Colour and Chemical Constitution. 
43 
ment of the visible band (at x 554 or X 555) is the same as mine. It should 
be noted that these wave-lengths are exactly in the ratio ^ : i = i, consequently, 
(1) the real fundamental absorption of alkaline phenolphthalein lies in the 
infra-red, at wave-length X 1109 (frequency 9'02) ; (2) the visible band in 
the green is its first harmonic (X 554, frequency 18"05) ; (3) the barely 
visible band in the extreme violet is its second harmonic (X 370, frequency 
27'07) ; and the band of X 277, frequency 36-1, is its third harmonic. 
In the case of a higher phthalein (presumably thymolphthalein, etc.) the 
same frequency-ratio of 2 : 3 : 4 was observed, the wave-lengths being about 
X 626, X 417 and X 313, thus fully confirming my observations about the 
effect of " loading " of the molecule. Solutions in alcohol were found to 
have higher wave-lengths for the bands than similar solutions in water (the 
difference is plainly visible to the naked eye) : alkaline phenolphthalein, 
which has X 554 in water, has its band-centre at about X 562 in alcohol, 
whilst in alcohol-ether (equal volumes) the band-centre is at X 567, with 
quite a violet-pink tinge. This is evidently a "loading" phenomenon 
exactly similar to that caused by substitution in the molecule : thus 
alkaline phenolphthalein in alcohol-ether has nearly the same spectrum as 
alkaline (di)orthocresolphthalein in water. By using isoamyl alcohol con- 
taining 1 per cent, of ethyl alcohol as the solvent the band of alkaline 
phenolphthalein is moved up as far as X 572, and no doubt if a suitable 
solvent of higher molecular weight could be found it would be possible to 
cause , alkaline phenolphthalein to exhibit a blue colour. For example, 
sodium o-cresolphthalein, which is red-violet in water (X 570 for centre of 
absorption), becomes blue-violet in amylalcohol (X 587 for centre). 
The definite discovery of these upper- harmonic ultra-violet bands in the 
spectra of the phthaleins has a marked value in unifying and simplifying the 
whole field of the research. For example, in Part I a mathematical formula 
was developed whereby the absorption-band (and colour) of a phthalein dis- 
solved in cone. H2SO4 can be calculated from the data given by the same 
phthalein in alkali— wherein it has a different colour. It was also remarked 
at that time how anomalous it is that loading " with II2SO4 increases the 
frequency. If now, however, we realise that the HoSO^ band is not the 
visible alkali band loaded, but is the invisible band loaded, the anomaly dis- 
appears. To take the simplest case, the visible band of alkaline phenol- 
phthalein is at X 554 in the green, whereas the visible band of phenolphthalein 
in II2SO4 is at X 499. Now " loading " the molecule in all other cases 
increases the wave-length (diminished frequency), so if we simj^ly assume 
that the X 499 band is the X 370 band " loaded " everything becomes consistent. 
3 \ 
The mathematical formula given in Part I was y — A^'' which x 
is the (visible) alkali frequency and y the II0SO4 frequency of the same 
phthalein. The new mathematical formula is much simpler. Since the 
