God nor too presumptuous ly near. Ut Sion iS by Sen Se, by memory, and by reaSoning ; this may be paralleled in spiritual vision. Visionis direct , refracted, or reflected: Spiritualty the first is divine, theseCond angeli C, the third human. Or, again, the sirst is the perfectvi Sion after the resurrection; the seConcl, besore resurrection and after death ; the third, the imperfeci vision os illa on earlli . . t 61 - 163
On the practical application of this science there is much to beSaid. Hy reflexion we Can multiply the images of objecis at will, a S by natural mirrors formed by Vapours in the Shy the image of the Sun and inoon are multiplied. Mirrors may be ere ted in elevated positions which may reveat the de talis of an enemy'S Camp, as is sald to have been done by Caesar frona the coasi os Gaul whenabout to invade Britain 164 165
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Having laid clown the generat principies of wisdom so far as theyare mund in language, in mathemati CS, and in optics, I pass to the
the prooD that si re burias, but will not be satisfied of it tili he has been buriit. Even in geometry the demonstration of the sirst propositionos Euclid fatis to carry conviction illi the figure has been inspected. When Aristolle spealis of knowledge of the Cause as a higher Lindof knowledge than that gained by experie iace, he is spe aking of mere empiric knowledge of a fact; Ι am Speaking of eXperimental knowledge of iis CauSe. There are numerous bellese commonly held in the abSence of experiment, and wholly salse, Such as that adamant can be brohen by goais' blood, that the beaver vhen Chaseo throri saway his testicles, that a vesset of hot water De eges more rapid lythan One of Cold, and So on. Experience is of two kinds : i) that in which we use our bodily senses aided by instruments. and by evidence of trustworthy WitneSSCS ; ano sa) internat experience of things spiritual, Whicli Comes of grace, and whicli osten leads toknowledge of earthly things. The mino stat ned with vice is lilae
It is sol ely by the aid of this science that we shali be able to dis-abuse men of the fraudulent tri Clas by whicli magicians have imposedon them. AS Compared with other sciences, this science has three Characteri Stics praerogativas ). of these the sirst is, that it con-
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it is rectangular, Some time S Cii Cul Rr ....... 171
Armed with these terrestriat sacis, the experimenter pro CeedS to examine the celestial phenomenon. He finiis, on examining the Stan' saltitude and that of the summit of the bo , that the two vary inverSely. The bow is alWays opposite the sun. A line may be drawn froni the Centre os the sun through the eye of the observer and the Centre of the circle of whicli the bow is an arc to the sun'S nadir. AS oneextremi ty of this line is depressed, the other i S elevate d. It becomesthus possibi e to pompute the altitude of the sun beyond whicli norainbow is possibie, and at So the maximum altitude of the bow. It vi l be Mund both by calculation and experience that this altitude in the latitude os Paris i S forty-t o degrees . . . . . t 75-178CHAPTER V. Stili surther investigating the s hape of the iris, and the portion os itthat Can be seen, the experimenter Conceives a Cone of whicli the apexis the eye, the base is the circle of the iris, the axis being the lineat ready describe d dra via Dom the sun'S centre through the eye to the Sun 'S nadir. In cases Where this Cone is very shori, the whole of the base may be above the hor gon, as may osten be Seen in the Sprayos a waterfall. In the shy however the Cone is too elongated to admitos this : the base is bisected in various proportions by the plane of the
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In some latitudes there Cara be no rainbow at noon even in thewinter solstice. When the latitude i. e. the distance hom the genit lito the equator) is 248 25 , the sun's altitude at noon in the winter solstice will be 42', therefore there Can be no bo N. Passing northsrom this latitude, there Can always be a noon rainbow till we come tolatitude 66' 25 , when at the winter Solstice there is no sun. Similarcalculations cara be made for other latitudes .... 181 185
V e have now to inquire whether the iris comes hom incident, reflected, or refracted rays. IS the bow an image of the sun i Arethe colours ora the clouds real Θ Why is the iris of circular sorm tbiere we Cali experiment to our at d. We find on trial that is we move in a direction parallel to the rainbow it follows us with a velocityeXRCtly equat to Our own. Is we approach it, it recedes: is we recede, it sol lows. The sanie phenomenon occurs with respect to the Sun. We have Seen that the sun is alWays opposite the rainbow; theli ne belween the Centre of the bow and the Centre of the sun passing through the eye of the observer. Is the sun were apparently stationary, this Would involve the bow moving much faster than the observer, the lalter moving through the fame angle, hut at lessdistance Dom the apex. But this is not so. Theresere there is an apparent motion of the sun concurrently with that of the bow. The Case is analogous to what happenS when a hundred men are rangedin line facing the sun. Each sees the sun in front of him. Their Shadorus Seem parallel, though we know that in reali ty they must diverge, yet owing to the vast distance of the sun this divergen e is impercepti ble. we are thus brought to the conclusion thnt, SuppoSinga rainbow to occur, each of the hundred men, facing backwards, would see a disterent rainbow, to the centre of whicli his own Shadowwould potnt. The rays Causing the iris are therefore not incidentrRyS, Other i Se the Colour would appear fixed in the clo ad. An d fortite Same re ason they are not refracted rays, for in refraction thei mage does not solio K the change of place of the observer, as is theca se here. One Condition of the phenomenon is that the atmospherestiali be more illuminated at the Standpoint of the obServer, and leSS