MATHEMATICAL SECTION. 128 
The Chairman read an inaugural address, [given in full on pp. 
117 to 119 ante.] 
Mr. C. H. KuMMELL then began a paper on 
ALIGNMENT CURVES, 
which was not finished at the time of adjournment. 
38D MEETING. APRIL 26, 1888. 
The Chairman presided. 
Present, sixteen members and one invited guest. 
Mr. KuMMELL completed his paper, begun at the second meet- 
ing, on 
ALIGNMENT CURVES ON ANY SURFACE, WITH SPECIAL APPLICATION 
TO THE ELLIPSOID. 
[ Abstract. ] 
The attempt to put a number of points in line on a curved sur- 
face whose normals are supposed to be given (abstraction is made 
of deviations of the plumb-line and lateral refraction) gives rise to 
various curves, which I call alignment curves. There are two 
classes—alignment curves with two given termini and those with a 
starting point only. There are three distinct curves of the first 
class, viz.: 1. The normal section, if the surveyor directs his assist- 
ant to place staffs in line from one end of the line. 2. A curve 
described if the surveyor would align a point near him, then move 
up to this point, thence align another point, etc., until the terminus 
is reached. This process is that used in chaining, or more roughly 
by a pedestrian going towards a point, and is characterized by 
requiring only foresights. I call it prodrthode (xpo, 6p@cs, 6dds).* 
3. A curve resulting if a backsight is also taken. This curve is 
therefore defined by the condition that the normal plane at any 
point of it which passes through one end also passes through the 
other. I call it diorthode (0:4, épOds, bdds), because it may be con- 
* This and other names of curves were coined by my friend, Mr. Wm. R. 
Galt, of Norfolk, Va. 
