kee 
Yan. 19, 1871] 
equation between them is possible. or instance, if yellow be 
excluded, the other five must be arranged so that a mixture of 
red, green, and blue is matched with a mixture of black and 
white. The large discs of the three colours are taken and 
slipped on to each other, and similarly the small discs of black 
and white. When the small discs are placed over the others 
and the whole made to rotate rapidly on any kind of spinning 
machine, the colours are blended, those of the large discs and 
those of the small, each into a uniform tint. 
By adjustment of the discs an arrangement may be found after 
repeated trials, such that the colour of the inner circle is exactly 
the same both in tint and luminosity with that of the outer rim. 
The quantities of each colour exposed may then be read off on 
a graduated circle, and the result recorded. For instance 
(the circle being divided into 192 parts), eighty-two parts red 
mixed with fifty-six green and fifty-four blue, match thirty-seven 
parts white mixed with 155 black. In this way Maxwell ob- 
served the colour equations between each set of five, in all six 
sets formed by leaving out in turn each of the six colours. 
Moreover, for greater accuracy each set was observed six times, 
and the mean taken. But according to the theory these six final 
equations are not all independent of each other, but if any two 
of them are supposed known, the others can be found by asimple 
calculation, Accordingly, the comparison of the calculated and 
observed equations furnishes a test of the theory ; but in practice, 
in order to ensure greater accuracy, instead of founding the 
calculations on two of the actually observed equations chosen 
arbitrarily, it is preferable to combine all the observations into 
two equations, which may then be made the basis of calculation. 
Tn this way, a system of equations is found necessarily consistent 
with itself, and agreeing as nearly as possible with the actually 
observed equations. A comparison of the two sets gives evidence 
as to the truth of the theory according to which the calculations 
are made, or if this be considered beyond doubt, tests the accu- 
racy of the observations. In Maxwell's experiments the average 
difference between the calculaced and observed systems amounted 
to ‘77 divisions of which the circle carried 100. So good an 
agreement is regarded by him as a confirmation of the whole 
theory; but it seems to me, I confess, that only a very limited 
part of itis concerned. The axioms, in virtue of which it is 
permitted to combine the colour equations in the manner re- 
quired for the calculations, are only such as the following :—If 
colours which match are mixed with colours which match, the 
results will match. It is difficult to imagine any theory of colour 
which will not inciude them. What proves the threefold cha- 
racter of colour—the most important part of the doctrine—is 
simply the fact that with any five-coloured papers whatever a 
match can be made, while with less than five it cannot (except 
in certain particular cases). In regard to this point the value of 
the quantitative experiments is rather that they show of what sort 
of accuracy the eye is capable in this kind of observation. 
Those to whom the subject is new may think at first that if 
colour be threefold a match ought to be possible between any 
four colours. And so itis possible if there is no other limita- 
tion ; but in experiments with the revolving discs, we are subject 
to a limitation, being obliged to fill up the whole circumference 
somehow. The difficulty will clear itself up, when itis re- 
membered that one of the five colours may be black, so that 
with any four colours and d/acka match can be made with 
revolving discs. 
It was rather for my own satisfaction than with the hope of 
adding anything new toa subject already so fully and ably 
treated by Maxwell, that I commenced a repetition of his experi- 
ments. The colours used were, roughly speaking, the same as 
his, as was also the general plan of the observations. The 
agreement of the calculated and directly observed equations was 
‘very good, the average error being only *24 divisions of which 
the complete circle contained ninety-six, or one-third of the corre- 
sponding average error in Mr. Maxwell’s Table. A second set 
of observations and calculations made after a year’s interval with 
a different set of colours gave about the same result. I am 
inclined to attribute the considerably greater accuracy of my 
observations rather to an excellent perception of minute dif- 
ferences of colour (to which I have always found my eyes 
very sensitive) than to greater care in conducting the experiments. 
One precaution, however, I have found so important as to be 
worth mentioning. Unless the small discs are very accurately cut 
and centred, a coloured rim appears on rotation between the two 
uniform tints to be compared and adjusted to identity, which is 
exceedingly distracting to the eye, and interferes much with the 


NATURE 


235 
accuracy of the comparison, One set of observations made 
with the same care, and apparently as satisfactory as any of the 
others, puzzled me for some time on account of the great dis- 
crepancies with the others which it exhibitel. Ihave no doubt 
that the cause lay in the different character of the light on the 
day in question, which came from the unusually blue sky which 
sometimes accompanies a high wind. On the other days the 
light came principally from clouds, I have had no opportunity 
of confirming this opinion by a repetition of the experiment with 
a sky of the same degree of blueness, but that the disagreement 
was not the result of unusually large errors of observation, is, I 
think, to be inferred from the fact that the observations under 
the blue sky were as consistent among themselves as any of the 







other sets. As the point is of some interest, I give the 
figures in full. 
Black. White. Red. Green. Yellow. Blue. 
July 23, blue sky. 
Oo +30 +122 +40; —77 —I1I5_ obs. 
oO + 32°2 + 120°8 + 39°1 — 78°8 — 113°2 calcd. 
+ 94 O32 eo eiss i) 943) obs! 
eae Spams Tea a a ati ee Sl 
— 138 —54 Oo +24 +50 +118 obs. 
= O + 23° + 49°5 + 119°5 calcd, 
fP"92, “F504 50 o —66 —126 obs. 
+ O41 + 495 + 48°5 oO — 65:2 — 126°7 calcd. 
—154 —38 + 86 + 52 Oo + 54 obs. 
SAO 37) 04 0 5g Oo + 54°3 calcd. 
+139 +18 — 128 —64 + 35 oO obs. 
+ 1385 + 19°7 — 1275 — 64°5 + 33°9 o calcd. 

The numbers read off for the big discs are written with the sign 
+ prefixed, and those corresponding to the little dises with —. 
Thus the first line may be read : — 30 parts white together with 
122 red and 40 green, match 77 yellow and 115 blue. The upper 
line, of each pair represents the actual observation, and the 
second is the theoretical equation calculated from two in the 
manner described. The average difference between the two sets 
of numbers which may be taken as a measure of the inaccuracy 
of the observations amounts to 1'r. A similar table, formed 
from the observations of July 20 (cloudy), and which agreed 
very well with the results of other days, is as follows* :— 





Black. White. Red. Green. Yellow. Blue. 
o +30 +117 +45 —79 —113 
fo) Blt 1162448 79°99 «1122 
+ 90 o —128 —64 +56 + 46 
859 0 i284 635 570 49°0 
— 136 — 56 Oo +22 +52 + 118 
137 55 ° 2243: 50 1196 
+ 100 +50 + 42 o —64 —128 
992 51 419 ° 65 127°I : 
+135 +21 —123 —69 + 36 ° 
BSS Mgt SoD 122°7 69°3 348 ° 
—152 —4o0 + 80 + 56 o +56 
152°6 9395 81 56 fo) 55 

The average error is here 95, showing only a trifling better agree- 
ment than the former set, so that the blue sky observations are 
nearly as self-consistent as those made with cloud-light. More- 
over, the agreement is itself very good, being decidedly better 
than Maxwell’s, though his calculations refer to a mean of six 
sets of observations. 
While therefore there is no reason to distrust the results of July 
23 any more than of July 20, the differences between them are 
much greater than can be ascribed to errors of observation. It 
will be found that they relate principally to the quantities of red, 
the numbers under that head being considerably greater for the 
case of the blue light from the sky. I am not aware whether 
the difference of sky and cloud light has ever been made the sub- 
ject of direct investigation, but it would seem a fair inference that 
it must consist mainly ina relative deficiency of the red rays. If 
this be so, as I have other grounds for suspecting, the light of the 
* These calculations were made by means of Prof. Everett's Proportion 
table, which seems admirably adapted to work of this sort. 
