WAVB-LENCiTIhS IN TDE INVISIBLE TRISMATlt! SPEGTKUM. 



157 



With the aid of these constants, the wave-lengths corresponding to given refractive indices 

 were computed, and a curve representing the formula was ])h)tted. This curve, as well as those 

 representing Oauciiv's and Redtenbaciieu's formula', is shown in I'late XIX, where we may 

 obtain by simi)le inspection the actual errors of all the formulai in question, or we may take them 

 from the following table, whose results, I hope, will supply useful data for those who are interested 

 in theories of dispersion. 



Table IV. — Approximate errors in u-avalemjths by Briot^s, Gauchy's and Redtenbacher's formula: 



for cold bands in infrared. 



[Comparison of theories witli observation.] 



By obs. 



l.f)714 



1. 5687 

 1. 5678 

 1.5674 

 1..5668 

 1. 5636 

 1. 5616 

 1. 5604 

 1. 5576 

 1. 5572 

 1.5544 



to 

 1. 5.535 

 1. 5520 

 1. 5515 



Ob- 

 served 



0. 760 

 0. 81.''> 

 0.850 

 0.890 

 0.910 

 0.940 

 1. 130 

 1.270 

 1.360 

 1.540 

 1.580 

 1.810 



to 

 1.870 

 1.980 

 2.030 



Wave-lengths derived by extra-pobition. 



From Redtenbacher's formula. 



Value. 



0.760 

 0.820 

 0. 862 

 0.915 

 0. 941 

 0. 990 



Error. Value, 



0.000 

 0. 005 

 0.012 

 0.025 

 0.031 

 0. 050 



Imaginary. 



2. 230 

 2.170 

 2.060 



Error. 



1. 340 

 1.260 

 1.120 



Imaginarv. 



Note. — Apart of the above values of h, where determined from observation by the bolometer, are iiable to error 

 in the fourth decimal place For probale errors of A see Table 2. " X observed" is either from a direct observation or 

 from an interpolation between two closely contiguous observ.ations. 



It is evident that Briot's formula, though not exact, yet gives results much more trustworthy 

 than the others considered, and it was employed in constructing provisional maps of the normal 

 spectrum from the prismatic, until an apparatus was completed for determining the wave-lengths 

 of the invisible rays by direct measurement. 



We must evidently conclude from the numbers in Table 4, and from the curve in Plate XI, 

 which embodies them, that we in reality can scarcely assign any limit to the extent of the infra- 

 red prismatic spectrum, and that far from the curve having an asymptote parallel to the axis of 

 X, as Gauchy's theory requires, our curve (.so far as we can follow it) rather tends to ultimately 

 coincide with a straight line cutting the axis at a finite angle, and (if this axis pass through the 

 point n=\) at a great distance from the origin. 



With the danger of extra-polations presented to us in such examples as have been cited, we 

 shall not attempt to generalize the results of our observations, further than to remark that for the 

 prism in question, we find that the deviation tends within the limits of observation to become pro- 

 portional to the wave-lengths, as the deviation diminishes, and that as far as we can see at pres- 

 ent, there is scarcely any limit to the wave-length our prism can transmit except that fixed by ita 

 absorptive effect. 



The approximate limit of the solar spectrum of the Hilger prism is at n 1.5435, which ac- 



