Part 9

The Description Of The Glasses

by Rene Descartes Icon

We should first choose a transparent material which is:

  • easy enough to cut
  • hard enough to retain the shape given to it
  • the least colored and which causes the least possible reflection.

Glass has these perfectly and purely. It is composed of very subtle ashes.

Mountain crystal seems cleaner and more transparent. But its surfaces cause more rays to be reflected than those of glass, and so it may not be so clean for our purpose.

Now, in order for you to know the cause of this reflection, and why it is done rather on the surfaces both of glass and of crystal than not in the thickness of their body, and why it is greater there in crystal that in glass, you must remember the way in which I made you conceive above of the nature of light.

When I said that there was nothing else in transparent bodies than the action or inclination to move of a certain very subtle matter which filled their pores, and that you thought that the pores of each of these bodies transparencies are so smooth and so straight that the subtle matter that can enter them flows easily all along without finding anything to stop it; but that those of two transparent bodies of different nature, like those of air and those of glass or crystal, never relate so justly to each other that there are not always several of the parts of subtle matter which, for example, coming from the air towards the glass, are reflected there, because they encounter the solid parts of its surface: and all the same, coming from the glass towards the air, are reflected and return to the inside this glass, because they meet the solid parts of the surface of this air; for there are also many in the air which may be called solid in comparison with this subtle matter. Then, considering that the solid parts of the crystal are even larger than those of glass and its pores tighter, so that it is easy to judge that it is harder and heavier, we can well think that it must cause its reflections still stronger, and consequently give passage to less rays than does neither air nor glass, although nevertheless it gives it freer to those to whom it gives it, according to what has been said. above.

Having thus chosen the purest glass, the least colored, and that which causes the least possible reflection, if one wishes by its means to correct the defect of those who do not see objects a little distant so well that near, or near than far, the figures best fitted for this purpose are those which are traced by hyperboles. As, for example, the eye B or C[66], being disposed to cause all the rays which come from point H or I to assemble exactly in the middle of its background, and not those from point V or X, it is necessary, to make him see distinctly the object which is towards V or X, to put between two the glass O or P, whose surfaces, one convex and the other concave, having the figures traced by two hyperbolas which are such let H or I be the burning point of the concave, which must be turned towards the eye, and V or X that of the convex.

Diopter figure 27 28.jpg Figures 27 and 28. And if we suppose the point I or V quite distant, as only fifteen or twenty feet distant, it will suffice, instead of the hyperbola of which it should be the burning point, to make use of a straight line, and so to make one of the surfaces of the glass completely flat, namely the interior which looks towards the eye, if it is I which is far enough away; or the exterior, if it is V. For then a part of the object the size of the eyeball can take the place of a single point, because its image will hardly occupy any more space at the bottom of the eyeball. the eye as the end of one of the small threads of the optic nerve. And even, there is no need to use different lenses each time you want to look at objects a little more or less distant than the other; but it is enough for the use to have two of them, one of which is proportioned to the least distance from the things that we are accustomed to looking at, and the other to the greatest; or even just to have one that is midway between these two. For the eyes to which one wishes to appropriate them, not being quite inflexible, can easily change their shape enough to adapt it to that of such a glass.

That if we want, also by means of a single glass, to make accessible objects, that is to say those which we can approach the eye as much as we want, appear much larger and see much more distinctly than without glasses, the most convenient will be to make that of the surfaces of this glass which must be turned completely flat towards the eye, and give to the other the figure of a hyperbole whose burning point is instead where you want to put the object; but note that I say the most convenient, because I admit that, giving the surface of this glass the shape of an ellipse whose burning point is also at the place where you want to put the object, and at the other that of a part of a sphere whose center is in the same place as this burning point, the effect may be a little greater; but on the other hand such a glass cannot be so conveniently cut. Now this burning point, either of the hyperbole or of the ellipse, must be so close that the object, which must be supposed to be very small, being placed there, there remains between it and the glass only precisely as much enough space to give passage to the light which must illuminate it. And you have to set this glass in such a way that nothing remains uncovered except the middle, which is about the same size as the pupil or even a little smaller; and that the material in which it will be embedded be all black on the side which must be turned towards the eye, or even also it will not be useless that it be lined all around with an edge of breakdown or black velvet, so that it can be conveniently pressed close to the eye, and thus prevent any light from reaching it except through the opening of the glass; but outside it will be good if it is completely white or rather completely polished, and if it has the shape of a hollow mirror, so that it reflects on the object all the rays of light that come towards it. . And, to support this object in the place where it must be placed to be seen, I do not disapprove of these little vials of very transparent glass or crystal, the use of which is already quite common in France; but, to make the thing more exact, it will be better still that it be firmly held there by one or two small springs, in the form of arms, which come out of the frame of the telescope. Finally, in order not to miss any light, it will be necessary, while looking at this object, to turn it straight towards the sun. As if A[67] is the glass, C the interior part of the material in which it is embedded, D the exterior, E the object, G the small arm which supports it, H the eye, and I the sun , whose rays do not go directly into the eye, because of the interposition both of the telescope and of the object, but facing the white body or the mirror D, they are reflected first from there towards E, then from E they are reflected towards the eye.

That if we want to make the most perfect telescope that can be used to see the stars or other very distant and inaccessible objects, we must compose it of two hyperbolic lenses, one convex and the other concave, placed in the two ends of a pipe in the way you see represented here[68].

Diopter figure 59.jpg Picture 59.

And first, abc, the surface of the concave glass abcdef, must have the shape of a hyperbola which has its burning point at the distance at which the eye for which this telescope is prepared can most distinctly see its objects. As here the eye G being disposed to see more distinctly the objects which are towards H than any others, H must be the burning point of the hyperbole abc; and for old people who see very distant objects better than close ones, this surface abc must be completely flat; whereas for those who have very short sight it must be rather concave. Then, the other surface def must have the figure of another hyperbola, the burning point of which I being distant from it by the width of an inch or so, so that it meets towards the bottom of the eye when this lens is applied close to its surface. Note, however, that these proportions are not so absolutely necessary that they cannot be changed much; so that, without cutting the surface abc differently for those who have short or long sight than for the others, one can quite conveniently use the same telescope for all kinds of eyes by only lengthening or shortening the stem. And for the surface def, perhaps because of the difficulty we will have in digging it so much, as I said, it will be easier to give it the shape of a hyperbola whose burning point is a little more distant, which experience will teach better than my reasons. And I can only say in general that, other things being equal, the closer this point I is, the larger the objects will appear, because the eye will have to be placed as if they were larger. near him ; and that the vision may be stronger and clearer, because the other glass may be larger; but that it will not be so distinct if it is made too close, because there will be several rays which will fall too obliquely on its surface at the expense of the others.

For the size of this glass, the portion that remains uncovered, when it is embedded in the KLM pipe, only needs to slightly exceed the largest opening of the pupil. And for its thickness, it cannot be too small; for, although by increasing it we can make the image of objects a little larger, because the rays which come from various points deviate a little more from the side of the eye, we also make on the other hand, they appear in less quantity and less clear; and the benefit of making their images grow larger can best be gained by other means. As for the NOPQ convex glass, its NQP surface, which is turned towards the objects, must be completely flat; and the other NOP must have the shape of a hyperbola whose burning point I falls exactly at the same place as that of the hyperbola def of the other glass, and is as far from the point O as we want have a more perfect bezel. Then from which the magnitude of its diameter NP is determined by the two straight lines IdN and IfP, drawn from the burning point I, by d and f, the extremities of the diameter of the hyperbolic glass def, which I suppose to equal that of the pupil; where, however, it should be noted that even though the diameter of this NOPQ glass is smaller, the objects will only appear all the more distinct, and will not appear less for that or in less quantity, but only less illuminated : wherefore, when they are too much, one must have various circles of black cardboard or other such material, as 1,2,3, to cover its edges, and thereby make it smaller than the strength of the light which comes from the objects will be able to allow. As for the thickness of this glass, it can neither benefit nor harm anything, except insofar as the glass is never so pure and so clean that it does not always prevent the passage of something. few more rays than air. As for the KLM pipe, it must be of some fairly firm and solid material, so that the two glasses, set in at its two ends, always retain their exact same position; and it must be all black on the inside and even have an edge of panne or black velvet towards M, so that one can, by applying it close to the eye, prevent any light from entering it except through NOPQ glass; and for its length and width, they are fairly determined by the distance and size of the two glasses. Moreover, it is necessary that this pipe be attached to some machine, such as RST, by means of which it can be conveniently turned on all sides, and stopped vis-à-vis the objects which one wishes to look at; and for this purpose there must also be a sight or two pinnules, like VV, on this machine; and even, besides that, because inasmuch as these glasses make objects appear larger, the less they can show each time, it is necessary to join with the most perfect some others of lesser quality. force by the aid of which one can, as if by degrees, come to the knowledge of the place where is the object which these most perfect make perceive. As are here XX and YY, which I suppose so fitted with the most perfect QLM, that if the machine is turned in such a way that, for example, the planet of Jupiter appears through the two pinnae VV, it will also appear through the XX telescope, through which, in addition to Jupiter, we can also distinguish these other lesser planets which accompany it; and if we cause one of these lesser planets to meet precisely in the middle of this telescope XX, it will also be seen by the other YY, where, appearing alone and much larger than by the preceding one, we will be able to distinguish various regions: and once again, between these various regions, the middle one will be seen through the KLM bezel, and we will be able to distinguish several particular things there by means of it; but one could not know that these things were in such a place of such of the planets which accompany Jupiter without the help of the two others, nor also to dispose it to show what is in any other determined place towards which one wants to look.

We can still add one or more other more perfect glasses with these three, at least if the artifice of men can go so far; and there is no difference between the fashion of these more perfect and those which are less so, except that their convex glass must be larger, and their burning point further away; so that, if the hand of the workmen does not fail us, we will be able by this invention to see objects as particular and as small in the stars as those which we commonly see on the earth.

Finally, if we want to have a telescope that shows close and accessible objects as clearly as possible, and much more than the one I described earlier for the same effect, we must also compose it with two hyperbolic glasses, one concave and the other convex, embedded in the two ends of a pipe, and whose concave abcdef[69] is quite similar to that of the preceding; as also NOP the inner surface of the convex.

Diopter figure 60.jpg Figures 60.

But for the exterior NRP, instead of being entirely flat, it must here be very convex and have the shape of a hyperbola, of which the exterior burning point Z is so close that the object being placed there, it there remains between it and the glass only as much space as is necessary to give passage to the light which is to illuminate it.

Then the diameter of this glass does not need to be so large as for the preceding bezel, nor must it also be so small as that of the glass A[70] of the other before, but it must at approximately be such that the straight line NP passes through the inner hot point of the hyperbola NRP; for, being less, it would receive fewer rays from the object Z, and being larger, it would receive very little more; so that its thickness, having to be in much greater proportion than before, it would deprive them of their strength as much as its size would give them; and, besides that, the object could not be so illuminated. It will also be good to put this telescope on some machine like ST, which holds it directly turned towards the sun. And you have to encase the NOPR glass in the middle of a hollow parabolic mirror like CC, which collects all the rays of the sun at the point Z on the object which must be supported there by the small arm G, which comes out of some place of this mirror: and this arm must also support around this object some black and obscure body, like HH, precisely of the size of the NOPR glass, so that it prevents that none of the rays of the sun fall directly on this glass; for from there, entering the pipe, some of them could be reflected towards the eye and weaken the vision accordingly; even though this tube must be completely black on the inside, it cannot be so perfectly so that its material does not always cause some reflection when the light is very bright, as is that of the sun.

Besides this, this black body HH must have a hole in the middle, marked Z, which is of the size of the object, so that, if this object is in any way transparent, it can also be illuminated by the rays which come directly from the sun; or even again, if need be, by these rays picked up at point Z by a burning glass, like II, of the size of NOPR glass, so that there comes from all sides as much light on the object as there is. can suffer without being consumed by it, and it will be easy to cover a part of this mirror CC or of this glass II, to prevent too much from coming into it. You can see why I take so much care here to ensure that the object is very well lit, and that many of these rays come towards the eye; because the NOPR glass, which in this telescope performs the office of the pupil, and in which those of these rays which come from various points intersect, being much closer to the object than to the eye, is the cause that they extend over the extremities of the optic nerve in a space much larger than is the surface of the object from which they come; and you know that they must have so much less force there as they are more extended there, as one sees, on the contrary, that being gathered in a smaller space by a mirror or burning glass, they have more. : and it is from this that the length of this telescope depends, that is to say the distance which must be between the hyperbola NOP and its burning point; for the longer it is, the more extensive the image of the object is in the fundus of the eye, which causes all its small parts to be more distinct there: but this itself also weakens so much their action that finally it could no longer be felt if this telescope were too long; so that its greatest length can only be determined by experience, and even it varies according as the objects can have more or less light without being consumed by it. I know very well that some other means could still be added to make this light stronger; but, apart from the fact that they would be more difficult to put into practice, we would hardly find objects that could suffer more from them. One might well also, instead of the hyperbolic glass NOPR, find others which would receive somewhat greater quantity of rays, but where they would not cause these rays, coming from various points of the object, to assemble so exactly towards the eye at as many other different points, or it would be necessary to employ two glasses there instead of one, so that the force of these rays would not be less diminished by the multitude of surfaces of these glasses which it would be augmented by their figures, and finally the execution would be much more difficult. Only do I still want to warn you that these glasses can only be applied to one eye, it will be better to bandage the other or cover it with some very dark veil, so that its pupils remain as open as possible. may only leave it exposed to the light or close it with the help of the muscles which move his eyelids; for there is usually such a connection between the two eyes that one can hardly move in any way without the other preparing to imitate it. Moreover, it will not be useless not only to press this telescope close to the eye, so that no light can come towards it except through it, but also to have softened his sight beforehand by holding himself in dark place, and to have the imagination disposed as if to look at very distant and very dark things, so that the pupil opens all the more, and so that we can see an object all the larger. Because you know that this action of the pupil does not follow immediately from the will that one has to open it, but rather from the idea or the feeling that one has of the darkness and the distance of the things that we look.

Besides, if you reflect a little on all that has been said above, and particularly on what we have required from the external organs to make the vision as perfect as it can be, there is no You will not find it difficult to hear that, by these various forms of spectacles, one adds to them all that art can add to them, without it being necessary for me to stop to deduce the proof of it for you at greater length. It will not be difficult for you either to know that all those we have had up to now could not in any way be perfect, since there is a very great difference between the circular line and the hyperbola, and that we has only tried by making them use this one for the effects for which I have demonstrated that this one was required; so that we have never been able to find that when we have failed so fortunately, that, thinking of making spherical the surfaces of the glasses that we have cut, we have made them hyperbolic, or of some other equivalent figure. And this principally prevented that one could not make well the glasses which are used to see the inaccessible objects, because their convex glass must be larger than that of the others; and, besides the fact that it is less easy to find a lot than a little, the difference which is between the hyperbolic figure and the spherical one is much more noticeable towards the extremities of the glass than towards its centre. But, because the craftsmen will perhaps judge that it is very difficult to cut the glasses exactly according to this hyperbolic figure, I will still try here to give them an invention by means of which I am convinced that they can quite easily overcome.


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