unrecognized Wave-lengths. 167 



In Plate VI. we have graphically constructed the relations 

 between n and X for the rock-salt prism, as far as the above 

 wave-length of 5*- 3011 or Q'0053 millim. The ordinates are 

 proportional to the indices of refraction given on the axis of 

 Y, the abscissae to the wave-lengths on the axis of X. The 

 two vertical dotted lines carry the eye down to the corre- 

 sponding portion of the spectrum, which is visible. Between 

 these lines lie the points of the visible spectrum observed, 

 and the dotted curves show the results of extrapolations by 

 various formulae. 



The actual points settled by observation are certain mul- 

 tiples of the wave-length D 2 (0*0005890 millim.), and a small 

 circle whose diameter equals a unit in the third decimal 

 place of the scale of ordinates (indices) gives the position 

 fixed by observation, while the distance from the centre at 

 which the smooth curve cuts the little circle furnishes a 

 graphic representation of its difference from observation. The 

 labours of the past year, then, have enabled us to absolutely and 

 directly measure the index of refraction of rays whose wave- 

 lengths are greater than 0*005 millim., or, more exactly, which 



reach 53011 of Angstrom's scale ; and to do so with an error 

 which is probably in most cases confined to the fourth decimal 

 place of the index. As we shall see more clearly by Plate VI., 

 the relation between n and X has changed from that appa- 

 rently complex one we see in the visible spectrum, so that n 

 becomes almost a simple linear function of X, and the results 

 of extrapolation grow to a higher order of trustworthiness 

 than when made from points in the visible spectrum alone. 



It appears to us that no formula of dispersion with which 

 we aje acquainted * gives entirely correct results on extra- 

 polation, but that among the best are Briofr's and Wiillner's. 

 We have computed the wave-lengths corresponding to indices 

 of refraction from observed deviations in the visible spectrum 

 according to these formulas. The curve from Cauchy's 

 formula we do not give, because (at least when not more than 

 three terms are taken from observations in the visible part of 

 the spectrum) its results are here of little value, since it 

 declares all the radiations we are now actually dealing with 

 to be impossible of discrimination at all. Redtenbacher's 

 formula we have also shown in a previous memoir to be 

 scarcely worth further consideration. The graphically con- 

 structed values are obtained by applying the formula of 

 Briot, 



* That proposed by Ketteler has come to the writer's knowledge too 

 late for trial here. 



