CHAPTER XVII.
Make an astrolabe, and obtain the latitude of the island, and, by an eclipse of the moon, the longitude also. By means of the Epitome make a chart on Mercator's projection, and find out the distance from any known land.
I found in my book a description of an instrument used by the ancientsto ascertain altitudes and to measure angles, called an Astrolabe,which, upon careful study and examination of the cut, I felt confidentwould serve my purpose admirably. So to work I went, and in thismanner. I made first a strong four-legged stool or bench, about threefeet in height and four feet long, and two feet wide upon the top. Ithen took some nice planed pieces of my dark hardwood and made a smoothsurface about an inch thick and five feet square. On this, afterwardsto be erected on the stool at right angles like an inverted letter T,I drew a circle with a pair of immense dividers that I made for thispurpose, taking in all the area possible, which made my circle aboutfifty-nine inches in diameter, leaving a margin of one inch,--supposingmy inches to have been of the right length; and this I determined bythe length of the knuckle of my thumb, which I formerly used for quickmeasurement, and from which standard I constructed the only ruleI ever have used on the island. How nearly correct it is I have nomeans of knowing. This groove I impressed into the wood by repeatedlyturning the dividers around the circumference. I then went to workand subdivided this circle into degrees and minutes, which I did bymarking the circle once across at any angle passing through the centremark, and then by another mark crossing this one at exactly rightangles, which I determined by means of my dividers--as laid down inBowditch's Epitome--by the use of them at equal distances from thecentre on the line already marked, sweeping them till the two linescrossed beyond the circumference, making a small mark there so as toerect a perpendicular on the base already drawn. This cut my circleat once into quadrants of 90 deg. each, and these were subdivided againin like manner. I made the circle large on purpose, so as to be ableto mark it plainly to sections of one minute each, and by its sizeto avoid any error in any angle, the chances of which were greatlydecreased by every inch of diameter. As I constructed it, I had nearlyone-half an inch of circumference to mark sixty minutes upon, and asI only subdivided one of the quadrants it did not take me very long,each degree being represented by a space slightly smaller than a halfinch, which was a good large scale to work upon. Having finished themarking of my board I nailed it firmly to the stool in an uprightposition, with the quadrant, that I had carefully subdivided on themarked circumference, pointing with one of its angles to zenith, andthe other on a line with the top of the stool. I then procured a nicestraight piece of cane some six feet in length and about an inch indiameter, and with a heated rod of iron burned out all the pith betweeneach joint till I had made a nice tube of that length. Just within theaperture at one end I fastened with a little fish glue a large stronghair from the beard of one of my goats. I then fastened, by means ofa hole through the centre of my upright disc, this tube or telescopeto it on the side that was subdivided into degrees, and about an inchfrom the face. I fastened this so that it was held firmly in place,and yet could be moved upon its centre by the pressure of my hand oneither arm. This tube I then furnished with a small delicate pin onthe outside, in an exact line with the stretched hair inside the tube,and pointing to the degrees and minutes on the marked circumferenceon the disc, which it almost touched. In other words, if I moved onearm of the tube, the needle on the outside would follow the groovedcircumference on the disc, and upon being released would mark somegiven degree or minute. Having gotten this machine all in order andcomplete, I placed it one day so as to examine the sun near noon, andhere is how I obtained my latitude. What I was doing now was not sovery difficult. I well knew that there were several ways to determinelatitude. I was aware that the difference of a minute or two even inmy altitude, as apparently observed, would not disturb my computationmore than a mile or so. In fact each minute marked upon the discpractically stood for one mile of latitude, and the mean of severalobservations would correct even any errors from this cause.
I waited till I knew that it was nearly noon by the appearance of thesun, and then commenced operations. In the first place I aimed my tubeat the sun, and to be able to do so without injuring my eye, I wouldsay that I had fitted the orifice of the tube nearest to me with apiece of smoke-colored membrane or backbone of the squid, which is astransparent as glass, and very thin and delicate. Having, by movingthe tube with my hand, brought the sun so that it seemed to stand uponthe hair in the outer end of the tube, or like a great capital O upona base line [O_], I left it carefully in that position for a moment ortwo, and then applied my eye again, and found, as I supposed, that thesun no longer seemingly rested upon the hair in my tube, but had risen,which forced me to again lower the arm nearest me and elevate theother extremity, and proved to me that it was not yet noon, and thatthe sun had not yet reached the meridian. This I did many times, tillat last the sun seemed for a minute or so to stand still, as sailorssay, and I knew that it was at meridian. I took good care not to touchthe instrument, but waited quietly till, by glancing through it, I sawin a few moments the disc of the sun, or lower limb as it is termed,begin to drop below the hair in my tube, and I was then positive thatit had passed the meridian. Being assured of this, I went carefully tothe marked circumference on the upright disc and noted carefully thedegree and minute to which the needle in the side of the tube pointed,which in this case was 54 deg. 51'. Having carefully marked this downwith ink upon birch bark, I went again to the other end of the tube, and,elevating it, brought the outer end down toward the sea till the hairand the horizon seemed to be one. I then again carefully observed thedegree and minute at which the needle pointed, which in this case was7 deg. 16', and my task was done; for, by subtracting 7 deg. 16' from 54deg. 51' I obtained 47 deg. 35', which was exactly the apparent altitudeof the sun at noon on September 22, 1866, civil account; and, havingthat, it was easy to determine the latitude in the following manner:--
At noon observe the altitude of the sun's lower limb bearing North 47 deg. 35'
Add for semi-diameter, dip, etc. 12' ---------- 47 deg. 47'
Subtract from 90 deg. 00' ----------
Sun's zenith distance 42 deg. 13' S.
Declination for longitude, say 115 deg. W 8' S. ---------- Latitude by observation 42 deg. 21' S.
Thus I demonstrated the latitude of my island; but now for thelongitude. To obtain that I knew that I must first ascertain the timeat the island: I could do nothing without that; for longitude was,as I well knew, simply time changed into degrees. I thought of fiftydifferent ways to obtain correct time, but believed none of themsufficiently accurate for my purpose. I could make a sundial for onething, find out the length of the day by the Epitome and NauticalAlmanac, make candles to burn such a length of time, sand to run downan inclined plane at such a rate, but none of these would do.
The difference of a minute, or one-sixtieth of a degree, in an observedaltitude would only affect, as I have said, my latitude just onemile, whilst an error of time of one minute from true time would, asI was well aware, throw my longitude out just fifteen miles; hence itbehoved me to have exact time if I desired to get exact longitude, andtherefore I saw nothing for it but that I must construct a clock, andat it I went. It was not such an enormous undertaking after all. Ofcourse I should make it of wood, and in my boyhood I knew many woodenclocks that kept excellent time; besides, if I could only constructsomething that would keep time for an hour or two without much error,it would answer my purpose. If I had a clock that I could set at noonby my observation, nearly correct, I could correct it perfectly by anaft
ernoon observation, and have for an hour or so true time, even if itdid gain or lose a few minutes in twenty-four hours. So to work I set,and soon turned out the few small wheels necessary, and the weight andpendulum for the same. I spent little time upon the non-essentials, butput it together inside my house on the wall, open so that I could getat it, and furnished it with wooden hands and a thin wooden face.
After I had arranged it and found that it would tick, and byobservations at noon for a few days been able to regulate the pendulum,I went diving into the Epitome and the Nautical Almanac as to howI should utilize it so as to get my longitude, after all; when oneevening, in turning over the Nautical Almanac, which was calculated for1866, 1867, 1868, and 1869, my eye fell upon the following, and I feltthat my task was done:--
Total eclipse of the moon, September 30,1866, invisible at Greenwich, visible in South America, South Pacific Ocean, and parts of Africa, Asia, and Indian Ocean.
FORMULA (CIVIL ACCOUNT).
Day. Hour. Min. Moon enters penumbra 30 5 44 A.M. Moon enters shadow 30 6 53 " Total phase begins 30 8 49 " Total phase ends 30 9 39 " Moon leaves shadow 30 10 45 " Moon leaves penumbra 30 11 55 "
This was all I needed to verify my longitude past peradventure, and Iwent to work at once, calculating when the eclipse ought to take place,nearly, with me.
At a rough calculation I knew that my island was situated somewherebetween the 110 deg. and 120 deg. of longitude west of Greenwich, that isto say, in the neighborhood of seven hours' difference of time later thanGreenwich time. Therefore I knew that if the moon entered the penumbraat Greenwich (although invisible) on the 30d. 5h. 44 min. A.M. thatI ought to look for it to occur visibly to my eyes somewhere from oneto two o'clock in the afternoon of the same day, or seven hours later.The _exact_ difference in the time between Greenwich and that to beobserved on my island, changed into degrees and minutes, would, ofcourse be the true longitude west of Greenwich.
It was with the utmost anxiety that I awaited the coming of the 30thof September, for it all depended upon pleasant weather whether or notI should be able to make my observation. I placed my astrolabe so asto be able to move it quickly in any needed direction, as I intendedto use the tube to look at the sun through so as not to blind my eyes.I also prepared my birch bark in the house, and commenced practisingmyself in counting seconds, for I should have to leave my instrumentand go to the house, counting all the time to note the time markedby my clock. I found upon practice that I could not make this workvery successfully, and that according to the state of my feelings orexcitement I counted long and short minutes. This would not do; I mustinvent something better; and I finally bethought myself of counting thebeatings of my pulse with the finger of one hand upon the wrist of theother, and applying the proportion to the interval between the observedtime by my clock.
The morning at last came that I so much desired, and nothing could bemore beautiful than the balmy, spring-like day that surrounded me. Thesky was cloudless and the sun shone down in splendor through a clearand pure atmosphere. The morning passed slowly away, and it seemedas if the moon and sun would never approach each other; but finally,in the afternoon, the heavens showed me that the eclipse would soontake place, and I made my arrangements to take four observations, asfollows: Time when moon entered shadow; time when total phase began;time when total phase ended; time when moon left shadow.
Nothing could have been better than the afternoon I experienced to makethese observations, and in less than six hours the whole affair wasover, with the following result, I having carefully regulated my clockas near as possible by an observation at noon:--
Day. Hour. Min.
Moon enters shadow at island (civil account) 30 2 50 P.M. Moon enters shadow at Greenwich 30 6 53 A.M. ------------------------ Difference 7 57
Total phase begins at island 30 4 48 P.M. Total phase begins at Greenwich 30 8 49 A.M. ------------------------ Difference 7 59
Total phase ends at island 30 5 34 P.M. Total phase ends at Greenwich 30 9 39 A.M. ------------------------ Difference 7 55
Moon leaves shadow at island 30 6 41 P.M. Moon leaves shadow at Greenwich 30 10 45 A.M. ------------------------ Difference 7 56
Hours. Min. Sum of differences, four observations 31 47
Hours. Min. Sec. Mean of same 7 56 45
Which, reduced to time, gives the longitude of the island 119 deg. 11' 15'' west of Greenwich.
There, my problem was done and I was for the moment happy. Perhapssome will wonder why I cared to obtain the latitude and longitudeof my island at all. Let me explain. My Bowditch's Epitome gave thelatitude and longitude of all prominent capes, harbors, headlands,light-houses, etc., in the whole Pacific Ocean. In other words, knowingnow the latitude and longitude of my own island, I had only to projecta chart on Mercator's projection, pricking off the relative positionsof the land on all sides of me, as well as the position of my island,to have a practical and useful chart. Of course I should not be ableto draw the coast line or the circumference of any island, but mychart would show just what latitude and longitude Easter Island wasin, for instance, and just how far and in exactly what direction myisland lay from it. Also, how far I was from the American coast, andthe exact distance and course from any of the principal ports such asLima, Valparaiso, Pisco, etc. How far from New Zealand and the SocietyIslands, and in what direction from them.
Having marked the exact latitude and longitude of each of these places,which were fully given in the Epitome, on my chart, I could call uponmy memory often to fill in the coast lines, and even if I should inthe case of the islands, make them even imaginary, there would be noharm done, for the little black star on each would show me where thelatitude and longitude met exactly, and I should be furnished with apractical chart as far as sea navigation was concerned, but not onethat would be of much account in entering any harbors.
I cannot say that at this time I had any fixed plan of escaping fromthe island, but I very well knew that nothing in the world would aidme so much in the attempt as to know the position in latitude andlongitude that the island occupied, and a chart of the surroundingseas, with its numerous islands and headlands on the main land. It canwell be conceived that my first task after determining the position ofmy island was to turn to the Epitome to ascertain the nearest land tome there marked down, and after diligent search this is what I found:--
"Easter Island Peak," 27 deg. 8' south latitude and 109 deg. 17' westlongitude.
"Island," 28 deg. 6' south latitude and 95 deg. 12' west longitude.
"Group of Islands," 31 deg. 3' south latitude and 129 deg. 24' westlongitude.
"Massafuera," 33 deg. 45' south latitude and 80 deg. 47' west longitude,which I speedily worked out, by the principles of Mercator's sailing, tobe in course and distance from my island, as follows:--
Course. Distance.
Easter Island Peak N. N. E. 1/2 E. 1,040 miles. Island N. E. 3/4 E. 1,440 " Group of Islands N. W. 3/4 N. 840 " Massafuera N. N. E. 1/4 E. 1,540 "
Of these four places only two ever had a name, and I did not know
whether Easter Island was inhabited or not, and about Massafuera I wastotally ignorant.
Easter Island, I knew, of course, was one of the so-called SocietyIslands, and was the nearest practical land to which I could escape.But how was I safely to pass over a thousand miles of water? Thisinvestigation only proved to me what I had so long feared, namely, thatmy island was out of the track of all trade, and that it would be amiracle should I be preserved by the arrival of any vessel. I knew nowthat I must really give up all hope in that direction, and set to workseriously to help myself.
I therefore applied myself with great vigor to my chart which Ioutlined upon nice goatskin parchment, which I glued together till Ihad a surface nearly four feet square, upon which I could lay out allthe Pacific Ocean on a nice, large scale, by Mercator's projection.I went on with my daily work, and made this matter one for eveningamusement, and as I pricked off the latitude and longitude of somewell-known place, that I in former years had visited, my heart swelledwithin me with grief and mortification, and I had often to stop andwipe the tears from my eyes before I could proceed.
Release from my prison seemed farther from me than ever, as I advancedin my task, and although I had a sort of morbid pleasure in my work,and a fascination to linger over it, yet I saw plainly that I wasindeed cast away; for what could I do alone in a boat, even supposingthat I could build one strong enough to resist one thousand miles ofwater? Who was to steer when I was asleep? and then supposing I shouldbe able to arrive at Easter Island, what guarantee had I that I shouldnot be murdered at once by the natives?
No, here I was fixed beyond fate upon my own island, where, with theexception of companionship, I had everything that human heart couldwish for. But on the other hand, without companionship I lackedeverything that is worth living for in this world. I felt that theproblem of all problems hereafter to me would be how can I escape tosome civilized country in safety? And from what I now knew, it seemedas if it would remain a problem till my bones were left whitening inthe Hermitage.
My discovery of the latitude and longitude of the island had brought meno comfort, and I felt much more uneasy now than I did before finishingmy task. But as the summer weather came on, I regained to a degreemy good spirits, keeping, however, the problem of escape continuallyworking in my mind, for I knew that there must be some way to solve it,especially with the resources that I had gathered around about me.