6 PROCEEDINGS OF THE CALIFORNIA 
facts of there being three separate instruments and requiring the simultaneous 
and rapid manipulations of two observers (and their subsequent efforts in 
setting off the angles on the protractor) have long been felt to be defects. 
And the hydrographic world has studied, but unsuccessfully, to devise an in- 
strument that would do the work of these three. But this problem finds a 
solution in my protracting sextant, which enables one observer to accomplish 
in hydrography the desideratum of measuring at the same instant two angles, 
and plotting them with the same instrument. 
We have represented here in the annexed figure, ‘‘ The Protracting Sex- 
tant,’’ consisting of a circle D, graduated to degrees and minutes from the 
zero point around by the right and left each way to one hundred and eighty 
degrees, and three radiating protractor arms, f,g andh. The arm g, is fixed 
with its true edge at the zero point of graduation, and the other two, f and h, 
are capable of being revolved around the hollow cylindrical axis of the circle. 
Between this fixed, and each of these movable protractor arms, we have an 
index arm—and each of these indices, m and n, also find in the center of the 
circle a common center of motion, and carries an index-mirror mounted per- 
pendicular to its plane of motion but slightly eccentrically so that the hollow 
axis of the instrument can be readily gotten at. Along these index arms m 
and n, are cut rectangular slots (whose longitudinal axes are radii of the cir- 
cle), in which slide the projecting ends of the pivots which rivet the equal 
rectangular bars, 0, s, and u, w, together. And these indices and protractor 
arms are so connected by means of jointed parallelograms that the right hand 
index-arm always bisects the angle included between the fixed and right 
hand protractor arms, and the left hand index always bisects the angle con- 
tained by the fixed and left protractor arms. 
Now by a well-known optical principle we know that the angular distance 
moved over by a mirror while measuring an angle is only one-half of the ac- 
tual angle measured, and since each of the movable protractor arms of this 
instrument is by means of this jointed parallelogramic gearing, driven along 
its are simultaneously with, and twice as fast as its corresponding index-arm 
(and mirror), we hence see that the angles included between the fixed and 
movable protractor arms are the actual angles which the indices (and their 
mirrors) have measured. 
The index niirrors, y and z, may be mounted to move either in the same or 
in parallel planes, as shown in the forms of the writer’s two-angle sextants 
described in the proceedings of the Academy, February 16th, 1874. A horizon 
glass, x, half-silvered to admit of direct and reflected vision is attached to the 
frame of the instrument nearly opposite the index mirrors, with its plane 
perpendicular to the plane of the instrument. The arms, f and h, are clamped 
and adjusted with the ordinary clamp and tangent screws, / and k. 
The requisite adjustments of the ‘‘ Protracting Sextant”’ are the same as 
those of the ordinary sextant. When observing with the new Protracting 
Sextant, the hydrographer holds it lightly in his right hand and movesit until 
its face is in the plane passing through his eye, 7, and the three objects, A, B, 
C, whose angular distances are required, and then sets and clamps his in- 
dex arm so that the reflected and direct images of the objects (say left hand 
and middle) of one of the angles which he is to measure, are not coincident 
