DIFFERENTIAL CALCULUS. 235 DIFFRACTION. DIFFERENTIAL CAL'CULUS. See Cai.- Cl I.l ■■*. DIFFERENTIAL EQUATION. See Equa- tion. DIFFERENTIATION. See. Calculus. DIFFERENTIATION. In biologj". the pro- cess by xvliicli llif liody becomes more complex by becoiiiiiig diderenl iu its different parts. Botb p'hylojrenetically and ontogenetieally. orj»anisnis begin in a relatively simple state: evolution and individual development are both accompanied by specialization of organs and division of labor among the various parts of the body. DIFFICULTY, The Hill. An impediment in Christian's journey to the Celestial City, in Banyan's Pilr/rim's Frogresx. DIFFRACTION AND DIFFRACTION GRATINGS I from Lat. diffriiujcre, to break in pieces, from dis-, apart + frangere, to break). Tien shadows are cast on a screen by allowing light from a small opening or source to pass an opaque body, it is noted that the shadows are not sharp, as would be expected if 'light traveled in straight lines.' Thus, if light from the sun or from any source of light falls upon a large ojiaque screen in which there is a narrow slit; and if there is placed some distance from this another opaque body with a sharp edge (e. g. a knife-blade) parallel to the slit, the shadow of the latter cast by the light from the slit will have several peculiarities. Calling the geometri- cal shadow the region where there would be darkness if light traveled in straight lines, it will be observed that the actual shadow begins a slight distance within the geometrical one — in other words, the light is bent slightly into the latter: further, on the edge of the geometrical shadow, where one might expect uniform illumi- nation, there are series of narrow colored bands, parallel to the edge, that is, there is first a strip brightly illuminated with one color, then an- other band with a different color, etc., the colors merging into each other: at a distance of a few millimeters from the edge of the shadow, how- ever, the field is uniformly illuminated. If in- stead of having white light as the source, a col- or'^d lianie is used. e. g. light from a flame con- taining sodium, the bands outside the geometri- cal shadow become simply alternations of light of the colors of the ilame. and darkness. This phenomenon is called 'ditTraction,' and was first observed by Grimaldi, profes.sor in the Jesuits' College, Bologna, in 1665. It was studied later by Xewton, but was not explained until Fresnel made his classical research in 1810. Similarly, if light from a pin-hole open- ing falls upon any opaque object, casting a shadow of it on some suitable screen, difTraction b.ind~ may be obsered outside the geometrical shadow, following the general contour of the latter; and the light enters slightly into the shadow. For other cases of difTraction. reference should be made to some treatise on Light. One of the best is Preston's Theori) of Tjifjht (London. 189.5). It was shown hy Fresnel that diffraction phe- nomena are explained by the fact that liglit is due to a wave-motion (see LiOHTI : consequently, ditTraction is possible with other waves, o. g. those in air which produce the sensation of sound. Vi.i. VI —If.. The colors of the feathers of many birds and of 'mother-of-pearl' are due to diffraction ; so are the colors seen wlien one looks at a bright light through a piece of thin dotli. If a great number of fine scratches, evenly spaced, are made on a piece of glass, or on a polished mirror, there is formed a 'ditlracting grating.' The former is called a "triinsniission" grating: the latter, a re- flecting one. If, as in a previous experiment, white liglit from a slit in an opaque screen is allowed to fall perpendicularly upon a trans- mission grating, the slit being parallel to the scratches, the transmitted light will be broken up into spectra, regularly spaced on both sides of the line drawn from the slit to the grating, ex- cept iu the direction of this line. Thus, if the transmitted light falls upon a white screen paral- lel to the grating, there will be a central white spot, and on each side of this, along a line at right angles to the lines on the grating, a suc- cession of colored spectral bands. This spreading sidewise of the light is due to its ditTraction through the narrow, transparent slits between the scratches; and the dispersion of the white light is occasioned by the fact that the amount of difTraction varies with waves of diil'erent wave-number, i. e. with difTerent colors (see Light). The same phenomena are observed with reflection gratings if the screen is placed on the same side as the slit of light and provided with an opening to allow the light to fall upon the grating. Gratings are of the utmost importance in spectroscopy (q.v.). as they furnish a means of measuring the wave-lengths of ether-waves. They were invented and first used by Joseph von Fraunhofer, of ilunich. in 1821. 'To be of value, gratings must be ruled with the scratches at exaclhi equal intervals. This is secured by plac- ing the surface to be ruled on a platform, which is carried forward by a long screw, whose thread is perfectly unifonii, and by having a diamond point so arranged as to draw lines at right angles to the direction of the screw. By means of a toothed wheel fastened to the screw, it is turned through a definite proportion of one com- plete revolution, thus carrying the platform for- ward a definite distance; for example, if the threads of the screw are at a distance 1-l.ith of an inch apart, and if the toothed wheel has 1000 teeth, then if this wheel is pushed round by an amount equal to one tooth, the screw will turn through 1-1 000th of a complete revolution, and will carry the platform forward M.5.000th of an inch. Then the diamond is drawn across the surface of the grating, making a groove: it is raised, pushed back to the other side of the grating, dropped down and again drawn across the surface, the platform in the interval of time, while the diamond is pushed back, having been carried forward another step. The process is continued until as many lines are made as are desired. Such a machine is called a 'dividing' or a 'ruling engine.' (See Di-TniNO Engine.) The most perfect gratings now in use have been made at the physical laboratory of .Tohns Hop- kins I'niversity. where Professor Rowland super- vised their preparation. His gratings have, as a rule. 15.000 lines or scratches to the inch; and the grating surfaces vary from two inches to six in width. To use gratings ruled on plane surfaces for .spectroscopic purpose*, it is necessary to com-
