DISPERSION. 



DISPOSITION. 



; -..i 



UBM, but frequently ibow kriglti line*, of which the light of the 

 electric spark i almost wholly made up. 



In the formula (S) suppose the angle of the prism i, and consequently 

 the deration o, to be very null, then 



D-0.-1) .', (5) 



a formula which may be readily shown to remain true so long a* the 

 angle of incidence U mall, even though the angle* of incidence and 

 emergence ihould no longer be equal. 



SuppoM now that while n,n relate to ran of mean refrangi- 

 bility they become D,,H. and D..M. for two definite kinds of ray* 

 cbo*rn a* nearly u may be at the red and violet oztnmitie* <( the 

 pectnuu. The formula (8) shows that the ,l!ftrtnn of deviation 

 D, D,, or S o, that U the length of the spectrum, U expressed by 

 (ff MI) or '/ The ratio of the difference of deviation ln.i to the 



mean deviation (ji 1) I, or :, depends (for given selected rays) only 



on the nature of the nulwtance of which the prism in made, and U 

 called the ditftrtitt pmetr of the subrtauce. 



Newtn supposed that all substances disperse light in the game 

 proportion u they refract it, and concluded that iu refracting tele- 

 scopes it wai impossible to get rid of the defects mixing from the chro- 

 matic dispersion of the object glass. Mr. Hall was the first to point 

 out Newton's mistake, and to apply the fact of the difference of 

 dispersive power of substances to the construction of an achromatic 

 telescope (Uerschel's ' Light,' art. 425); but the discovery fell into 

 oblivion, and it was not until after the fact had been rediscovered by 

 Dollond, and reapplied to the same object, that the achromatic tele- 

 scope came into general use. The mode in which the compensation U 

 effected by the use of two lenses may be readily understood from the 

 following consider 1 1 



Imagine a single ray to be transmitted through a convex lens in a 

 direction nearly parallel to its axis, but at a good distance from its 

 centre. If tangent planes be drawn at the two points where the ray 

 cuts the surfaces, the refraction of this single ray will be the same as if 

 the lens were replaced by a slender wedge or priinn of the same material 

 bounded by those tangent planes. Consequently the ray will be not 

 only deflected as a whole, but " dispersed." If now we consider all 

 the rays m"*'"g from a distant point in the axis of the lens we 

 readily see that the violet rays will be brought to a point or focus in 

 the axis of the lens sooner than the green, the green than the red, &c. 

 At no one distance will all the rays be brought to a focus together, 

 and consequently the image will be confused. 



.Suppose now we have two slender prisms, composed of different 

 materials, in contact with one another or nearly so, with their angles 

 i, i' turned in contrary directions ; and let a ray of white light be 

 incident nearly perpendicularly upon the system. The deviations 

 produced by the two prisms being (/ l)i and (jtf l)i', the whole 

 deviation will be 



(M-l) i - (ji'-l) ,-', (8) 



while the difference of deviation of the rod and violet rays will be 

 In . i-lf,' .i' (4) 



Unless therefore 4> : M 1 : : '/*' '-V-' 1. that is unless the dispersive 

 powers of the two substances are the same, the difference of deviation 

 may be destroyed without at the same time destroying the common 

 deviation of the two kinds of rays. The outstanding deviation will be 

 in the direction of that produced by the prism of smaller dispci .-ive 

 power. 



Suppose now that a compound lens is formed consisting of a convex 

 and concave of substances differing in dispersive power ; and imagine 

 the course of a ray incident towards the edge in a direction nearly 

 parallel to the axis. By drawing tangent planes as before, the lenses 

 may, as regards the course of this single ray, be replaced by a p.iir of 

 prisms turned in contrary directions. The small chromatic variations 

 of the points of incidence, and consequently of the angles of the prisms, 

 arising from the dispersion of the ray during its passage through the 

 linsc, may be altogether neglected. Now the deviations being on the 

 one hand as (jt 1) to (/'!) i", and on the other inversely as the 

 focal lengths r, r' for parallel rays, we have (ft 1) r .' = 0*' 1) r'.t, and 

 substituting in (4) equated to zero we find 

 M 1 V 1 f 



it i y~ IL i ' 



or iu order that the dispersion may be corrected, the focal lengths 

 must be as the dispersive powers. 



The dispersive power of substance is most accurately determined by 

 forming the substance into a prism of considerable angle (supposing 

 it sufficiently homogeneous), and determining, as before explained, the 

 refractive indices for two properly selected and perfectly definite 

 points of the spectrum, such as two fixed linen. The ratio of the 

 dispersive powers of two substances, which is all that is required for 

 the construction of an achromatic object-glass, may, however, be 

 determined by different methods of compensation. One of the in<| I. -i. 

 at least in theory, which has been much employed by Dollond and 

 practical opticians up to the present day, consists in forming two 

 prisms of the substances with small angles, and altering by trial the 

 angle of one of the prisms until an object seen through both appears 



as free as possible from fringes of colour, when the dispersive powers 

 are inversely as the deviations produced by the two prisms re- 



-; ' '- -': 



When different substances are formed into slender prisms through 

 which light passes nearly perpendicularly, not only does the separation 

 of the extreme rays bear to the mean deviation a different ratio in 

 the different substances, but the ratio of the angular extent 

 |x>rtion of the spectrum to that of another portion changes from 

 substance to substance. Thus if three definite points, (such as three 

 fixed linen,) be taken in the red, the green, and the violet, the ratio 

 of the separation of the violet from the green to that of the green Jr.. in 

 toe red will be greater in flint glass than in crown. This want of 

 proportionality is termed the irrationality of ditptrtum, and the out- 

 standing spectrum formed when two prisms as nearly as possible com- 

 pensate each other, which U coloured green on one side and purple 

 (from a mixture of red and blue) on the other, is called a tmmdary 

 Ipettrvm. This irrationality prevent* the compensation in the ewe of 

 a double object glass from being perfect, and constitutes one of the 

 chief obstacles to the perfection of large refracting telescopes. 



The rainbow is a beautiful natural exhibition of the dispersion of 

 light into spectral colours. [RAINBOW.] 



Two simple propositions relative to the effect of chromatic dis- 

 persion in a single lens are here subjoined. 



To find the longitudinal chromatic aberration of a lens, or the 

 interval on the axis between the foci of extreme red and violet rays. 



Let the red rays converge to the point B, and the violet to the point 

 v in the i 



Let/, F be respectively the focal distances for the given system of 

 rays, and a parallel system ; then the fundamental equations for lenses 



(neglecting their thickness), give 5 ~ = constant, since the rays of all 



colours in the compound incident beam have a' common origin ; now 

 differentiate relative to n, the variable index of refraction : hence, 



_ 

 dn~r- ' dp.' 



1 dr 1 

 but since F is proportional to ft - 1, therefore . -\ = - r ; and if 



S ft denote the total variation of n from extreme red to violet, and 8 / 

 the corresponding variation of/, or longitudinal aberration, and finally 

 A, the dispersive power of the medium, we have 



To find, in the same case, the radius of the circle of least chromatic 

 dispersion. 



By referring to the same figure, we may observe that the foci K . v 

 are respectively the vertices of red and violet conical surfaces, having 

 the lens as a common base. Let these surfaces intersect in a circle, of 

 which the radius is D E ; then it is plain that all the intermediate 

 coloured rays pass through this circle. It is therefore that of least 

 dispersion : 



The preceding figure representing a plane section of the whole 

 system taken through the axis, it is obvious that, from the smallness 

 of R v relative to c it, the angles o v B, c R A are sensibly equal, or 

 the triangle v B D is exceedingly nearly isosceles, and therefore o K 



bisects VB, or ER = -77- and DE = KB . == .- , CA. andfor 



f CA f 



parallel incident rays DE = 5 . CA. 



DISPOSITION, in the law of Scotland, is the name given to an 

 instrument, or as it would be termed in England, deed poll, by which 

 a party solemnly makes over to another nul property. It may be 

 used as a title to moveables alone, but it is in the law of real property 

 that it is of most frequent use and of highest importance, the con- 

 veyance of moveables being usually by assignation or assignment. 

 When a new feu or fief is created, it is by charter or contract of feu, 

 containing a disposition in itself, or disposition in feu ; but when a 

 feu, fief, or estate is transferred from one holder to another it is by 

 Disposition, in which all the conditions on which the property is to 

 change hands are set forth. 1W i>; given to the disponee, it is in his 

 hands a personal obligation by the disponer to give him a full title, and 

 contains the warrants for getting the title made real by registration, 

 and by obtaining the superior's sanction to the new investiture. As 

 heritable property cannot be bequeathed by testament iu Scotland 



