BINOCULAR INSTRUMENT

binocular instrument, or briefly binocular,[1] an apparatus through which objects are viewed with both eyes. in this article only those instruments will be considered in which solid objects or _objects in space_ are viewed; reference should be made to the article stereoscope for the instruments in which _plane_ representations are offered to both eyes. the natural vision is such that different central projections of the objects are communicated to both eyes; the difference of the two perspective representations arises from the fact that the projection centres are laterally separated by an interval about equal to the distance between the eyes (the inter-pupillary distance). binocular instruments should aid the natural spatial or stereoscopic vision, or make it possible if the eyes fail. if the objects be so far distant that the two perspectives formed by the naked eye are no more distinguished from each other, recourse may be had to binocular telescopes and range-finders; and if the objects be so small that, in order to observe details on them, we must bring our eyes so close to the objects that they cannot accommodate the images, recourse may be had to binocular microscopes and magnifying glasses. the construction of binocular instruments dates back over several centuries, and has now been brought to great perfection. the subject of their theory and history has been exhaustively treated by m. von rohr, _die binokularen instrumente_ (berlin, 1907), the first publication to present a complete account of these instruments. [illustration: fig. 1.] telescope. _binocular instruments for observation only._--the first binocular telescope, consisting of two telescopes placed side by side, was constructed in 1608 by johann lipperhey, the inventor of the ordinary or dutch telescope. the subject was next taken up by the monks. the capuchin antonius maria schyrlaeus (schyrl) de rheita (1597-1660) described in 1645 the construction of double terrestrial telescopes. greater success attended the efforts of the capuchin cherubin d'orleans, who flourished at about the same time, and constructed large double telescopes of the dutch type of high magnification, for use in war, and smaller instruments of lower magnification; these instruments were provided with mechanism for adjusting to the interval between the eyes of the observer (fig. 1). after these discoveries the subject received no more attention until the 19th century; no improvements of these instruments are recorded in the literature of the second half of the 18th century. [illustration: fig. 2.] the re-invention of the dutch binocular telescope apparently dates from 1823, and is to be assigned to the viennese optician, johann friedrich voigtlaender (1779-1859); but the credit of having placed these instruments on the market probably belongs to j.p. lemiere in paris, who, in 1825, took out a french patent for an improvement of the dutch double telescope. lemiere's instruments were furnished with a common focusing arrangement, and the adapting to the inter-pupillary distance was effected by turning the two parallel telescopes round their common axis. the development of this instrument was studied by opticians for the remainder of the first half of the 19th century; the last improvement apparently was made by p.g. bardou in 1854, and by h. helmholtz in 1857 when he described the telestereoscope (fig. 2) with telescopic magnification. by utilizing the telescope with prism-inversion, devised in 1851 by ignazio porro (1795-1875), a.a. boulanger succeeded in producing a binocular of an entirely new type in 1859 (fig. 3). but he overlooked the possibility of increasing the distance between the objectives; camille nachet introduced this improvement in 1875, but his instruments did not meet with much popularity. this was probably due to the fact that, at this time, the manufacture of the glass for the prisms was too difficult; this was overcome by e. abbe, after the founding of the glass-works at jena, who effected, independently of his predecessors, the wider separation of the objectives (fig. 4), and increased it in the telestereoscope (fig. 5), or relief telescope, in a manner nearly approaching to helmholtz's proposal. [illustration: fig. 3.] [illustration: fig. 4.] [illustration: fig. 5.] microscope. the first binocular microscope was invented by the previously mentioned father cherubin, whose instrument consisted of two inverting systems, and consequently gave a totally wrong impression of depth, i.e. depressions appeared as elevations, and vice versa, or, as we must say after charles wheatstone, it presented a pseudoscopic impression; this quality, however, was not recognized by the microscopists of the time. the instrument subsequently fell into complete neglect for nearly two centuries, to be revived in 1852 by charles wheatstone, who has stated that he had previously studied the problem; the publication of his views in his second great paper "on binocular vision,"[2] in the _phil. trans._ for 1852, undoubtedly stimulated the investigation of this instrument, which was carried on with zeal and success more especially in england and the united states. in 1853 the american j.l. riddell (1807-1867) devised his binocular microscope, which contained the essentials of wheatstone's pseudoscope. f.h. wenham, another constructor, did not at first succeed in avoiding the pseudoscopic effect, but, by the application of _refracting_ dividing prisms, he subsequently arrived at orthoscopic representations and continued the development of the different methods for producing micro-photographic stereograms; this was effected in the first case by placing a diaphragm over one half of the objective for each exposure, and in the second case by a suitable direction of the illuminating pencil (fig. 6). of greater benefit, however, for stimulating interest in binocular microscopes, was his invention of _reflecting_ dividing prisms (fig. 7). other experiments, begun by powell and lealand, and developed with greater skill by wenham, were concerned with the binocular vision of identical images. such an impression could not possibly be stereoscopic, and these experiments led to the construction of a non-stereoscopic binocular microscope. of the other workers in this field mention may be made of alfred nachet, who in 1853, and subsequently in 1863, brought forward two forms of binocular microscope. [illustration: fig. 6.] [illustration: fig. 7.] [illustration: fig. 8.] the earliest stages of the development of the binocular microscope had been always confined to those instruments with _one_ objective, in the immediate neighbourhood of which the systems for dividing the pencil were placed. at a later date attempts were made to separate the two halves of the objective by modifying the eye-piece; this led to the construction of stereoscopic eye-pieces, initiated by r.b. tolles, e. abbe and a. prazmowski. of special importance is the work of abbe; although, as he himself has stated, his methods accidentally led to the wenham system, he certainly was far above his predecessors in his theoretical treatment of the problem, and in the perspicuity and clearness of his explanation. to him is also due the re-establishment of the instruments, which wenham had abandoned by reason of too great technical difficulties (fig. 8). the newest form of the binocular microscope is very similar to the oldest form in which two completely separated tubes were employed. the inventor, h.s. greenough, employs two systems for setting up the image, in order to avoid the pseudoscopic effect. after experiments in the zeiss works, the erecting of porro's prisms simultaneously permitted a convenient adaptation to the eye-distance of the observer. [illustration: fig. 9.] simple microscope. the first binocular magnifying glass or simple microscope (german, _lupe_) was devised by j.l. riddell in 1853; in this instrument (fig. 9) the pencil of light is transmitted to the eyes by means of two pairs of parallel mirrors. of the many different improvements mention may be made of a. nachet's. h. westien made use of two chevalier-bruecke's simple microscopes with their long working distances in order to form an instrument in which the curvature of the image was not entirely avoided. mention may also be made of the binoculars of k. fritzsch (formerly prokesch) and e. berger. _binocular instruments for range-finding._--for measuring purposes binocular telescopes with parallel axes are the only types employed. the measurement is effected by adjoining to the space or interval to be measured some means of measurement defined; for example, by a fixed scale which extends into the space, or by a movable point (_wandermarke_). this instrument shows a transition to the stereoscope, inasmuch as the scale or means of measurement is not directly observed, but to each eye a plane representation is offered, just as in the stereoscope; the space to be measured, on the other hand, is portrayed in exactly the same way as in the double telescope. the method for superposing the two spaces on one another was deduced by sir david brewster in 1856, but he does not appear to have dealt with the problem of range-finding. the problem was attacked in 1861 by a. rollet; later, in 1866, e. mach published a promising idea, and finally--independently of the researches of his predecessors--hektor de grousilliers, in partnership with the zeiss firm (e. abbe and c. pulfrich), constructed the first stereoscopic range-finder suitable for practical use. (o. hr.) footnotes: [1] the term binocular (from the lat. _bini_, two at a time, and _oculi_, eyes) was originally an adjective used to describe things adapted for the simultaneous use of both eyes, as in "binocular vision," "a binocular telescope or microscope"; now "a binocular" is used as a noun, meaning a binocular microscope, a field-glass, &c. [2] the first part appeared in 1838. binomial (from the lat. _bi-, bis_, twice, and _nomen_, a name or term), in mathematics, a word first introduced by robert recorde (1557) to denote a quantity composed of the sum or difference to two terms; as a + b, a - b. the terms trinomial, quadrinomial, multinomial, &c., are applied to expressions composed similarly of three, four or many quantities. the _binomial theorem_ is a celebrated theorem, originally due to sir isaac newton, by which any power of a binomial can be expressed as a series. in its modern form the theorem, which is true for all values of n, is written as n.(n-1) (x + a)^n = x^n + nax^(n-1) + ------- a squaredx^(n-2) 1.2 n.(n-1).(n-2) + -------------a cubedx^(n-3) ... + a^n. 1.2.3 the reader is referred to the article algebra for the proof and applications of this theorem; here we shall only treat of the history of its discovery. the original form of the theorem was first given in a letter, dated the 13th of june 1676, from sir isaac newton to henry oldenburg for communication to wilhelm g. leibnitz, although newton had discovered it some years previously. newton there states that m m - n m - 2n (p + pq)^(m/n) = p^(m/n) + -- aq + ----- bq + ------ cq ... &c., n 2n 3n where p + pq is the quantity whose (m/n)th power or root is required, p the first term of that quantity, and q the quotient of the rest divided by p, m/n the power, which may be a positive or negative integer or a fraction, and a, b, c, &c., the several terms in order, e.g. m (m - n) a = p^(m/n), b = -- aq, c = ------- bq, and so on. n 2n in a second letter, dated the 24th of october 1676, to oldenburg, newton gave the train of reasoning by which he devised the theorem. "in the beginning of my mathematical studies, when i was perusing the works of the celebrated dr wallis, and considering the series by the interpolation of which he exhibits the area of the circle and hyperbola (for instance, in this series of curves whose common base or axis is x, and the ordinates respectively (1 - xx)^(0/2), (1 - xx)^1/2, (1 - xx)^(2/2), (1 - xx)^(3/2), &c), i perceived that if the areas of the alternate curves, which are x, x - (1/3)x cubed, x - (2/3)x cubed + (1/5)x^5, x - (3/3)x cubed + (3/5)x^5 - (1/7)x^7, &c., could be interpolated, we should obtain the areas of the intermediate ones, the first of which (1 - xx)^{1/2} is the area of the circle. now in order to [do] this, it appeared that in all the series the first term was x; that the second terms (0/3)x cubed, (1/3)x cubed, (2/3)x cubed, &c., were in arithmetical progression; and consequently that the first two terms of all the series to be interpolated would be (1/2)x cubed (3/2)x cubed (5/2)x cubed x - -----, x - -------, x - -------, &c. 3 3 3 "now for the interpolation of the rest, i considered that the denominators 1, 3, 5, &c., were in arithmetical progression; and that therefore only the numerical coefficients of the numerators were to be investigated. but these in the alternate areas, which are given, were the same with the figures of which the several powers of 11 consist, viz., of 11 deg., 111, 11 squared, 11 cubed, that is, the first 1; the second, 1, 1; the third, 1, 2, 1,; the fourth 1, 3, 3, 1; and so on. i enquired therefore how, in these series, the rest of the terms may be derived from the first two being given; and i found that by putting m for the second figure or term, the rest should be produced by the continued multiplication of the terms of this series m - 0 m - 1 m - 2 ----- x ----- x ----- ..., &c ... 1 2 3 this rule i therefore applied to the series to be interpolated. and since, in the series for the circle, the second term was (1/2x cubed)/3, i put m = 1/2.... and hence i found the required area of the circular segment to be 1/2x cubed (1/8)x^5 (1/16)x^7 x - --- - -------- - ---------, &c. ... 3 5 7 and in the same manner might be produced the interpolated areas of other curves; as also the area of the hyperbola and the other alternates in this series (1 + xx)^(0/2), (1 + xx)^1/2, (1 + xx)^(2/2), &c. ... having proceeded so far, i considered that the terms (1 - xx)^(0/2), (1 - xx)^(2/2), (1 - xx)^(4/2), (1 - xx)^(6/2), &c., that is 1, 1 - x squared, 1 - 2x squared + x^4, 1 - 3x squared + 3x^4, - x^6, &c., might be interpolated in the same manner as the areas generated by them, and for this, nothing more was required than to omit the denominators 1, 3, 5, 7, &c., in the terms expressing the areas; that is, the coefficients of the terms of the quantity to be interpolated (1 - xx)^1/2 or (1 - xx)^(3/2), or generally (1 - xx)^m will be produced by the continued multiplication of this series m - 1 m - 2 m - 3 m x ----- x ----- x ----- ... &c. 2 3 4 the binomial theorem was thus discovered as a development of john wallis's investigations in the method of _interpolation_. newton gave no proof, and it was in the _ars conjectandi_ (1713) that james bernoulli's proof for positive integral values of the exponent was first published, although bernoulli must have discovered it many years previously. a rigorous demonstration was wanting for many years, leonhard euler's proof for negative and fractional values being faulty, and was finally given by niels heinrik abel. the _multi_- (or _poly_-) _nomial theorem_ has for its object the expansion of any power of a multinomial and was discussed in 1697 by abraham demoivre (see combinatorial analysis). references.--for the history of the binomial theorem, see john collins, _commercium epistolicum_ (1712); s.p. rigaud, _the correspondence of scientific men of the 17th century_ (1841); m. cantor, _geschichte der mathematik_ (1894-1901). binturong (_arctictis binturong_), the single species of the viverrine genus _arctictis_, ranging from nepal through the malay peninsula to sumatra and java. this animal, also called the bear-cat, is allied to the palm-civets, or paradoxures, but differs from the rest of the family (_viverridae_) by its tufted ears and long, bushy, prehensile tail, which is thick at the root and almost equals in length the head and body together (from 28 to 33 inches). the fur is long and coarse, of a dull black hue with a grey wash on the head and fore-limbs. in habits the binturong is nocturnal and arboreal, inhabiting forests, and living on small vertebrates, worms, insects and fruits. it is said to be naturally fierce, but when taken young is easily tamed and becomes gentle and playful.