THE THEOEY OP COMPOUND COLOUES. 
78 
mean error of the sum of the three standards, which is 2 ‘6 7, while the square root of 
the sum of the squares of the errors is 1*76. 
§ X. Eecluction of the Observations. 
By eliminating W from the equations of page 71 by means of the standard equation, 
we obtain equations involving each of the fourteen selected colours of the spectrum, 
along with the three standard colours ; and by transposing the selected colour to one 
side of the equation, we obtain its value in terms of the three standards. If any of the 
terms of these equations are negative, the equation has no physical interpretation as it 
stands, but by tmusposing the negative term to the other side it becomes positive, and 
then the equation may be verified. 
The following Table contains the values of the fourteen selected tints in terms of the 
standards. To avoid repetition, the symbols of the standard colours are placed at the 
head of each column. 
Table VI. 
Observer (K.) . 
(24.) 
(44.) 
(68.) 
44*3(20)= 
18*6 
+ 0*4 
+ 2*8 
16*1(28) = 
18*6 
+ 5*8 
- 0*1 
22*0(32)= 
18*6 
+19*3 
- 0*1 
25*2(36) = 
12*2 
+ 31*4 
- 0*8 
26*0(40)= 
3*3 
+ 31*4 
- 0*2 
35*0(46) = - 
1*2 
+ 31*4 
+ 0*3 
41*4(48)=- 
2*6 
+ 31*4 
+ 3*5 
62*0(52) = - 
3*4 
+ 31*4 
+ 17*5 
61*7(56) = - 
3*1 
+21*0 
+ 30*5 
40*5(60) = - 
1*9 
+ 7*7 
+ 30*5 
33*7(64)=- 
1*1 
+ 1*1 
+ 30*5 
32*3(72) = 4- 
0*6 
+ 0*2 
+ 30*5 
44*0(76)= + 
1*1 
+ 0*7 
+ 30*5 
63*7(80)= + 
0*3 
- 1*8 
+ 30*5 
From these equations we may lay down a chart of the spectrum on Newton's dia- 
gram by the following method : — Take any three points. A, B, C, and let A represent 
the standard colour (24), B (44), and C (68). Then, to find the position of any other 
colour, say (20), divide AC in P so that (18*6)AP=(2*8)PC, and then divide BP in Q 
so that (18*6 4-2 •8)PQ=(0*4)QB. At the point Q the colour corresponding to (20) 
must be placed. In this way the diagram of fig. 4. Plate I. has been constructed from 
the observations of all the colours. 
