190 
Proceedings of the Royal Society 
tances for the red, yellow, green, and blue, were 5’9, 5*5, 5*025, 
and 4-25 inches respectively. The wave lengths calculated from 
these data are in millimetres — 
1 
5*9 
1 
25*4 _ 
*000624 millimetre for the red. 
2 * 
2 ’ 
20 
' 3000 
1 
2 * 
55 
2 * 
1 
20' 
25*4 _ 
' 3000 
*000582 
,, yellow, 
1 
5*025 
1 
25*4 
•000531 
2' 
2 * 
20 
' 3000 “ 
„ green, 
1 
4*25 
1 
25*4 
•000449 
„ blue. 
2 * 
2 ’ 
20' 
3000 
The apparatus contrived and constructed by the author to pro- 
duce these tine gratings has not been described, because its con- 
struction involves considerable trouble and expense, which the 
experimenter may avoid by applying to an instrument-maker who 
has a dividing machine. The difficulty of getting a sufficiently 
fine dark ground upon the glass will also be avoided if the dividing 
machine be fitted with a diamond point, which will scratch com- 
paratively opaque lines on the transparent surface of the glass. 
The finest gratings constructed are produced in that way. 
5. Note on Linear Partial Differential Equations. By 
Professor Tait. 
The equation 
^ du _ du du 
P di + Q ‘dy + = 0 
may be put in the very simple form 
S(o- V)u — 0, 
if we write 
< t ~ = $"P T^Q T' /rR, 
and 
. d . d d 
^ ~ 1 dx 3 dy+ c dz 
This gives, at once, 
Vn = mV Ocn t 
where m is a scalar and 6 a vector (in whose tensor m might have 
