Wave-lengths in the Invisible Prismatic Spectrum. 197 



have been in fact derived, and where they are comparatively 

 unneeded). They contradict each other, as will be seen as 

 soon as they are called on for information, in the region outside 

 of it, where they would be chiefly useful. 



The present work has been preceded by a new map of 

 the invisible prismatic spectrum, where the abscissa were 

 proportional to the deviations in a certain prism (Phil. 

 Mag. vol. xv. pi. iii.). And the immediate object of this 

 research is to pass from the arbitrarily spaced prismatic scale, 

 belonging to the particular prism in question, to a map on 

 the normal and absolutely general one^ which was indeed also 

 presented in the same issue, but in advance of the present 

 description of the means used to obtain it. 



I should perhaps make the cautionary remark, that the 

 general conclusions here offered, as to the relation of wave- 

 lengths and indices of refraction, have been drawn from 

 the observations on a single prism and have not been ex- 

 perimentally verified on others. This is on account of the 

 extremely slow and laborious character of the process used 

 (which has involved some months of labour for this special 

 prism). Though there seems no reason to doubt the gene- 

 rality of our conclusions, it may be hoped that these experi- 

 ments will be repeated with prisms of other material, and by 

 other observers, now that the preliminary obstacles have been 

 removed. 



In order to map the spectrum on the normal scale, where 

 the wave-lengths are equally spaced, from such a map as that 

 shown in plate iii. vol. xv. of this Journal, in which the con- 

 sideration of wave-lengths does not enter, it is necessary to 

 establish some relation between the wave-lengths of rays and 

 their deviations, or between their wave-lengths and refractive 

 indices, which are connected with the deviations by the well- 

 known formula / . A 



. (a + d) 



sm 2 



. a ' 

 sm 2 



where a = the refracting angle of the prism, cl = the devi- 

 ation, and n = the corresponding index of refraction. In 

 the visible spectrum the deviation, in any prism, of the 

 Fraunhofer lines (whose wave-lengths have been very accu- 

 rately determined) can be measured by means of an eyepiece 

 with cross wires ; and from a sufficient number of such 

 measurements, by making ordinates proportional to indices of 

 refraction (or deviations) and abscissae proportional to wave- 

 lengths, a curve may be found whose equation is w = (<£)\ or 



