8 PROCEEDINGS OF THE CALIFORNIA 
limbs of the protractor at the same time, then set off the supplement of the 
left hand angle on the right hand limb, and the supplement of the right hand 
angle on the left hand limb; cause the right and left arms of the instrument 
to traverse points A and C, respectively, and draw a line along the middle 
arm, then shift the center of protractor (taking care to keep the points A and 
C bisected by the true edges of right and left arms), and draw another line 
along middle arm and the intersection J, of the two lines thus drawn, will be 
a point on the right line through point B, and the required place of observation ; 
draw this line through Band J, and with the center of the instrument on 
this line, cause the fiducial edges of the right and left arms to traverse A and 
C respectively; dot the center, and this is the place of observation. 
Another method of plotting a position by supplementary angles is to set 
off the right hand angle on the left hand limb, and the sum of the supplements 
of the observed angles on the right hand limb of the protractor—cause the 
left, middle and right arms to traverse the middle, right and left signals, 
respectively; dot the center, and it is the required position. 
And this instrument also enables the hydrographer and topographer to 
determine and plot their positions by the two point problem (in a manner 
equal in accuracy and second only in point of simplicity to that by the three 
point problem), as shown by the writer at page 18, Vol. 2 of ‘‘ The Analyist.”’ 
And, in fact, with one piece of tracing paper and the Alidade, the topographer 
can plot his position, by the three point problem—and with two pieces of 
tracing paper and the Alidade, he can plot his position by either the two or 
four point problems shown by the writer at page 146, Vol. 1, of ‘“The Analyist.”’ 
This instrument also furnishes the ready means of orienting the sounding bout. 
If out in a bay, lake orriver, or along near the sea coast, and your compass 
functions badly, and you have while angling and plotting, or for some other 
reason lost your bearings, and hence wish to catch some fixed object ahead 
or astern on the general direction of the line you wish to ram—then take from 
the sheet, with the Protracting Sextant, the angle between some visible signal 
and the general direction on which you desire to continue your line of sound- 
ings, and then lifting the instrument to your eye, shift it until you bring the 
image of this signal into the horizon glass, and whatever fixed object this 
image then covers will be a point on the desired course. By this means, the 
hydrographer, even if out on a large expanse of water, and swept about by 
winds and currents, with his compass crazed by localattraction or the heaving 
of the waves, may “* orient himself,’’ and thus ply the helm more intelligently. 
And, in fact, by this maneuver, and by observing (and plotting as you go) 
twice or thrice as many angles as must necessarily be recorded, the boat can 
be steered without the aid of the compass. These practical hints will be 
found to come most opportunely to the relief of the distressed hydrographer 
when surveying close in shore along much of the Pacific coast, with its beaches 
of ferruginous sand, or along the iron bound shores of Lake Champlain, 
where the magnetic needle often becomes worse than useless. 
In nothing will the skill and dexterity of the hydrographer be more 
advantageously displayed than in deciding at once upon the line his boat is to 
pursue, and with the glance of intuition grasping all the conceivable combin- 
ations of visible points that will determine his position. But in practical 
