bias must be discounted, as must also that of the physiologist. APPENDIX. The following is extracted from Maxwell’s paper. The following table contains the means of four sets of observations by the same observer (K.):-- TABLE IV. (K.) 44·3 (20) + 31·0 (44) + 27·7 (68) = W. 16·1 (28) + 25·6 (44) + 30·6 (68) = W. 22·0 (32) + 12·1 (44) + 30·6 (68) = W. 6·4 (24) + 25·2 (36) + 31·3 (68) = W. 15·3 (24) + 26·0 (40) + 30·7 (68) = W. 19·8 (24) + 35·0 (46) + 30·2 (68) = W. 21·2 (24) + 41·4 (48) + 27·0 (68) = W. 22·0 (24) + 62·0 (52) + 13·0 (68) = W. 21·7 (24) + 10·4 (44) + 61·7 (56) = W. 20·5 (24) + 23·7 (44) + 40·5 (60) = W. 19·7 (24) + 30·3 (44) + 33·7 (64) = W. 18·0 (24) + 31·2 (44) + 32·3 (72) = W. 17·5 (24) + 30·7 (44) + 44·0 (76) = W. 18·3 (24) + 33·2 (44) + 63·7 (80) = W. X.--REDUCTION OF THE OBSERVATIONS. By eliminating W from the equations above 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 transposing 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) = + 0·6 + 0·2 + 30·5 44·0 (76) = + 1·1 + 0·7 + 30·5 63·7 (80) = + 0·3 - 1·8 + 30·5 Mr. James Simpson, formerly student of Natural Philosophy in my class, has furnished me with thirty-three observations taken in good sunlight. Ten of these were between the two standard colours, and give the following result:-- 33·7 (88) + 33·1 (68) = W. The mean errors of these observations were as follows:-- Error of (88) = 2·5; of (68) = 2·3; of (88) + (68) = 4·8; of (88) - (68) = 1·3. The fact that the mean error of the sum was so much greater than the mean error of the difference, indicates that in this case, as in all others that I have examined, observations of equality of tint can be depended on much more than observations of equality of illumination or brightness.