PHYSICS: ST. JOHN AND BABCOCK 
295 
If 61 is a linear function of x, y, z, it is possible to choose the quadric 
(5) so that by means of (7) and (14) di/ Vo- is expressible as a homogene- 
'ous linear function of X, Y, Z, W, involving W at least. Hence: 
When the function 61 determining a transformation K of a surface S is 
a linear function of the cartesian coordinates of S, the corresponding tan- 
gent planes to S and its transform meet in line of a fixed plane. 
1 Transformations of conjugate systems with equal point invariants, Trans. Amer. 
Math. Soc, 15, 397-430 (1914). This will be referred to as memoir Mx. 
2 Conjugate systems with equal tangential invariants and the transformation 
of Moutard, Palermo, Rend. Circ. Mat., 39, (1915). This will be referred to as 
memoir M^. 
' Guichard, Ann. set. Ec. norm., Paris, Ser. 3, 14, 492 (1897). 
ON THE POLE EFFECT IN THE IRON ARC 
By Charles E. St. John and Harold D. Babcock 
MOUNT WILSON SOLAR OBSERVATORY. CARNEGIE INSTITUTION OF WASHINGTON 
Presented to the Academy, April 14. 1915 
In a communication to the Academy which appeared in the Proceed- 
ings for March 1915, we reported some results of our investigations 
on the pole effect in the iron arc under normal conditions. We have 
found between two and three hundred lines whose wave-lengths at the 
negative pole are distinctly longer than when the Hght is taken from a 
cross section at the center of the arc. 
Aside from the theoretical interest in such changes in wave-length, 
reference may be made to the following points: 
1. A number of these lines are included among the international 
standards of the second order. Their wave-lengths depend upon inter- 
ferometer measurements made by three independent observers, the means 
of which have been adopted as standards by the International Union for 
Cooperation in Solar Research. 
2. There is a region of the iron spectrum extending from X 5500 to 
X 6000 in which no other class of lines is available for standards. 
3. In various laboratories there are in progress redeterminations, 
based upon the iron standards, of the wave-lengths in international 
units of the lines of many elements. In these redeterminations the 
instrument most frequently used is the concave grating in the usual 
Rowland mounting. In ordinary practice, the slit of the spectro- 
graph is parallel to the axis of the arc and includes the major portion 
of its length. We have found that the pole effect appears at a con- 
siderable distance from the negative pole and that for high precision 
