170 PROCEEDINGS OF THE CALIFORNIA 
These are the solutions of the case of this problem where only two known 
signals are involved. There are, however, two other cases: First, where from 
one position of the boat signals A and B are visible, but from the other only 
B and C are seen; here the boat’s positions are equally well determinate, and 
¢he geometrical construction and graphic solutions are the same as above 
given—but the trigonometrical analysis varies slightly (see Narrien’s Geod- 
esy). And in the second case, where first position of boat sees only signals 
A and B, and its second position only C and D, these positions are still deter- 
minate, and the graphic solutions and geometrical construction are identical 
with those already given, but the trigonometrical analysis is different, as 
shown by the writer on page 19, vol. 2, of The Analyst. 
The two-point problem may, moreover, be found most serviceable in restor- 
ing lost stations. Suppose the case illustrated in Fig. No. 4—where (the sur- 
face mark of) station @ is lost and its restoration is desired. Having an ap- 
proximate idea of the position of the lost station, , choose two such points, 
Mand P, as make at once the quadrilateral, A 6 P M, and the triangles, A 
MG, BP Gand G M P, ‘“ well conditioned.’’ Then at Mand P successive- 
ly measnre the angles B MA, B MP, A P B and A P M, and find—either 
by construction or computation, as above shown—the unknown sides and 
angles of the quadrilateral, A B P M. Now from the original triangulation 
are known the sides @ A and G B, and angles G A B, and G B A; and the 
angle 4 B P=P BA—G BA. We hence have two sides, G B and P B, and 
included angle, G B P, to find P G and angle B P G, the distance and direc- 
tion of the lost station, G, from the point, P. But if no linear measure is 
available, then mark the direction of G from the point, P, by range poles, n 
o, and shift the theodolite to M. Find angle, A M G, in like manner to that 
which found angle, B P G. Then cover A with telescope, turn it in azimuth 
equal to angle, A M G, and mark the direction of its line of sight with poles, 
ih. We then have marked out two ranges, 7h and o n, intersecting at ‘‘ the 
lost station,’’ G. 
And equally applicable when on land searching for a lost station with three 
signals in sight, is the maneuver so well understood in hydrography of taking © 
from the sheet the angles subtended by the three signals at the lost station, 
setting them off on two one-angle, or one two-angle sextant, and shifting the 
position of the observer till the images of these signals coincide in his horizon 
glass, when he will be close on the ‘‘lost station.”’ 
Dr. Blake read the following: 
On the Results of Glacial Action at the head of John- 
son’s Pass, in the Sierras. 
BY JAMES BLAKE, M. D. 
In a recent trip in the Sierras, at the head of the south fork of the American 
River, I met with some evidences of glacial action which I think are worthy 
of being recorded as furnishing some indications of the character of the 
climate during the middle part of the glacial epoch. The head of the valley 
