242 SPECTRUM equal in length to about -00077 mm. ; for the extreme violet rays the angle N e F is at its minimum, and al is equal to about -00039 mm. ; therefore the violet ends of the spectra will always be toward the hnage of the slit. The determination of a wave length consists in the measurement of the length al. To measure this length, we first determine the distance between the centres of two contiguous open- ings in the grating, and then the angle N c F corresponding to any given tint or fixed line in the spectrum ; and as the angle a bl is equal to the angle N" c F, al is equal to a ft multiplied by the sine of N c F. Let stand for a b, d for the angle N c F, and I for al, or the wave length; then Z = xsin. d. If the ray a e, and symmetrically placed rays, be in- clined to the plane of the grating so that the perpendicular bl cuts off on a e a distance al equal to two wave lengths, we shall have the same actions over again, only the spectra pro- duced by them will be more deflected to the side of the image of the slit; and thus are produced the spectra of the 2d, 3d, 4th, &c., orders. The length of any one of these spec- tra will necessarily be nearly as the num- ber of the order of the spectrum. The wave K'ujrth of the same tint, or of the same fixed line, can be determined from angular measures made on this tint or line, in the spectra of all orders. From such measures we obtain mul- tiples of the wave length, and the formula for measures on the nth order of spectrum becomes Z= . In the actual measures which have been made, to form what is called a map of " the normal solar spectrum," the plane of the grating is placed in the axis of a divided circle, and is generally adjusted so that this plane is at right angles to the line of collimation of the collimating telescope carry- ing the slit. The observing telescope is placed on the other side of the grating, and has at- tached to it verniers, or reading microscopes, which it carries over the divided circle as it rotates around its axis, as is shown in fig. 4. Measures of the wave lengths of the rays forming the solar spectrum have been made by Fraunhofer (Denkschriften der munchener Akademie, vol. viii. ; Gilbert's Annalen, vol. Ixxiv.), Ditscheiner (Berichte der wiener Aka- demie, vols. 1. and Hi.), Van der Willigen (M&' moires d'optique physique, Haarlem, 1868), Mascart (Comptes rendus, Iviii., p. Ill ; An- nales scientiftques de Vecole normale superieure, vol. iv.), Angstrom (Recherches sur le spectre solaire, Berlin, 1869), Eisenlohr (Poggendorff's Annalen, vol. xcviii.), and Stefan (Berichte der wiener Akademie, liii.). Mascart made an important modification in the process, as above described. In his measures he placed the plane of the grating at such angles to the axis of the collimator that the observed line was seen with its minimum angle of devia- tion, and thereby obtained greater simplicity of adjustment with superior accuracy in his mea- sures. In his method the formula becomes Z=^xsin. -|> He came to the conclusion that the upper or more refrangible of the two D lines of Fraunhofer has a wave length of 0005888 of a millimetre. This result agrees with the determination made by Fraunhofer, and physicists now generally adopt this deter- mination as exact. If the wave length of any one ray is known to the last degree of preci- sion, the position of this ray may afterward serve as a point of departure in the determi- nation of other rays merely by observing their angular departure from this standard ray ; and if we knew with certainty the wave length of a definite ray, we might adopt this dimension as a standard of length ; for from observations on this ray's angular position in the spectrum, we could determine the distance separating the centres of two contiguous openings in the gra- ting, and hence determine the length occupied by any known number of lines in a uniform- ly cut grating. The following table gives the wave lengths, in ten millionths of a metre, of the principal Fraunhofer lines, as determined by the observers named : FRAUNHOFER LINES. Fraunhofer. V. d. Willigen. DiUchelner. Angstrom. Stefan. Mascart. A a 0007609 0007604 8 xi ::;:::;:::::: 0006878 mi HIV I 0006871 ' 6666883 0006667 0006878 0006867 D, 5 0005888 0005896 0005899 0005889 0005893 1 0005888 b. &,.... 0005265 0005272 0005186 0005278 0005192 0005269 0005183 0005271 0005268 0005182 f~. > ::::::::::: 0004851 0004864 0004842 '0005181 0004868 0004346 0005172 00048CO 0004340 0004869 0005165 0004860 H... 6604292 0004311 0004817 0004307 0004291 0004808 i .:::::::::::::::::::::::::: j- -0008945 1 -0008983 0003974 0003940 0003968 0008983 j-' 0003959 j 0008967 The considerable differences observed in the determinations of the wave length of the same ray by different observers are not alone owing to the variations always existing in honest measures of precision, but chiefly to the diffi nnlfw *-vf >-vK> *rr. I 1 1 __ i i , . to the resulting uncertainty in the knowledge of the distance separating the centres of two contiguous openings in the grating. All phy- sicists .have until recently obtained their gra- tings from Nobert. Lewis M. Rutherfurd of m, uut . iciijr v tings irom JNobert. Lewis M. Kutnerfurd 01 btammg regularly ruled gratings, and New York has for several years past given
