STEREOSCOPE. 



STEREOSCOPE. 



830 



above it) ia projected inside the great circle on which projection is 

 made; and all the rest outside : when this projection is employed in 

 maps, it is usual to place all the part of the globe to be projected 

 below the plane of projection. 



The second property is, that the angle made by two circles which 

 meet on the globe, is equal to the angle made, at the point of meeting, 

 by the two circles which are the projections of those circles, the angle 

 made by two intersecting circles being always that made by their 

 tangents. This property is easily proved as follows : Draw through 

 the point 'of intersection of the two circles (A and B) which are to be 

 projected, two other circles (A' and B'), which have the same tangents, 

 and pass through the eye. Then the tangents of A' and B' at the eye 

 make the same angle as those at the other point of intersection ^ 

 that is, as the tangents of A and B at the point to be projected. But 

 these tangents of A' and B' at the eye are parallel to the projections 

 of the tangents of A and B at the point to be projected : whence the 

 projections of these tangents of A and B make the same angle as the 

 tangents themselves. 



The first property was known to Hipparchus and Ptolemy : the 

 history of the second is rather curious. The first writer who seems to 

 have looked attentively for a discoverer was Delambre (' M<5m. Inst.', 

 vol. v., p. 393), who could not find it in Clavius, Stoffler, nor in any of 

 the writers of the middle ages, who have treated pretty voluminously 

 on the astrolabe, which word, as used by them, merely meant a stereo- 

 graphic projection. That it was mentioned (without demonstration) 

 in the French Mathematical Dictionary of Savdrien (1753), in an 

 article which was copied word for word into the ' Encyclopedic,' was 

 all that Delarabre could then say of its origin. He afterwards, in 

 writing his ' History of Astronomy in the Middle Ages,' found the 

 proposition demonstrated in the ' Compleat System of Astronomy,' by 

 Charles Leadbetter, London, 1728 ; but. judging from the rest of the 

 work, he presume* that Leadbetter could not have been the discoverer. 

 N'o claim was, however, at the time put in for any one else, and 

 Save'rien's article, which appeared in the ' Encyclopedic,' first called 

 general attention to the property, and this can be traced to Lead- 

 better's work nearly. For we find that Saverien translated his article, 

 word for word, from the second edition (1743) of Stone's ' Mathematical 

 Dictionary.' Stme was a contemporary of Leadbetter, and several 

 times refers to his writings. 



On consulting the third edition of Dr. Harris's ' Lexicon Technicum ' 

 (1716), and feeling sure, with regard to that work, that such a 

 proposition as the one called Leadbetter's would be stated, if it were 

 then known, we turned to the article ' Spherick Geometry,' and there 

 we found it, with a demonstration, enunciated as follows : " All 

 Angles made by Circles on the Superficies of the Sphere are equal to 

 those made by their Representatives on the Plane of the Projection." 

 The claim of Leadbetter is therefore overthrown. In the preface, 

 Hays that under (among others) ' Spherical Geometry ' will be 

 found entire treatises, which, if he mistakes not, are as short and plain 

 as any extant. If this proposition had been new, he would probably 

 have notl it here, particularly if it had been his own. We find how- 

 ever, finally, that the property has been shown (' Encyc. Brit.', ' Pro- 

 jection ') to have been demonstrated by Halley in No. 219 of the 

 ' Philosophical Transactions,' and is attributed by him to De Moivre or 

 Hook. 



The consequence of this theorem is, that any small portion of 

 the sphere is projected into a figure very nearly similar to itself, so 

 that any not very large portion of the earth preserves its figure with 

 t< 'l'-rable accuracy in the map. Hence some writers have said that 

 there is no distortion in the stereographic projection, which is not 

 'i-ly true, though nearly so of countries which bear no greater 

 proportion to the whole earth than most of them. 



The mode of laying down the stereographic projection is briefly 

 stated, nd a diagram given, in the article MAP ; it will be found at 

 greater length in the memoir of Delambre above cited, or in any good 

 work on the construction of maps. 



ST Kit K< S('( 1 1 ' K. from trrtptts (solid), and <mmii (a view, or tntonfa, 

 to view), an instrument by which two pictures of any object, taken 

 from different points of view, are Been as a single picture of that object, 

 having the natural appearance of relief or solidity. 



the< pry of the stereoscope is sufficiently discussed under Si<:nT. 

 The reflecting stereoscope was first described in a paper by 1'r 

 Wheatstone, entitled ' Contributions to the Phyrtologr of Vision: 

 Part I. On some Remarkable and hitherto Unobserved Phenomena of 

 liinrx'nl.ir Vision,' read before the Royal Society, June 21st, 1838, and 

 printed in the ' PI/ -us ' a few months later. The 



refracting stereoscope is described by Sir David Ilrewstcr in a paper 

 ' l>u the Law of V P i Binocular Vision, and 



on the BeprweerUtton of Solid Figure* by the Union of Di- 

 s on the lietinse,' which he communicated to tli- 

 Edinburgh in January, 1843. He further explained and 

 defakMd his views in subsequent papers, which, like the former, 

 appeared in the ' Edinburgh Transactions ' of that and following years. 

 Tin' opinions of Sir D.ivid Brewster are further set forth in his work 

 'Tli.- Stereoscope' (8vo, 1866); those of Mr. Wheatstone must be 

 in the paper already referred to, and in another which formed 

 kerian Lecture of the lloyal Society for 1852, being ' Part II. of 

 ( Vntributions to the Physiology of Vision, and on Binocular Vision." 



The dissimilarity of the pictures, as seen by each eye separately, does 

 not appear to be a modern discovery. It was recognised by Euclid 

 2000 years ago, and minutely described by Galen. The idea was 

 revived by Baptista Porta in 1593; also by Leonardo da Vinci; by 

 Aguilonius, in a work on the vision of solids (1613); by Harris, in 

 1775; by Dr. Smith, Dr. Porterfield, and others. Thus, as Brewster 

 remarks, writers in every age knew the two facts that the pictures on 

 the retina; of the two eyes wore dissimilar, and that by the union of 

 these two flat distinct pictures we obtain the vision of solids. But in 

 order to obtain accurate pictures of objects as seen by each eye, and 

 the method of uniting them, photography and the binocular camera 

 were required. The first was already sufficiently advanced, and the 

 latter was introduced by Brewster ; while, in order to view the pictures 

 with effect, the lenticular stereoscope was contrived. The first instru- 

 ment of this kind was constructed by the late Andrew Ross for the 

 inventor, and was exhibited to the British Association in Birmingham 

 in 1849. It did not, however, attract attention until the French 

 optician Du Boscq showed his remarkable collection of stereoscopic 

 views in the Great Exhibition of 1851, after which the demand for the 

 stereoscope warmed into a passion which has scarcely since cooled 

 down. The lenticular stereoscope, as described by the inventor, 

 " consists of a pyramidal box of wood or metal, or any other opaque 

 material, blackened on the inside, and having a lid for the admission of 

 light when the pictures are opaque. The box is open below, in order 

 to let the light pass through the pictures when they are transparent. 

 Another lid is sometimes added, so as to open externally on the bottom 

 of the box, for the purpose of exhibiting dissolving views in the stereo- 

 scope. The bottom of the box is generally covered with ground-glass, 

 the surface of which ought to be very fine, or very fiue-grained paper 

 may be used. The top of the box consists of two portions, in one of 

 which is the right eye-tube, containing a semi-lens, or quarter-lens, and 

 in the other the left eye-tube, also containing a semi-lens or quarter- 

 lens. These two portions may be advantageously made to approach or 

 recede, in order to suit eyes at different distances from one another ; 

 and the tubes containing the lenses should draw out, in order to suit 

 long- and short-sighted eyes." The two dissimilar pictures (which, for 

 convenience, are mounted on a thick card, forming the universally 

 known " slide ") are placed in a groove in the bottom of the box, when, 

 on looking through the eye-tubes, they are seen united into a single 

 picture, and the object or objects, if a proper amount of light is 

 obtained, stand out with an almost magical appearance of relief and 

 soliditv. For opaque slides, a mirror may be used, and made to move 

 on a hinge, so as to throw light into the instrument. The employment 

 of photography for the stereographs has wonderfully extended the 

 range of the instrument. 



The quarter- or semi-lens may also be used in the binocular camera. 

 And here we may state the advantage of dividing the lenses. Whole 

 lenses were originally used ; but as the outer half of each lens is useless, 

 as the eyes only look through the inner halves ; moreover, as it is 

 impossible to give two lenses precisely the same focal length and 

 magnifying power, it was found to be more accurate, and even cheaper, 

 to cut each lens into halves or quarters, and to shape each half or 

 quarter into a round disc, with the thin part of each turned inwards 

 in the instrument. In this way a single lens could be made into one 

 semi-lens or two quarter-lens stereoscopes. It is evident that these 

 ].or'i"iis, cut from the same lens, must have the same focal length and 

 magnifying power. It is by means of these semi- or quarter-lenses that 

 the stereoscopic effect is produced, though they do not themselves pro- 

 duce that effect. What they accomplish is the transference of the two 

 dissimilar pictures or stereographs to a middle point. The union of 

 these two pictures, or their superposition on that middle point, 

 produces the stereoscopic effect. [SIGHT.] The half- or quarter-lenses 

 are placed 2J inches apart, corresponding to the distance between the 

 gjef. 



Among the various forms of the instrument, we may mention 

 Smith and Beck's achromatic stereoscope ; the reflecting stereoscope ; 

 Claudet's itercomnnoscopc ; and Skaife's putologrtoph, consisting of a 

 combination of lenses of small size (one inch in diameter, and the 

 focal length of the combination one inch). In this last instrument 

 the thickness of the glass through which the light passes is small, and 

 hence the actinic rays are so powerful that a photograph may be taken 

 almost in an instant, and is not liable to the errors which the use of 

 large lenses occasions. The small pictures, or jiistolnr/rams, as they .are 

 < Ml. -il. may bo magnified by an enlarging camera. The small picture 

 may also be inclosed between two plates of glass, and raised to a tem- 

 perature sufficient to fuse the three glasses into one, effectually pro- 

 tecting the picture from the presence of the air, and forming what is 

 B chromo-cryital. 



l-'i-oin what has been said, it will be gathered that the truthfulness 

 of tBe stereoscopic picture must depend mainly on the character of the 

 dissimilar pictures or stereographs. Stereographic portraits are usually 

 taken with cameras contrived for the purpose. In order to take stereo- 

 graphs of landscapes, buildings, statuary, &c., the ordinary landscape 

 camera is employed ; the camera being removed, after the first picture 

 is taken, to a position parallel to that just occupied, and at an equal dis- 

 tance from the principal object, but more or less distant from the first 

 position in proportion to the distance from the object to be repre- 

 sented. The stereoscopic angle, as it is called, has been laid down at 1 



