UC-NRLF 
 
 III 
 
 $B EST blM 
 
 ia\L COMMISSION OF 
 
 : Cll. FRED. HARTT, CHTEF. 
 
 ;APHICAL SURVEYING, 
 
 BE YEAUX CARPENTER, C 
 
 Geographer to the Commission. 
 
 FROM VAN NOSTKAND'S MAGAZINE 
 
 NEW YORK: 
 
 JSTOSTRAND, PUBLISHER, 
 
 | MURRAY AND 2T WARREN STREET. 
 
 1O K o 
 O / O . 
 
VAN NOSTRAND'S SCIENCE SERIES. 
 
VAN NOSTRAND^UCIENCE SERIES. 
 
 No. 17. WATER AND WATER SUPPLY, By 
 PROF. W. H. CORFIELD, M. A., of the 
 University College, London. 
 
 No. 18. SEWERAGE AND SEWAGE UTILI- 
 ZATION. By PROF. W. H. CORFIELD, 
 M. A., of the University College, Lon- 
 don. 
 
 No. 19. STRENGTH OF BEAMS UNDER 
 TRANSVERSE LOADS. By PROF. 
 W. ALLEN, Author of " Theory of 
 Arches." With Illustrations. 
 
 No. 20. BRIDGE AND TUNNEL CENTRES. 
 
 By JOHN B. MCMASTERS, C. E. With 
 
 Illustrations. 
 No. 21. SAFETY VALVES. By RICHARD H. 
 
 BUEL, C. E. With Illustrations. 
 
 No. 22. HIGH MASONRY DAMS. By JOHN B. 
 MCMASTERS, C. E. With Illustrations. 
 
 No. 23. THE FATIGUE OF METALS UNDER 
 REPEATED STRAINS, with various 
 Tables of Results of Experiments. From 
 the German of PROF. LUDWIG SPANGEN- 
 BERG. With a Preface by S. H. SHREVE, 
 A. M. With Illustrations. 
 
 No. 24. A PRACTICAL TREATISE ON THE 
 TEETH OF WHEELS, with the Theo- 
 ry of the Use of Robinson's Odonto- 
 graph. By S. W. ROBINSON, Prof, of 
 Mecha.iiical Engineering. Illinois In- 
 dustrial University. 
 
 No. 25. THEORY AND CALCULATIONS OF 
 CONTINUOUS BRIDGES. By MANS- 
 FIELD MERRIMAN, C. E. With Illustra- 
 tions. 
 
 No. 26. PRACTICAL TREATISE O^T THE 
 PROPERTIES OF CONTINUOUS 
 BRIDGES. By CHARLES BENDER, C. E . 
 
 No. 27. ON BOILER ^INCRUSTATION AND 
 CORROSION. By F. J. ROWAN. 
 
GEOLOGICAL COMMISSION OF BRAZIL, 
 
 PROFESSOR CH. FRED. HARTT, CHIEF. 
 
 GEOGRAPHICAL SURVEYING, 
 
 ITS USES, METHODS Al RESETS, 
 
 BY 
 
 FRANK DE YEAUX CARPENTER, C.E, 
 
 Geographer to the Commission. 
 
 REPRINTED FROM VAN NOSTHAND'S MAGAZINE. 
 
 NEW YORK: 
 
 D. VAN NOSTRAND, PUBLISHER, 
 23 MURRAY AND 27 WARREN STREET. 
 
 1 8 78. 
 
Copyright ; 
 
 18T8, 
 
 By D. VAN NOSTRAND. 
 "' 
 
PREFACE. 
 
 CHAKLES FKEDERIC HAKTT, Professor 
 of Geology in the Cornell University, 
 and Chief of the Geological Commission 
 of Brazil, died on the eighteenth of March 
 last, in Rio de Janeiro, where he was 
 engaged in preparing the reports of his 
 Survey. 
 
 His death and the dissolution of the 
 Commission, of which he was the founder 
 and director, have prevented the realiza- 
 tion in Brazil of the plan of surveying 
 proposed in the accompanying pages. 
 
 F. D. Y. C. 
 
 NEW YORK, July, 1878. 
 
GEOGRAPHICAL SURVEYING. 
 
 IN this paper I shall present a scheme 
 for the organization, the gradual develop- 
 ment, and the prosecution of a geographi- 
 cal survey in connection with the 
 Geological Commission, which, in the 
 efficiency of its results, will satisfy not 
 only the present demands but also the 
 future needs of the Empire of Brazil for 
 very many years to come. In the rapidi- 
 ty of its progress, this survey will be 
 especially adapted to a country of so 
 vast an area and comparatively sparse 
 population, and as an adjunct to the 
 above Commission, and in great part 
 carried on by the members of the same, 
 without interfering with the ends of 
 that body, it can be maintained at an 
 expense so moderate as to be in con- 
 formity with the present desire for econ- 
 
6 
 
 omy and retrenchment in the public 
 service. 
 
 THE PROPOSED PLAN OF SURVEY. 
 
 The immense empire of Brazil is yet 
 without reliable geographical maps. 
 These are necessary to the national wel- 
 fare. The question arises as to what 
 kind of maps will be sufficient to satisfy 
 the imperative needs of the country and 
 of science. The plan of survey which I 
 shall advocate is a mean between that 
 system which takes cognizance of every 
 house in a village and every little undula- 
 tion in the landscape, and that want of 
 system in which are represented whole 
 mountain-chains that do not exist, or 
 actual topographical features are delin- 
 eated with gross inattention to accuracy. 
 It is a judicious mean between the slow 
 and laborious processes used, for in- 
 stance, in the Ordnance Survey of Great 
 Britain, and the sketchy and unreliable 
 information gained by the early ex- 
 plorers of the New World, from whose 
 results our first maps were compiled. 
 
These last are scarcely more graphic and 
 complete than our present maps of the 
 moon, and in fact, speaking broadly, 
 they are not so accurate as the latter, 
 which are, in great part, photographs of 
 the surface which they represent. With 
 these mere hints of the geography of its 
 country a people should not feel obliged 
 to rest satisfied until it can sustain a 
 minutely topographical survey. 
 
 AN EVOLUTION IN CARTOGRAPHY. 
 
 The demand for maps depends upon 
 the population and civilization of a 
 country. In the beginning a rough 
 sketch will answer the purposes of the 
 pioneer. As the region becomes inhab- 
 ited better maps are wanted, and finally 
 the people require the nearest possible 
 approach to absolute accuracy in the de- 
 lineation of topographical features. Map- 
 making in every country must follow a 
 regular evolution from the incomplete to 
 the complete. 
 
 Reviewing the origin and growth of 
 the cartography of a country, we see how 
 faulty it is liable to be. The first ex- 
 
plorer is the first contributor to the 
 geography of a region. By way of il- 
 lustration, let us follow one of these 
 pioneers as he traverses Brazil from 
 South to North. Following up a branch 
 of the River Plate, he records the ap- 
 proximate directions and distances of his 
 journey, which he obtains, perhaps by 
 the use of unreliable pocket instruments, 
 perhaps by an occasional glance at the 
 sun and his watch, or, more probably, 
 by estimating at night the latitude and 
 departure which he has made during the 
 day. At a certain period of his march 
 he finds a river entering from an easterly 
 direction, whose volume he measures 
 with a glance of the eye. Farther on, 
 he encounters a tribe of Indians, whose 
 village is situated upon the west bank of 
 the river; he counts their houses, and 
 makes the number of these a key to the 
 extent of the population. At the fol- 
 lowing night he camps at the foot of a 
 cataract. Impressed by its grandeur, and 
 also by a kind of optimism, common to 
 early explorers, and which will not allow 
 
him to underrate any of the glories 
 which he sees, he estimates its height to 
 be at least twenty meters, when in reality 
 it is but ten. 
 
 At a certain point whose latitude and 
 longitude he determines in a rude and 
 hasty way with the sextant which he 
 carries, he leaves the main stream and 
 follows a tributary to its head in the 
 highlands, where he crosses the divide be- 
 tween the great Parana Paraguay basin 
 and that of the Amazon. Upon the 
 summit of the plateau he te'sts his alti- 
 tude above the sea by noticing the tem- 
 perature of boiling water, or by reading 
 the indication of his single aneroid, un- 
 reliable methods which have been known 
 to give results even a thousand meters 
 wide of the truth.* Continuing down 
 
 * Gibbon's observations at the head of the Amazon, 
 both the mercurial and thenno-barometer being used, 
 show a discrepancy between the two which is equivalent 
 to 300 meters of altitude. The height of Mount Hood, in 
 Oregon, as given by one authority, who determined it by 
 the boiling point of water, is almost 2,000 meters greater 
 than that indicated by the cistern barometer and by tri- 
 angnlation. In the writer's own experience he has en- 
 countered an aneroid record, upon one of the peaks of 
 
10 
 
 the Araguaya, he observes the trend of the 
 mountain-range along his route, and, de- 
 scending the Tocantins, he makes, a simi- 
 lar survey extending to Para. 
 
 We do not disparage the work of this 
 man. Under the circumstances of hard- 
 ship and peril by which he is surrounded 
 he does all that is possible, and his re- 
 port is really of great value until some 
 more reliable exploration can be made; 
 still, for all of that, it is none the less in- 
 correct and incomplete. 
 
 It is from such sources as this that the 
 material for our first maps is drawn. In 
 later revisions there may be introduced 
 the results of desultory explorations of 
 mines, railway routes and navigable 
 waters, as well as the meagre topograph- 
 ical data acquired by the land surveyor 
 
 the Sierra Nevada Mountains of the United States, which 
 made the height of this mountain to be 3,000 feet above 
 its true altitude. It is a noteworthy fact that these pre- 
 liminary determinations, made with the above faulty 
 methods, resemble the estimates of the early explorers, 
 inasmuch as they almost invariably give exaggerated alti- 
 tudes ; perhaps the opinions and imagination of the ob- 
 server are allowed to form, in some unaccountable way, 
 a factor in these results. 
 
11 
 
 in running boundary lines of private 
 estates, but still, taken at its best, a map 
 constructed in this way falls far short of 
 its purpose as a picture of the conforma- 
 tion of the earth's surface, or as a guide to 
 the traveler, the geologist, or to the capi- 
 talist who wishes to invest his money in 
 the development and internal improve- 
 ment of his country. 
 
 FAULTS IN EXISTING MAPS. 
 
 In his compilation of the scattered in- 
 formation at his disposal the cartog- 
 rapher finds that a certain district of 
 country has never been entered by the 
 engineer. He knows, however, that two 
 rivers rise somewhere in this terra in- 
 cognita, and he feels it safe to predicate 
 a divide between them. He also thinks 
 it safe to presume that this divide is a 
 range of mountains, of greater or less 
 height, and, in his desire to give an ap- 
 pearance of finish to his chart, he does 
 not scruple to insert at this place an 
 ideal mountain system, and represent 
 it as drained by the upper tributaries of 
 
12 
 
 the two rivers, concerning|whose head- 
 waters in reality nothing is known. 
 These physical features soon come to be 
 reproduced, with more or less variation, 
 in other maps, and in this manner errors 
 are grounded in the national geography, 
 from which they can only be eliminated 
 by a systematic geographical survey. 
 Like national myths they stubbornly 
 refuse to give way until eradicated by 
 true scientific research. 
 
 Supposing, on the other hand, that 
 the compiler, accepting the report of the 
 explorer, who claims to have discovered 
 a range of mountains between the Rio 
 Parana and the Rio Araguaya, wishes to 
 represent them upon the map. He has 
 no mathematical data to insure their 
 position, and no sketches or other in- 
 formation from which to draw their in- 
 tricate topographical features, and so he 
 evolves from his imagination an utterly 
 impossible chain of mountains, out of 
 place, artificial, conventional, and even 
 mechanical in their regularity. These 
 he depicts in that stereotyped form of 
 
13 
 
 delineation, which is known in the 
 modern geographical draughting-room 
 as the " caterpillar " formation. 
 
 THE RELATIONS OF GEOGRAPHY TO GEO- 
 LOGY. 
 
 Upon such an unfaithful map as this 
 it is impossible to faithfully represent 
 the geology of a country. If the geolo- 
 gist attempts to lay down his conclusions 
 upon a sheet of this kind, its' errors will 
 continually clash with his truths. The 
 configuration of the land, as it appears 
 upon this erroneous drawing, might in- 
 dicate that it belonged to a certain geo- 
 logical age, and that, in fact, it could 
 not be referred to any other; the geolo- 
 gist, visiting and studying the country 
 itself, finds that it is of a later and 
 entirely different period. But if he 
 paints it as it really is he publishes a 
 glaring anachronism to the world, for 
 the color which represents the rock of 
 one geological epoch overlies, upon the 
 map, the physical features which are 
 peculiar to another age. As in the 
 
14 
 
 artistic and true delineation of tbe 
 human figure every feature must be the 
 exponent of anatomical structure, so in 
 topography, every representation of 
 topography must be true to geological 
 structure. Ranges of mountains mean 
 disturbance or great erosion of certain 
 strata, and each has its own characteris- 
 tic features as sharply defined as those 
 of an animal. This should be thoroughly 
 understood, and those immense lines of 
 sierras which are supposed to separate 
 certain river basins, or are delineated in 
 the very heart of regions of which we 
 have no knowledge whatever, should be 
 erased from the national maps until 
 these districts can be explored. In the 
 course of his travels the geologist may 
 find some physical feature of great im- 
 portance, which he wishes to portray, 
 in area and position, upon his chart, but 
 the best maps at his disposal represent a 
 topography utterly at variance with 
 geological structure, perhaps a sharp 
 ridge of mountains where there should 
 be a plain, and so they are of no use to 
 
15 
 
 him. Or he may find himself obliged to 
 color the top of a mountain peak with 
 the tint conventional to the bed of a 
 lake, and in this manner science is made 
 ridiculous. 
 
 To take an illustration nearer home, 
 suppose that the group of mountains that 
 abut into the sea in the vicinity of Rio 
 de Janeiro have intervening valleys filled 
 with alluvium, which is really the truth. 
 Suppose that the limits of these mount- 
 ains have never been accurately determ- 
 ined, which is also true. In this case, it 
 is easy to be seen that if the geologist 
 lays down upon the map the alluvial 
 deposits in their true extent, they will 
 here and there encroach upon and over- 
 lap the rugged masses of gneiss, and in 
 places will extend far up the steep preci- 
 pices of the mountain side. To avoid 
 this absurdity the geologist is forced to 
 be as inaccurate as those who have gone 
 before him, and, in general, every error 
 in the geographical map must be con- 
 tinued and apparently sanctioned in the 
 geological chart that is based thereon. 
 
16 
 
 It becomes therefore absolutely neces- 
 sary that the work of the geologist 
 should be preceded by and based upon 
 that of the geographer, and that he 
 should work in conjunction with the lat- 
 ter. In the exploration of a new coun- 
 try the geological party should make its 
 own topography ; and in the United 
 States of North America, where the ex- 
 periment has been most efficiently tried, 
 this is always the case. 
 
 A good geographical map would give, 
 with sufficient completeness, all the lead- 
 ing topographical features of the region 
 explored, delineating with especial care 
 those peculiarities of structure which are 
 the keys to the different formations. It 
 would display the shape and position of 
 bodies of water, and show how the di- 
 rection of a stream is changed and de- 
 termined by the accidents of a broken 
 and displaced stratification, and by other 
 circumstances of its boundaries. If re- 
 strained by canon walls its route would 
 be angular; down a steep gradient it 
 would be direct; and in the level allu- 
 
17 
 
 vium near the sea its track would be 
 tortuous and broken into bayous. This 
 map would distinguish between the 
 rounded slopes of a synclinal valley and 
 the abrupt sides and angular cross sec- 
 tion of an anticlinal cleft; and between 
 the sharp edges of the volcanic rock and 
 the eroded angles of the sand-stone. If 
 there was exposed a great " fault " in the 
 stratification, it would show it at a 
 glance, with its precipitous bluff of ex- 
 posed strata on one side, and, on the 
 other, its gentle declivity of tilted sur- 
 face rock. And, drawn in contour lines, 
 it would reveal, not only the heights of 
 peaks and passes and other vertical dis- 
 tances from plane to plane, but also the 
 various orographic forms, each of which 
 is full of meaning to the geologist. 
 
 ECONOMICAL USES OF THE PROPOSED 
 MAPS. 
 
 Aside from being quite indispensable 
 to a scientific commission, in the various 
 ways that have been mentioned, these 
 maps can be made a graphic supplement 
 
18 
 
 to their report in numerous other par- 
 ticulars, and can be made to embody the 
 stores of practical information which 
 they gather incidentally to their regular 
 work. Upon it they can display the 
 valleys of arable land and the plains 
 adapted to grazing. The forests of tim- 
 ber can be laid down, and, from this 
 drawing, their areas and values can be 
 closely estimated. Advantageous sites 
 for colonies can be noted here. The 
 superficial contents of coal-beds and ore- 
 deposits are given, and not only does a 
 geological chart reveal where the 
 precious and useful minerals are, or may 
 be found, but it also furnishes that nega- 
 tive information, equally valuable to the 
 miner, which defines to him the larger 
 districts in which it is impossible for 
 them to exist, and in which, consequent- 
 ly, it is a waste of effort to search for 
 them; it is here that the science of 
 palaeontology is especially useful. If 
 any portion of the country lies at a great 
 elevation, the altitude limits of the vari- 
 ous forms of vegetable growth may be 
 
19 
 
 traced, and also the limits of the possible 
 culture of grain, coffee, cotton, and the 
 other principal products. In this man- 
 ner the map is made a general statistical 
 report upon the value of the national 
 domain. 
 
 The economical ends served by a work 
 of this nature in the development and 
 settlement of a new country, cannot be 
 too highly esteemed. Every stream of 
 importance is surveyed, in all except 
 those minor branches whose courses can 
 be traced in from the adjacent mountain 
 stations. The frequent tests for altitude 
 along its banks determine the rapidity 
 of its descent, the amount of water- 
 power which it represents, and its value 
 as a motor for machinery, and as an 
 agent in hydraulic mining and diamond- 
 washing. This profile of the bottom of 
 the valley also decides the feasibility of 
 railways or other lines of communication 
 by this route, while the sketches of the 
 adjacent hills show what room there is 
 for such a road, and, in connection with 
 this, the geologist's report will give a 
 
20 
 
 general idea of the rock or other ma- 
 terial with which the engineer will have 
 to contend and work. In the survey of 
 a range of mountains careful readings 
 for altitude are made, not only on the 
 summits of the peaks, but also at the 
 passes, or low depressions in the divide, 
 while the slope of the descent from the 
 summit to the valley will be delineated 
 in contour lines, drawn at such vertical 
 distances as circumstances may require. 
 It must be admitted that these contours 
 will only approximate to their true 
 places, yet their number will be correct, 
 and their positions will be such that they 
 will give with sufficient certainty the 
 various gradients that occur in the as- 
 cent, so that, by counting the meters of 
 rise for every kilometer of horizontal ad- 
 vance, as shown by the scale of the map, 
 the engineer or capitalist, in his distant 
 office, with this sheet before him, can 
 form a very satisfactory idea of the 
 practicability of a proposed railway, and 
 can select the most advantageous route 
 for the preliminary survey. 
 
21 
 
 The meteorological data accumulated 
 in the process of this work are valuable, 
 not only in the determination of the ver- 
 tical elements of the survey, but also as 
 an illustration of the general laws of 
 drought and excessive rainfall. At in- 
 tervals throughout the country, the de- 
 clination of the compass needle will be 
 observed, and will be published for the 
 guidance of land surveyors who may not 
 be proficient in astronomical observation. 
 The positions and supra-marine eleva- 
 tions of all villages, important fazendas, 
 medicinal and thermal springs, ancient 
 ruins or other discoveries in archaeology, 
 supplies of water in a dry country, or of 
 pasture in a barren district, and all other 
 places of interest to the traveler, will 
 be determined. The roads and trails 
 already in existence will be surveyed 
 and mapped, while a leading object of 
 this enterprise will be to find shorter and 
 easier lines of travel. The explorer who 
 opens a new pass through the mountains 
 is a far greater benefactor to mankind 
 than he who discovers and names a con- 
 spicuous peak. 
 
22 
 
 Many of the national surveys of 
 Europe were founded on military 
 necessity, that is, the necessity of having 
 correct information to govern the move- 
 ments of armies in time of war and the 
 incessant transfer of troops in time of 
 peace. In some of these countries their 
 early maps were withheld from the 
 citizen whose taxes had paid for their 
 construction, and to as recent a date as 
 1857, in one or two cases, they were 
 kept secret for use in some contingent 
 war. This argument of military necessi- 
 ty will have but little weight in Brazil, 
 whose rulers, knowing that a country 
 strong in peace will also be strong in 
 war, take the enlightened and advanced 
 policy of encouraging the peaceful pur- 
 suits of life, as the surest basis of nation- 
 al strength. Still it must be acknowl- 
 edged that these maps would be of 
 excellent service in the administration 
 of the affairs of distant provinces, in the 
 transportation of military supplies, and 
 in the garrisoning of frontier posts, 
 although the country is to be congratu- 
 
23 
 
 lated that, for every soldier to whom 
 they would be useful, a hundred immi- 
 grants would be benefited by them. 
 
 THE INTENTS OF THIS ESSAY. 
 
 While entertaining no wish to make 
 this article popular, in the ordinary sense 
 of the word, I shall seek to exclude from 
 it all formulas, equations for computa- 
 tion, and other material, purely mathe- 
 matical, upon which the surveyor bases 
 his work, and as far as possible I shall 
 avoid those technical terms which would 
 be embarrassing to the reader who is not 
 an engineer. The fundamental princi- 
 ples of geographical engineering are the 
 same all the world over, and in every 
 mathematical library there are books of 
 reference which give all the laws and 
 formulas necessary for a work of this 
 kind. Therefore, nothing would be 
 gained by their repetition here. Spe- 
 cialists in geodesy, astronomy, and 
 hypsometry have investigated their vari- 
 ous branches, have published their re- 
 sults, and these, in their purity, are 
 
24 
 
 applicable to any quarter of the globe. 
 One, for instance, has applied the theory 
 of least squares to geodetic computa- 
 tion; another has invented the zenith 
 telescope for latitude observations; and 
 a third has traced the horary curve in 
 the barometric record. All of these dis- 
 coveries fall within the comprehensive 
 department of the geographer, who 
 supplements these studies by utilizing 
 their results in his labors in the Held 
 and office; or, if he is about to write a 
 brief exposition of the subject of geo- 
 graphical surveying, it is his business to 
 describe, in a straightforward manner, 
 the way in which practical application 
 of these truths is made. 
 
 This paper will be, in general, a 
 description of the most approved meth- 
 ods, the economical devices, and the 
 practical results of a successful geo- 
 graphical survey, working in obedience 
 to the directions of the chief of the 
 commission to which it is attached, and 
 covering such areas as may be designated 
 by him as most worthy of geological 
 
25 
 
 and geographical delineation. From 
 time to time, as occasion may offer, and 
 especially at the conclusion, the project 
 will be adapted to the Empire of Brazil, 
 as it is quite impossible to propose a 
 plan of survey which will be applicable 
 to all countries. Although, as has been 
 stated heretofore, the general principles 
 underlying this kind of work are the 
 same wherever physical laws prevail, 
 and the face of the country is wrinkled 
 with mountains and valleys and furrowed 
 with the river-bed and canon, yet there 
 are physical conditions peculiar to every 
 land, as well as circumstances of area, 
 population, and wealth, which require 
 that it should have its own type of geo- 
 graphical survey, and not copy too ex- 
 actly those of any other nation. 
 
 THE BEST TYPE OF SURVEY FOR BRAZIL. 
 
 Considering the circumstances of area, 
 population, and wealth it is evident that 
 the national surveys of Brazil should be 
 " geographical " in a very liberal sense of 
 the word; that is, that they should be 
 
26 
 
 comprehensive in their scope, rapid in 
 their execution, and sufficiently accurate 
 without being too punctilious and too 
 excessively minute. It is only within 
 the present generation of engineers, and 
 particularly in the western hemisphere, 
 that there has grown up an important 
 distinction between topographical and 
 geographical surveying, and even now it 
 is hard to define the limit between them. 
 The latter is an outgrowth and extension 
 of the former and an adaptation of it to 
 the mapping of large domains at the 
 least possible expenditure of money and 
 time. 
 
 DISTINCTION BETWEEN THE GEOGRAPHER 
 AND TOPOGRAPHER. 
 
 As one of the many points of differ- 
 ence between the geographer and the 
 ordinary topographer, we may mention 
 that the former, in his travels and sur- 
 veys, accommodates himself to the roads, 
 trails, or other open and easy routes that 
 already exist, and it is but seldom that 
 he finds himself obliged to make a path 
 
27 
 
 for his survey to follow. In the ascent 
 of some mountains it may be necessary 
 to cut a road, and in the measurement of 
 the base line for his triangulation he may 
 have to prepare the ground before him, 
 but these are almost the only instances. 
 The topographer, however, in tracing a 
 contour line around the side of a mount- 
 ain, or in making parallel profile sec- 
 tions of the land, is not allowed to devi- 
 ate therefrom, and if the way is not 
 clear, he must wait, perhaps at great loss 
 of time, until his assistants have removed 
 the brushwood, or whatever other obsta- 
 cles may intervene ; in this respect he 
 resembles the railway engineer. Again, 
 in the selection of the stations for his 
 triangulation, the geographer makes the 
 best possible use of the mountains 
 of a country as he finds them, generally 
 accepting them as they occur; though 
 their arrangement, it may be confessed 
 here, is not always in such well-condi- 
 tioned triangles as he would desire. The 
 topographer, on the contrary, delays his 
 work by the establishment of arbitrary 
 
28 
 
 stations where natural points are lacking, 
 and by the erection of artificial signals 
 on those mountain tops which the former 
 observes without such aid. 
 
 In the end it will be found that the 
 topographer's notes are so numerous and 
 in such detail that it may require several 
 centimetres of map to represent one kilo- 
 metre of the earth's surface; while to 
 the geographer, who is satisfied with the 
 general shape of a mountain- spur, the 
 approximate width of a valley, and the 
 more important bends of a stream, a 
 scale of one centimetre to several kilo- 
 metres may be sufficiently large for the 
 portrayal of the earth as he finds it. But 
 it will also be observed, by an economi- 
 cal government, that while the topog- 
 rapher consumes several years in the 
 survey of a thousand square kilometres, 
 the geographer will obtain a very satis- 
 factory knowledge of thousands of 
 kilometres in one year. And, in general, 
 the superior accuracy, or rather detail, of 
 the former, is purchased at an expendi- 
 ture of time and money so great that 
 
29 
 
 only the older and wealthier nations 
 can afford the investment; while I hope 
 to demonstrate that the geographer's re- 
 sults are sufficiently complete for the 
 needs of Brazil. 
 
 THE GEOGRAPHER'S PROFESSION. 
 
 The geographer's work is a peculiar 
 and difficult one, and one for which his 
 ideas must become enlarged by a special 
 training. This is a branch of our pro- 
 fession for which no training-school pre- 
 pares its student and no text-book yet 
 published can instruct him. This is a 
 field in which the experienced topog- 
 raphical engineer, fresh from his labors 
 on park and landscape, or on the detailed 
 surveys of thickly-populated Europe, 
 finds himself unhandy and incompetent, 
 for much of the experience and tradition 
 that he brings with him is an incubus 
 to retard him. To become efficient in 
 this new service he must forget much of 
 the rule and routine that he has learned, 
 and accustom himself to taking broad 
 and bird's-eye views of the country. 
 
30 
 
 Strange as it may sound, he must 
 make it a matter of duty and pride to 
 overlook and neglect much that is near 
 at hand, and remember that, although a 
 mole-hill at a distance of a few feet sub- 
 tends a greater visual angle than a 
 mountain as many miles away, yet it is 
 the mountain, and not the mole-hill, that 
 deserves delineation upon his map. 
 Hitherto he has been local and narrow in 
 his range; he must now become geodetic, 
 else he will accumulate a mass of minu- 
 tiae, whose representation would be in- 
 finitesimal on a map of the proposed 
 scale, and which is hence but an incum- 
 brance to his books, and even worse than 
 cumbersome, inasmuch as its presence 
 excludes other and more valuable data. 
 In short, the topographer considers the 
 earth minutely, and with a microcosmic 
 view, but the geographer is a man of no 
 such narrow horizon, and trains himself 
 to look upon it as a macrocosm, or great 
 world. 
 
31 
 
 THE INSTRUMENTS USED. 
 
 Of scarcely secondary importance to 
 the men of a geographical corps, are the 
 instruments with which they shall work. 
 The tools which have been devised for the 
 ordinary surveys of land and landscape 
 must be left at home with the slow and 
 tedious methods from which they cannot 
 be divorced. In a work of geographical 
 extent the spirit-level, chain, and tally- 
 pins are out of place, and whosoever, 
 making accuracy his plea, attempts to in- 
 troduce them there, will find his own 
 ends defeated by them. Once upon a 
 time, for instance, an engineer was in- 
 trusted with the survey of a large tract 
 of new country. A certain sum of 
 money and a limited period of time were 
 given to him, a stated area of territory 
 was assigned to him, and in return the 
 authorities expected of him the most ac- 
 curate and impartially complete map 
 that his means would allow. 
 
 The time and resources granted him 
 would permit him to touch the country 
 but lightly and by swift marches, but, as 
 
32 
 
 this was intended to be only a reconnois- 
 sance, nothing more was expected of him 
 than to trace the conformation of the 
 land in a general way. He was an 
 honest and conscientious engineer, and 
 so great was his zeal for accuracy, or 
 nicety rather, that he was scrupulous to 
 a fault. He abused the maxim which 
 says that whatever is worth doing at all 
 is worth doing well. For determining 
 the altitude of stations along the route 
 he used the spirit-level, and their inter- 
 mediate distances were found by stadia 
 measurements, which system, though 
 considered incautiously rapid in topogra- 
 phy, is too laggardly slow for the or- 
 dinary purposes of geography. In this 
 manner he crossed his territory with a 
 few lines of march whose profiles were 
 as trustworthy as those of a railway sur- 
 vey, and far more accurate than the pub- 
 lic interest demanded, while between 
 them there were large areas untouched 
 and unseen, and of these the public, 
 whose agent he was, had commissioned 
 him to obtain information. The failing 
 
33 
 
 of this engineer was a common one; he 
 neglected to distribute his resources 
 fairly and impartially, and while half of 
 his map is reliable the other half is con- 
 jectural. 
 
 It would be too long a task to de- 
 scribe in detail all the instruments used 
 in geographical work, or to rehearse all 
 of the devices employed in its prosecu- 
 tion; however, the most necessary and 
 novel features will be noticed here. At 
 the basis of the work is the transit, or 
 theodolite, which, with compass-needle 
 attached, is the engineer's constant com- 
 panion, without which his occupation is 
 gone, no matter in what field his labor 
 may lie. As an appurtenance to this, 
 not the chain nor the stadia, but the 
 odometer wheel, has become the recog- 
 nized means of linear mensuration in the 
 survey of streams and the determination 
 of those distances of route and detour 
 which are so useful in filling in a trian- 
 gulation chart. Instead of the level, the 
 cistern barometer gives the heights of 
 mountains, mines, passes, camps, vil- 
 
34 
 
 lages, and other important positions, 
 while the aneroid barometer, portable as 
 a watch, and as easily read, will tell the 
 altitude of minor points and give with 
 sufficient closeness the data from which 
 may be plotted the profile of the odome- 
 ter's itinerancy. 
 
 THE PERSONNEL OF A GEOGRAPHICAL 
 CORPS. 
 
 These are the three classes of instru- 
 ments that are indispensable; the purely 
 geographical party required to use them 
 need consist of but three men, the en- 
 gineer, the meteorologist, and the 
 odometer recorder. To this corps it 
 may be deemed advisable to add a fourth 
 member to act as an assistant to the en- 
 gineer, and, by personal obervation and 
 experience acquire that facility in the 
 practice of his profession which will fit 
 him, in the course of a brief period of 
 training, for the responsible position 
 above him. Such a person should al- 
 ready have the theoretical education of 
 an engineer, and some skill in drawing. 
 
35 
 
 If it is not practicable to make this ad- 
 dition to the corps, it is well to choose 
 as an odometer recorder one who pos- 
 sesses the acquirements stated above, 
 and to consider that position, whose 
 appertaining duties are light, as prepar- 
 atory to the grade of engineer. As for 
 the meteorologist, his is an intricate 
 science which cannot be studied too 
 thoroughly, and barometric hypsometry 
 should be regarded as a profession quite 
 distinct from the engineer's, although 
 necessarily subordinate to it. 
 
 The various duties involved in the 
 measurement of the base-line, at the 
 opening of the season, may demand the 
 services of a larger body of men than 
 this, but, once in the field, any addition 
 to the above number, except as muleteers 
 and servants, will be superfluous, as far 
 as the geographical work is concerned. 
 One surveyor can see as far as two, and 
 one man is able to take note of all of the 
 country visible from his route of travel. 
 No axemen are needed, for if there is a 
 tree in the way, the line must yield to 
 
36 
 
 the tree; the resultant error will be trif- 
 ling and will not be apparent in a map 
 which represents several kilometres of 
 territory on one centimetre of space. 
 Neither is there any necessity for rod- 
 men, with rods of two targets for mi- 
 crometer measurements or one target for 
 levels, who would retard the corps by 
 the long delays consequent upon their 
 transfer from the stations in the rear to 
 those in advance. This party travels as 
 a unit, moving as fast as its animals can 
 walk, and is never broken, a considera- 
 tion which is of value in a country of 
 hostile people. 
 
 Of course the scope of the work may 
 require the service of a great number of 
 professional men, but its best progress 
 demands that they should be divided 
 into corps of the above size, which shall 
 work in concord and under one general 
 liead. This director will assign to each 
 party its territory for the season, and 
 tupon the borders of these areas, the va- 
 rious engineers will make rendezvous 
 from time to time, as circumstances may 
 
37 
 
 admit, with their neighbors of the ad- 
 joining fields, for the purpose of 
 reorganization, exchange and issue of 
 material, and especially for the compari- 
 son of sketches and geodetic data, so as 
 to insure the proper union of their sev- 
 eral schemes of triangulation. In order 
 to make the different systems of trian- 
 gles interlock in one grand plan, the 
 observer will frequently be obliged to 
 read angles to stations which lie in an 
 adjacent district, and which will be oc- 
 cupied by his co-laborers for the purpose 
 of reciprocal observations. It is there- 
 fore necessary that they should meet in 
 occasional conference for the mutual 
 identification of those stations. 
 
 THE STATIONS OF SURVEY. 
 
 Guided by these thoughts, let us sup- 
 pose that we have completed our organi- 
 zation for a season in the field, and that 
 we are now on the ground ready for 
 work, at the place selected as the initial 
 point of the survey. As with all surveys, 
 this one will be executed from stations, 
 
38 
 
 meaning thereby any points at which a 
 tripod is planted and an instrument ad- 
 justed, angles are read and sketches may 
 be made. Of these we shall occupy 
 four orders, of which, in importance, and 
 consequently in accuracy, the astronomi- 
 cal is first. Then comes the geodetic, or 
 triangulation station; the topographical 
 station, so designated for the sake of con- 
 venience; and, finally, the odometric, or 
 route station. In addition to the ends 
 which they are especially intended to 
 serve, each of these will be a meteorologi- 
 cal station as well. These five classes, 
 with the incidental details pertinent to 
 them, will now be considered in the 
 order named. 
 
 THE ASTRONOMICAL STATION. 
 
 Since the positions determined by tri- 
 angulation, or other system of survey in 
 which terrestrial objects alone are con- 
 sidered, are only relative to each other 
 and to the first station occupied, it is 
 evident that a map may be completed, 
 which, in itself, will have all of the ex- 
 
39 
 
 actness of perfect truth, but whose place 
 on a projected surface of the globe will 
 still be uncertain. A map of a conti- 
 nent may be made, and this may be of 
 great use in the guidance of travelers 
 across the continent, and for the local 
 information of its inhabitants, but still 
 it does not play its proper part in the 
 grand plan of this earth's geography, and 
 define the situation of this land relative 
 to the other continents of the earth, 
 until it is bound into place by the meri- 
 dians and parallels, which are the warp 
 and woof of the structure of geography. 
 Therefore, in order to adjust our map, 
 when made, into its true place, we must 
 have the absolute determination of one 
 or more of its positions. 
 
 Now there is but one way of finding 
 the absolute position of an object on the 
 earth, and that is by going beyond the 
 earth, consulting the stars, and ascer- 
 taining its place relative to them. Hav- 
 ing two triangulation stations thus 
 located, the whole chart becomes ad- 
 justed to its place. Or, having the lati- 
 
40 
 
 tude and longitude of our initial point 
 and the astronomical azimuth of a side 
 of a triangle leading from this origin, the 
 former serves to pin the plot to the pro- 
 jected map, and the latter is instrument- 
 al in orienting it into the area to which 
 it belongs. 
 
 POSITION OF THE ASTRONOMICAL STATION. 
 
 For every base-line measured and 
 developed there should be an astronomi- 
 cal station occupied, and as a matter of 
 convenience and co-operation they should 
 be in the same vicinity, although it is 
 not necessary that the station should be 
 directly over either end of the base. 
 Indeed, owing to great exposure to 
 the wind, or to inconvenience of ap- 
 proach, it may not be found practicable 
 to locate the astronomical station at any 
 of the points of the triangulation system, 
 or, to secure proximity to the telegraph, 
 whose office may be hidden in the heart 
 of a town, or the bottom of a valley, it 
 may be so secluded as to be quite in- 
 visible from those points. 
 
41 
 
 If so, it may be easily connected with 
 them by running a careful linear survey 
 from the astronomical station to the 
 nearest geodetic station. If, owing to 
 the disadvantageous nature of the 
 ground, or other obstacles in the way, it 
 may be impossible to measure the dis- 
 tance directly between these two points, 
 the engineer can connect them by a 
 broken line, reading at the astronomical 
 station the angle between the meridian 
 mark, already fixed by the astronomer, 
 and the direction of his first course, and 
 afterwards referring the direction of each 
 measured section of his traverse to that 
 immediately preceding. From these re- 
 sults he calculates, in meters, the differ- 
 ence of latitude and departure between 
 the two points, and then, transforming 
 the meters into seconds of arc, he com- 
 putes their difference of latitude and 
 longitude. 
 
 NUMBER OF ASTRONOMICAL STATIONS. 
 
 For a commission of moderate size, in- 
 cluding one, two, or three engineering 
 
42 
 
 corps, the triangular development of one 
 base will cover as much territory as can 
 be surveyed by them in a single cam- 
 paign, and therefore one astronomical 
 position a season is all that this survey 
 would require during the first year or 
 two of its organization. A series of ob- 
 servations extending through a couple of 
 weeks, in favorable weather, or through 
 a month at the farthest, will determine 
 the geographical co-ordinates of our 
 point of departure. These can be made 
 by the astronomer while the engineers 
 are measuring the base-line and develop- 
 ing the same, the director is perfecting 
 his arrangements, and the purveyors are 
 preparing and distributing the supplies, 
 instruments, and all of those numerous 
 articles of equipment which are the fur- 
 niture of a scientific field season. At 
 the same time, the meteorologist, by a 
 set of hourly barometric and psychro- 
 metric readings accumulates data whose 
 digest will give the vertical co-ordinate 
 of this place with the possible error of a 
 very few feet, and this completes the de- 
 
43 
 
 termination of its position with reference 
 to a system of co-ordinates whose origin 
 is at the level of the sea at the point 
 where the first meridian crosses the 
 equator. 
 
 For so short an annual term of service 
 it might not be advisable to keep an as- 
 tronomer constantly in commission, nor, 
 at present, might it be well to go to the 
 expense of the costly and elaborate in- 
 struments requisite for the best astro- 
 nomical observation, provided that the 
 co-operation of the Imperial Observatory 
 could be secured and an astronomer 
 could be detailed from there for that 
 purpose. In addition to the gratification 
 to be derived from the warranted excel- 
 lence of the results which would be fur- 
 nished by the skilled assistants of that 
 institution, this cooperation would be a 
 matter of economy to the Government? 
 and also, what is especially to be desired 
 between any two scientific bodies, a 
 means of friendly relation and inter- 
 change of information which would cer- 
 tainly prove of mutual value. 
 
44 
 
 ASTRONOMICAL METHODS. 
 
 For the determination of the latitude 
 of our point of outfit the zenith tele- 
 scope would be used; while the longitude 
 would be found by the telegraphic ex- 
 change of time signals, a method which 
 has lately been so successfully introduced 
 by the Astronomical Commission. The 
 present wide-spread extension of lines 
 of electric telegraph within the borders 
 of Brazil is especially favorable for a 
 survey of this nature, whose longitudes 
 would be based upon telegraphic commu- 
 nication with the national observatory. 
 The lines along the coast afford a gen- 
 eral connection with the northern and 
 southern provinces of the Empire, while, 
 by the numerous branches which accom- 
 pany the railways into the interior, points 
 which lie far to the inland could be re- 
 ferred to the meridian of Eio de Janeiro, 
 which, in its turn, has communication 
 by cable with the observatories of Eu- 
 rope. 
 
 Thus it will be seen that the engineer 
 need not be confined to any unfavorable 
 
45 
 
 locality in the selection of the ground 
 for his base line, nor need the chief of 
 the commission be restricted in his choice 
 of areas to be surveyed. From the 
 railways either constructed or contem- 
 plated it would probably be possible to 
 reach any of the settled portions of 
 Brazil without seriously overtasking the 
 accuracy of the triangulation, and, if it 
 were required to carry the survey still 
 farther, longitudes determined by the 
 method of moon-culminations would be 
 sufficiently exact for the less important 
 regions beyond. 
 
 ORIGIN OF THE TKIANGULATION. 
 
 An inland survey, based upon trigono- 
 metrical methods, progresses most suc- 
 cessfully from an initial source concen- 
 trically outwards. The most fortunate 
 location for the initial line is in the cen- 
 ter of some broad valley or intermontane 
 plateau, whose level expanse offers fair 
 ground for the measurement of the base, 
 and whose open field is favorable for the 
 gradual and symmetrical development 
 
46 
 
 of the same until it shall reach the lines 
 of the remotest triangles, in which it be- 
 comes a metrical standard for finding 
 their length. In an extensive survey, 
 lasting for years and covering broad ter- 
 ritory, a series of bases are indispensa- 
 ble. These act as checks upon each 
 other, and the net-works of triangles 
 emanating therefrom are dovetailed into 
 each other, and, in their adjustment to 
 fit, each to each, what little error they 
 may have accumulated is reduced to a 
 minimum. 
 
 For instance, on each side of a range 
 of mountains there is an open basin. In 
 each of these an astronomical station is 
 established and a base is measured. On 
 the comb of the intervening sierra, one- 
 hundred miles apart, stand two pre-emi- 
 nent mountain peaks. The latitude and 
 longitude of each of these, with the 
 distance between them, is determined 
 from the two origins independently. 
 They check each other, verifying, in 
 their agreement, the accuracy of both 
 systems, or showing by their disagree- 
 
ment that there is an error somewhere^ 
 and the long line, drawn by the labor- 
 saving appliances of trigonometry, 
 through a hundred kilometres of aerial 
 route, a thousand meters above the val- 
 leys and chasms which it spans, is now 
 ready to be used as a new base in the 
 primary triangulation. 
 
 It may be difficult to find a favorable 
 locality for the source of a triangulation 
 immediately upon the sea-shore, as there, 
 unless there are islands in the adjacent 
 ocean, one side of the field is quite open 
 and affords no stations to be occupied. 
 If it were not for this objection it would 
 seem best to measure a succession of 
 bases along the coast of Brazil, and 
 thence develop them westward. A tri- 
 angulation is always most accurate in 
 the vicinity of its origin, and as it be- 
 comes more and more remote from its 
 initial ground it becomes less reliable, 
 owing not only to the continued multi- 
 plication of the original error of the 
 base, but also to the accumulation of in- 
 
48 
 
 accuracy and mistake * from other 
 sources. Now, the population of Brazil 
 is thickest along the sea, and thence, into 
 the interior, at least in many provinces, 
 it gradually thins out. The importance 
 of the country and the necessity of 
 having truthful maps correspond to the 
 density of the population. Add to this 
 the fact that the most interesting geology 
 of Brazil is on the sea-board, and, 
 furthermore, the important considera- 
 tion that the coast of a country, for pur- 
 poses of navigation, demands a more 
 rigorous geographical determination than 
 the interior, and it will be seen that the 
 triangulation upon which this delineation 
 depends should not originate too far 
 away. In a general survey of Brazil, 
 therefore, the first series of astronomical 
 stations and bases should be established, 
 if not upon the sea-shore itself, at least 
 
 * There is an important difference in the meanings of 
 the terms "mistake" and "inaccuracy." If a man, 
 carelessly reading a vernier whose indication is 38' 45", 
 calls it 39' 45", he is guilty of a mistake. If from parallax 
 or some defect in vision or judgment, he calls it 38' 40", 
 he is inaccurate. Mistakes are due to want of care ; in- 
 accuracy, to want of precision. 
 
49 
 
 upon the first plateaus that are encount- 
 ered between the mountains of the in- 
 land. 
 
 POSITION OF THE BASE-LINE. 
 
 In its direction and position the base- 
 line should bear judicious relations with 
 certain hills, knolls, corners of terraces, 
 or other prominent elevations in the vi- 
 cinity, which may be selected as sites 
 for the stations to be occupied in its de- 
 velopment. The plans for its expansion, 
 matured before its position is selected, 
 should include two prominent peaks in 
 the horizon, remote from the origin and 
 from each other, whose distance apart 
 this measured length will be instrumental 
 in determining. The ground upon which 
 it is to be measured should be as smooth 
 and bare as possible. It should be free 
 from brush, tall grass, or other vegeta- 
 tion, and also from hillocks and gulches, 
 which are serious impediments to a work 
 of delicate mensuration. Whether it is 
 level or not, provided its slope be grad- 
 ual and even, is of secondary importance, 
 
50 
 
 as corrections may be easily applied to 
 cancel the effect of its gradients. 
 
 LENGTH OP THE BASE. 
 
 The length of the base may vary from 
 two to ten kilometres. In the opinion 
 of many engineers more than four kilo- 
 metres of measured length is zeal gone 
 astray, for the advantages of accuracy 
 gained by such excess would be obtained 
 more easily by devoting the extra time 
 to a more elaborate trigonometrical de- 
 velopment. No arbitrary rule can be 
 applied here, however. All must depend 
 upon the judgment of the engineer, who 
 will consider his surroundings, and if 
 they are favorable for a slow and pro- 
 gressive development, a short base will 
 answer; but if he is obliged to carry his 
 triangulation from the base stations to 
 the distant mountains by an abrupt 
 transition, a longer one will be required, 
 to prevent too great acuteness in those 
 remote angles. 
 
 INSTRUMENT OF MEASUREMENT. 
 
 Since rapidity, as well as accuracy, is 
 
51 
 
 an object, we use a steel tape, ten or fif- 
 teen metres in length, as a measuring 
 unit. In the swivel at one end of this 
 there is a thermometer which tells the 
 heat to which the tape is exposed at 
 any time; there is also a micrometer 
 screw, by which it can be lengthened or 
 shortened in compensation for any possi- 
 ble change of temperature; and there is 
 a dynamometer attached to govern the 
 tension applied, which should amount to 
 three or four kilograms, being at every 
 application the same as it was in the orig- 
 inal test for length, to which the tape 
 was subjected. 
 
 Thus, as this apparatus is applied, in 
 the process of measurement, it is under 
 a constant strain, which preserves it 
 from the error from sagging, to which 
 all flexible cords are liable, and its length 
 is always corrected to meet the contrac- 
 tion and expansion which the metal is 
 constantly undergoing as the tempera- 
 ture varies. Should this micrometer be 
 but incompletely graduated, so, for in- 
 stance, as to be adjustable only for every 
 
52 
 
 five or ten degrees of thermometric 
 change, or should it even be wanting 
 entirely, very good results can still be 
 obtained with the steel tape by reading 
 the thermometer at every application, 
 and, in the final computations for length, 
 making the necessary temperature cor- 
 rections. Used carefully and with intel- 
 ligence, this instrument is one of the 
 most valuable adjuncts of the geograph- 
 ical survey, and, in the hands of consci- 
 entious and interested observers, it is 
 capable of results that are very near the 
 exact truth; the error ought not to ex- 
 ceed one centimeter for every kilometer 
 of measured distance. 
 
 METHOD OF MEASUREMENT. 
 
 The mensuration may be made on 
 wooden plugs, with smooth, flat upper 
 surfaces. These are driven firmly into 
 the ground along the alignment at inter- 
 vals equal to the length of the tape, and 
 should be allowed to project above the 
 earth sufficiently to permit this cord to 
 swing clear of all inequalities in the 
 
53 
 
 surface, or other obstacles between the 
 two stations. Or, instead of these, little 
 stools of plank may be used; these 
 should have short, pointed iron legs, to 
 be forced into the ground, so as to hold 
 the wooden block firmly in position. 
 
 When all things are ready a distance 
 of one or two kilometers can be meas- 
 ured in one day. But, on account of any 
 possible inefficiency in the compensation 
 for temperature, and also because even 
 the best assistants are liable to a per- 
 sonal equation in sticking the marking 
 pin, some invariably inserting it to the 
 right of perpendicular, and others the 
 reverse, it is well that it should be 
 measured several times, and by different 
 persons, and a mean of the results taken. 
 Then it should be leveled, in order that 
 each tape-length may be corrected for 
 its gradient, which is done by a simple 
 trigonometric process, and finally it is 
 reduced to its corresponding concentric 
 arc at the level of the sea, when it is 
 ready for use in the system of triangu- 
 lation. 
 
54 
 
 THE ASTRONOMICAL BASE. 
 
 The method of base-measurement by 
 astronomical observation is sometimes 
 resorted to in geographical surveying, 
 but this process will be noticed here 
 only sufficiently to point out the serious 
 objections that there are to its use. 
 Having the latitudes of the two ends of 
 the base and the azimuth of one from 
 the other, it is a simple matter to com- 
 pute their distance apart. This seems to 
 afford an economy of labor, over the 
 former method, that involves the determ- 
 ination of the latitude and longitude of 
 the first station, the azimuth of the i ase- 
 line, and its length by direct measure- 
 ment; this one requires the determina- 
 tion of the latitude and longitude of the 
 first station, the azimuth of the base- 
 line, and the latitude of the second 
 station. The latter is apparently the 
 simpler and shorter task, and since both 
 methods are based upon astronomical 
 observation they would appear to be 
 equally reliable. But they are not. 
 
 Experience has long since taught the 
 
55 
 
 scientific world that the probable error 
 of any ordinary astronomical result is 
 several meters at the very least, and that 
 it is not safe to put absolute reliance in 
 those reports which give a latitude down 
 to a very small fraction of a second. 
 Now, in that system of triangulation 
 whose position is based upon the astro- 
 nomical determination of one point only, 
 an error of a few meters in the latitude 
 of that point will not do material injury. 
 It will simply displace the entire trian- 
 gulation scheme, as a whole, so much to 
 the north or the south, while, since the 
 length of the base, or measuring unit of 
 the proportions of * this scheme, was 
 accurately found, there will be no error 
 in these proportions. But, in the astro- 
 nomical measurement of a base, suppose 
 its two terminal points to be in their 
 most favorable position, that is, on the 
 same meridian. The latitude determina- 
 tion of the southern station places it 
 several meters too far to the south of 
 its true position ; that of the other, per- 
 haps, makes it an equal distance too far 
 
56 
 
 to the north. Hence it follows that 
 there is an error in the length of the 
 base equal to the sum of the two astro- 
 nomical errors, and this, in the develop- 
 ment, is multiplied almost indefinitely, 
 being repeated in any side of triangle as 
 often as the length of the base is con- 
 tained in the length of that line. This 
 is supposing the base to be an arc of 
 meridian; the greater its divergence 
 from the meridian, the more seriously, 
 for obvious reasons, will an error in the 
 astronomical determination affect the 
 length of the base. An astronomical 
 base-line, therefore, should only be used 
 when there are difficulties which make a 
 direct measurement impossible. 
 
 THE DEVELOPMENT OF THE BASE. 
 
 In the early stages of the develop- 
 ment, occurring, perhaps, on the level 
 surface of the plain, it will be found 
 necessary to use artificial signals. Great 
 tripods of frame-work, ten or fifteen 
 meters high, are constructed, leaving 
 ample space within for the observer and 
 
5? 
 
 his instrument. In erecting these, care 
 must be taken that none of the legs of 
 the tripod interfere with the view to- 
 wards any of the proposed triangulation 
 stations. Each of the signals terminates 
 at the summit with a flag-staff, to which 
 voluminous folds of white muslin are 
 nailed, while the body of the steeple is 
 wrapped with the same material and 
 decked with loose tatters and streamers, 
 which, by their ceaseless flutter in the 
 wind, offer occasionally a surface from 
 which the light is reflected to the eye of 
 the distant observer. The same purpose 
 may sometimes be better served by the 
 use of glittering sheets of tin, or by a 
 cone of the same material. These meth- 
 ods all have one very great advantage 
 over the more accurate heliotrope, that 
 is, they are always in position, and ready 
 for observations to be directed upon 
 them at any time. The use of the re- 
 fleeting mirror, however, unless there are 
 a number of heliotropes in the field, in- 
 volves the loss of much time, as the in- 
 strument is transferred from one to an- 
 other of the neighboring stations. 
 
58 
 
 The development stations should be 
 erected in conspicuous places, on high 
 ground or the salient angles of bluffs, 
 that the observer may know where to 
 direct his instrument in searching for 
 them, as it is extremely difficult to pick 
 out the faint glint of a few yards of 
 muslin on the broad light surface of a re- 
 mote plain. As the development con- 
 tinues and climbs from the foot-hills into 
 the high and peaked mountains, these 
 natural points are sharp and distinct 
 enough, being projected against the sky 
 beyond, and the labor of station-building 
 ceases, except in cases that are very un- 
 favorable. 
 
 True, this triangulation by natural 
 points is not so precise as it is in some 
 geodetic surveys, and especially in the 
 surveys of coasts, where even the phase 
 of the conical signal is considered too 
 important an element of error to be neg- 
 lected; nor is it wise that it should be so, 
 for a fault of a few meters in the posi- 
 tion of a mountain-top in the remote in- 
 terior of Brazil, located by this plan, is 
 
59 
 
 at present of no practical consequence, 
 and the nation cannot afford to purchase 
 an accuracy imperceptibly greater than 
 this by an expenditure that would many 
 times exceed the cost of this method of 
 survey. Considering a mountain as a 
 land-mark by which travelers are assured 
 of their place and are guided as they go, 
 it will be seen that, to men who travel 
 by land, a small fraction of a kilometer, 
 in latitude and longitude, is a deviation 
 which they cannot notice; to the voya- 
 ger at sea, however, the exact site of the 
 sunken rock which he shuns should be 
 known to him, in order that he may cer- 
 tainly avoid it. This is why the coast 
 survey, in most countries, precedes that 
 of the inland in the degree of accuracy 
 which characterizes it, as well as in the 
 amount of expense which attends it. 
 
 TRIANGULATION BY NATURAL POINTS. 
 
 It must not be inferred, however, that 
 the use of natural points in triangulation 
 necessarily involves a serious accumula- 
 tion of error. In general, the engineer, 
 
60 
 
 looking from one station to the next, can 
 readily cover, with the thickness of the 
 spider-line of his instrument, the highest 
 ground of the distant mountain, and 
 that point is selected as a correlative 
 station, because that is the spot which 
 can be most easily identified, either from 
 a distance, or upon the ground itself. 
 If this place is uncertain, as where there 
 are a number of pinnacles of equal alti- 
 tude, or not sufficiently prominent, as in 
 a plateau summit, some peculiar object, 
 as a solitary tree, or an isolated boulder, 
 should be chosen as a center upon which 
 to sight. If the profile of the mountain 
 has but little curvature, its culminating 
 point is usually determined by a pile of 
 rock, a clump of vegetation, or other 
 body upon its crest, which, although it 
 may not be distinctly visible from a dis- 
 tance, yet has the effect of increasing 
 the apparent altitude at that precise 
 locality. In the same way the useful- 
 ness of a monument of rock, which a 
 party should always leave behind it 
 upon a mountain, as a signal to look 
 
61 
 
 back upon, does not terminate at that 
 distance at which it becomes apparently 
 invisible. The eye will still be im- 
 pressed with the superior elevation of 
 the place where it stands. 
 
 If the round top of a mountain is per- 
 fectly bare, and offers none of these ac- 
 cidental aids to the observer, it is well 
 for him, in reading his first angle to it, to 
 keep the horizontal cross-wire tangent to 
 the surface, while he makes a careful 
 and deliberate search for its highest 
 point. Having decided upon this, he 
 brings the vertical wire upon it, and then 
 follows down the thread with his eye 
 until he finds it bisecting some well- 
 defined body in the field before him, 
 such as a corner of rock or the trunk of 
 a tree, and, in his repetitions of the 
 angle he fixes the vertical wire always 
 upon this object, while keeping the hori- 
 zontal thread tangent to the surface. In 
 this manner he secures to each of the 
 following readings the advantages of the 
 prolonged study given to the first, and 
 not only are his results more accurate, 
 
62 
 
 as a whole, but they also agree better 
 among themselves, which is always a 
 source of gratification to the engineer. 
 
 THE MOUNTAINS OF BEAZIL. 
 
 In those lands which are remote from 
 the equator the summits of the high 
 mountains, of an altitude of three thou- 
 sand metres or more, are above all vege- 
 tation and in the belt of perpetual snow, 
 and their occupation is a work of great 
 privation and exposure. The mountains 
 of Brazil are exempt from that disad- 
 vantage to triangulation, as the climate 
 is never rigorously cold here, and the 
 elevation of the highest land is less than 
 three thousand metres. The only ob- 
 stacles to be feared here are the oppo- 
 site disadvantages of too much vegeta- 
 tion, either hiding the tops of the peaks, 
 or embarrassing the ascent to them, and 
 too little height, whose result is liable to 
 be a system of round, well-preserved, 
 and insufficiently pointed mountains. 
 But if those in the vicinity of Rio de 
 Janeiro are to be accepted as a criterion, 
 
63 
 
 nothing more could be desired in the 
 way of natural aids to triangulation. 
 
 PROGRESS OF THE TRIANGULATIOX. 
 
 In some cases it may be absolutely 
 necessary to send a party in advance to 
 erect monuments of stone, or signals of 
 timber upon proposed stations which are 
 at the same time important and unfavor- 
 able for observations ; or, should the 
 mountain be covered with forest, it may 
 be necessary to send axemen to clear 
 away all but the largest and most cen- 
 tral of these trees. Such action, how- 
 ever, causes a vexatious delay on the 
 part of the engineer, and is contrary to 
 the fundamental principles of this 
 method of survey, whose work should 
 be a steady and unretarded progress, 
 and should be reconnoissance and com- 
 pletion in itself. 
 
 From the top of his first high mountain 
 station the engineer sees his allotted 
 territory spread out before him, and he 
 immediately begins to lay his plans for 
 the coming season. He selects two dis- 
 
64 
 
 tant peaks, which, with his present 
 station, will form a grand triangle. Be- 
 yond these, far in the distance, there is 
 yet another, and these four constitute a 
 great quadrilateral, the lengths of whose 
 diagonals may each l>e determined by 
 two independent sets of observations, 
 checking each other. In like manner 
 he makes the circuit of the horizon, util- 
 izing, as best he can, the peaks which 
 rise around him. 
 
 Although, owing to the many obsta- 
 cles and unforeseen difficulties which are 
 experienced in traveling through an un- 
 known country, he may be compelled to 
 modify and alter his first plans very 
 often, yet as soon as he abandons one 
 feature of his scheme he immediately 
 adopts a substitute to take its place. 
 To be provided for such an emergency, 
 if a distant peak, as,f or instance,one of the 
 sharp pinnacles of the Organ Mountains, 
 should appear impossible of ascent, he 
 will select another in the same vicinity, 
 and consider that as an alternate to the 
 first, reading angles to it and treating it 
 
65 
 
 in all respects as a regular station as 
 long as such a reserve may seem neces- 
 sary. 
 
 In proceeding from one mountain to 
 the next he surveys all of the interme- 
 diate country, his course being governed 
 by the advantages and obstacles whieh 
 present themselves from day to day. 
 His route should never be an arbitrary 
 one, determined at a distance and weeks 
 beforehand, but he should be free to act 
 upon the spur of the moment, following 
 a stream to its source here and stuvey- 
 ing a lake there, according as these geo- 
 graphical features may be encountered. 
 If these features are depicted on maps 
 already made, then there is no need of a 
 second survey of the country; if they 
 are not, he is not likely to know of their 
 existence until he finds them. 
 
 EQUIPMENT OF THE PARTY. 
 
 Since the terminus of a day's survey 
 cannot always be advantageously decided 
 upon, even in the morning on which it is 
 begun, it is especially desirable that th 
 
66 
 
 party may carry with it its own equipage 
 and supplies, so as to be prepared to 
 camp anywhere that night may over- 
 take it. As it is a part of the policy of 
 geographical work that the engineer 
 should never follow the same route 
 twice, a survey carried on by daily ex- 
 cursions from fazendas, settlements, or 
 other fixed points of supply, returning 
 to this base by the same road in the 
 afternoon, would cost a great waste of 
 time and energy. The necessary outfit 
 of a scientific corps, consisting of instru- 
 ments, clothing, cooking utensils, and 
 provisions, can be carried by a train of 
 pack-mules equal in number to the peo- 
 ple whom they accompany. With this 
 equipment the party are independent, 
 and can camp anywhere that wood for 
 fuel, forage for the animals, and a sup- 
 ply of water are found. This arrange- 
 ment is particularly necessary in the 
 occupation of a mountain station, upon 
 which, for successful observation, it may 
 be imperative to arrive at an early hour 
 in the morning and to remain through 
 
67 
 
 the greater portion of one, two, or three 
 days. From a camp near the summit 
 this may be reached in an hour or two; 
 but from a distant base almost the en- 
 tire day would be consumed in the jour- 
 ney to and fro. 
 
 THE TRIANGULATION STATION. 
 
 The mountain will be ascended by the 
 engineer, the meteorologist, and such 
 assistants as may be required to carry 
 the implements of the work and the food 
 and water necessary for the maintenance 
 of the party, and to build the stone 
 monument, which, if possible, should 
 always crown the peak, to receive the 
 records deposited here, to assist in the 
 future identification of this station, and 
 to serve as an object upon which to 
 direct the telescope in subsequent ob- 
 servations. One day will be a sufficient 
 time of occupation for the ordinary 
 triangulation station, provided the 
 weather be favorable. To the more 
 important ones, however, it may be 
 advisable to devote two days, spending 
 
68 
 
 one night upon the crest in astronomical 
 observations for the determination of 
 the azimuth of some line radiating from 
 here; this will serve as a check upon its 
 computed value, as derived from the 
 original azimuth determination made by 
 the astronomer at the base-line. In 
 times of high wind, or cloudy and stormy 
 weather, especially liable to occur upon 
 the summits of peaks, it may be several 
 days before satisfactory results are ob- 
 tained, and therefore the party should 
 always go well equipped for a prolonged 
 stay in their mountain camp. 
 
 PROFILE SKETCHES. 
 
 As an economy of time, which is of 
 the greatest value here, the observer 
 should make all reasonable haste in his 
 operations. Especially is this so in his 
 sketches, over which he must not linger, 
 which, if he is anything of an artist, he 
 will be sorely tempted to do. He may 
 see before him broader views and 
 scenery more grand and impressive than 
 ever was painted yet, but picturesque 
 
69 
 
 effects are no business of his. To the 
 geographer of artistic tastes there is 
 great temptation to finish his sketch by 
 inserting a pine-tree in the foreground, 
 and, perhaps, an eagle's-nest in the tree; 
 this is all very wrong, as such dalliance 
 may cost the omission of that far distant 
 peak, which is printed like a fine point 
 against the horizon, and which, insignifi- 
 cant and low as it appears, is yet of 
 vital importance to his scheme. 
 
 His sketch is perforce but the outline 
 and skeleton of a picture. Two con- 
 verging straight lines, with a few strokes 
 of shading, hastily thrown in, are suffi- 
 cient to represent the ordinary mountain 
 peak. Yet, if the peak should possess 
 any oddity or marked individuality of 
 shape, this feature should be preserved 
 and even magnified in the drawing, as a 
 key to the identification of this point 
 when seen from elsewhere at some other 
 time. Since any mountain, from differ- 
 ent points of view, presents phases that 
 are quite dissimilar, it is one of % the 
 greatest difficulties of triangulation to 
 
70 
 
 make sure of the identity of a station 
 previously occupied, or, where there are 
 a number of observers in the field, to se- 
 cure uniformity in the choice of the same. 
 
 CONTOUR DRAWINGS. 
 
 The expert geographer is proficient not 
 only in rapid profile but also in contour 
 drawing, and on every mountain station 
 he executes a contour plot of that scope 
 of country which he sees beneath his 
 feet, and of whose conformation he is 
 reasonably certain. But in the prepara- 
 tion of this local plot he should not be 
 too comprehensive, and go beyond the 
 bounds of certainty into the outer limits 
 of conjecture. Every mountain is sur- 
 rounded by valleys, on whose farther 
 side are other ranges perhaps as high as 
 this, and they form the limit beyond 
 which no contour sketch should presume 
 to go, else it becomes conjectural and 
 unreliable. It may include those en- 
 virons of valleys, with a periphery of the 
 foot-hills which are beyond them, and an 
 indication of the canons which indent 
 the same, but no more. 
 
71 
 
 In the office a contour sketch is ac- 
 cepted as truthful evidence of the ground 
 as it really is, while a profile drawing is 
 considered only a copy of the country as 
 it appears to be, when uncorrected for 
 the illusions of perspective, and is studied 
 and deciphered accordingly. Looking 
 abroad from this station, the successions 
 of distant ranges, which are in reality 
 separated by broad interspaces of valley 
 and plain, are projected into a dense and 
 circular wall, apparently unbroken by 
 pass or intermission, whose serrated out- 
 line is seemingly as continuous as the 
 horizon. It is an error to which the 
 human sight and judgment are subject, 
 and so, in orographic delineation, the 
 impressions of the eye are to be received 
 with caution, and only the readings of 
 the theodolite are to be accepted in full 
 faith. 
 
 PHOTOGRAPHS. 
 
 As a supplement to the pencil of the 
 engineer, the photographer's camera can 
 often be used to good advantage in se- 
 curing, in their true proportions, the 
 
72 
 
 many details of geological structure 
 which are necessarily omitted from a 
 hasty sketch. In the best geographical 
 delineation of a country, a series of 
 photographs are almost indispensable, 
 as, aside from affording much material 
 for the filling in of a map, they reveal 
 the nature of the surface which they 
 represent, showing whether it is regular 
 or broken, well-preserved or eroded, 
 whether a cliff is impassable or easy of 
 ascent, and whether a coast is smooth 
 and sandy, or irregular and rocky. All 
 of these conditions should be made to 
 appear in every good map, whether in 
 contour lines or hachures, and particu- 
 larly so, when, as in this case, the map is 
 intended as a basis for geological repre- 
 sentation. 
 
 READING THE ANGLES. 
 
 The instrument of triangulation is a 
 theodolite,- whose accuracy and weight 
 increase with the minuteness of the 
 graduation, but, in this work, in which 
 rapidity and ease of transportation are 
 
73 
 
 to be considered, there comes a limit be- 
 yond which it is imperative to sacrifice 
 nicety to portability. This is reached 
 when the limb is graduated so as to dis- 
 criminate to ten seconds of arc, between 
 which divisions the observer may esti- 
 mate to every intermediate five seconds. 
 With this he reads and repeats the 
 angles, singly and in combinations, that 
 lie between the visible points of the 
 triangulation scheme. It is advisable to 
 make at least six determinations of each 
 angle upon each of the two verniers of 
 the instrument, amounting to twelve 
 repetitions in all. The greater the num- 
 ber of readings from which the mean is 
 derived, the less will be the " probable 
 error of observation affecting that mean. 
 The observer may complete the repe- 
 tition of each angle by itself, or, what is 
 more convenient, he may read them in 
 conjunction, by making six complete cir- 
 cuits of the horizon. In either case the 
 graduated limb of the theodolite will be 
 turned 30 in azimuth at every return to 
 the initial point. In this manner each 
 
74 
 
 angle is read upon twelve different and 
 equi-distarit divisions of the circle, and 
 the faults arising from eccentricity or 
 imperfect graduation are reduced to a 
 minimum. 
 
 The most opportune moments of the 
 day will be devoted to this important 
 task, and all other duties will be neg- 
 lected for this. Successful triangulation 
 demands perfect quiet and a clear hori- 
 zon. In a dense and hazy atmosphere, 
 or in a region of low clouds, the observer 
 may find his opportunity in the evening 
 or early morning, when the sun is be- 
 hind the hills, and the rim of the earth 
 is seen in" silhouette against the rosy 
 background of the sky. 
 
 SUBORDINATE ANGLES. 
 
 Upon the triangulation station the 
 engineer also reads angles for the direc- 
 tion of the spurs which project from 
 here and of the streams that debouch 
 from here, estimating the distances of 
 geographical features in his immediate 
 vicinity. How far he may trust to his 
 
75 
 
 judgment in this respect, will be determ- 
 ined by the circumstances by which he 
 is surrounded. It is the engineer's duty 
 to make the best map of a country that 
 is possible with the advantages at his 
 command, and if he should see before 
 him a tract of country, distant even ten 
 or twenty kilometres, which he will 
 never see again, he should take note of 
 it on his contour plot; but if he knows 
 that some future route of his will cross 
 it, he can afford to neglect it now. 
 
 In addition he takes readings to infe- 
 rior elevations which, although they 
 may never be occupied for reciprocal ob- 
 servations, may yet be located by 
 intersections from two or more triangu- 
 lation stations. Some point, or "tit," 
 standing on the edge of an abrupt bluff, 
 where the rapid descent begins, is used 
 as a means of marking the end of a 
 neighboring mountain range. A solitary 
 butte on the plain, insignificant in itself, 
 is very useful in determining the locus 
 of the stream which flows by the side of 
 it. A promontory, jutting into the con- 
 
76 
 
 fluence of two rivers, is instrumental in 
 fixing the place of their union. Sights 
 are also taken to the junctions of 
 streams, the mouths of canons, and to 
 the church or other central object of a 
 distant village. A spot of green on the 
 desert, evidence of a spring of water 
 there, is located, for it will perhaps be 
 camping-ground some day for himself or 
 his co-laborers. A minute patch of 
 white lake-bed, or red escarpment, or a 
 solitary tree, is sighted upon, because on 
 such a day he made an odometric sta- 
 tion there, and this sight will serve to 
 check his position. 
 
 NOMENCLATURE. 
 
 In his note-book and mind he has 
 dubbed all of these things with graphic 
 titles, or designated them by letters of 
 the alphabet, and by these tokens he will 
 know them when he sees them again. 
 But this system of names is only a 
 transient device for the assistance of 
 himself and those who work in concord 
 with him, and should not appear upon 
 
the printed sheet to the exclusion of tae 
 native and established nomenclature of 
 the country, which should be investigated 
 as far as possible, and, upon the final 
 maps, should be adopted in preference 
 to the arbitrary naming of any one man. 
 The usefulness of a map, as a guide to 
 the traveler, is in a great degree invali- 
 dated by a nomenclature which is at 
 variance with that in use upon the ground 
 itself. Perhaps the modern geographer 
 is guilty of no more common and high- 
 handed outrage against right, conven- 
 ience, and beauty, than by ignoring the 
 appropriate titles which abound in every 
 country, however wild and uncivilized, 
 and attaching his own, or by mutual and 
 tacit agreement, the names of his com- 
 rades, to the mountains of that land, 
 thus announcing themselves to the world 
 as nostrums are advertised on the pyra- 
 mids. 
 
 THE TOPOGEAPHICAL STATION. 
 
 All of the preceding description that 
 does not refer to the triangulation pro- 
 cess is also pertinent to the topographical 
 
78 
 
 tation. This term is applied to those 
 isolated stations of survey, apart from 
 the route of the odometer, and interme- 
 diate to the points of primary triangula- 
 tion. They are more numerous than the 
 primary stations, being usually scattered 
 over the country at intervals of not 
 more than twenty kilometres, but are 
 less important, since there is no great 
 responsibility of accuracy resting upon 
 them. The topographical stations cor- 
 respond, in position and numbers, with 
 the secondary triangulation stations of a 
 more elaborate geodetic survey. 
 
 A SECONDARY TRIANGULATION. 
 
 Even here the topographical station 
 may be made a point in a subordinate 
 scheme of triangulation if its situation is 
 elevated, distinct, and capable of recog- 
 nition from a distance. Of course, it is 
 desirable that every occupied station 
 should subsequently be made an object 
 of reciprocal observations, and the engi- 
 neer should neglect no opportunity to 
 confirm his position in this manner. 
 
79 
 
 Each point thus fixed becomes the center 
 of a plexus of triangles, of each of which 
 the three angles have been observed; 
 the total error of observation in these 
 three angles becomes apparent, and the 
 computer is enabled to distribute it judi- 
 ciously among them before he proceeds 
 to the computation of the sides. 
 
 For this reason the observer upon any 
 topographical station will make careful 
 search for other points which he may 
 have occupied or may contemplate oc- 
 cupying, and will be more than usually 
 cautious in reading angles to them. On 
 his return to the office, at the end of the 
 season, he will pick out from the multi- 
 tude of his notes as many complete tri- 
 angles as he may have observed, and 
 these will be so much gain attained at a 
 cost of but little extra labor. But if he 
 makes it imperative upon himself to 
 carry on a complete and systematic tri- 
 angulation within the first, the additional 
 refinement gained will by no means com- 
 pensate him for the disadvantages of 
 reconnoissance and delay which this in- 
 volves. 
 
80 
 
 It is safe to say that it is a longer and 
 more laborious work to accomplish an 
 unbroken secondary triangulation than 
 a primary, as the stations are more nu- 
 merous, less elevated and conspicuous, 
 and oftener in the shadow. On the 
 other hand, the results are by no means 
 so valuable. The primary triangulation 
 sustains the general and continued accu- 
 racy of the survey; the secondary does 
 little more than to insure the individual 
 positions of its own stations. 
 
 POSITION OF THE TOPOGRAPHICAL STA- 
 TION. 
 
 Although not necessarily a point in 
 the triangulation proper the site of the 
 topographical station must afford angu- 
 lar data sufficient for the determination 
 of its position by the three-point problem. 
 After that, its predominant idea is that 
 it is a means of local geography, or to- 
 pography, and a center for a series of 
 contour sketches. In addition to these 
 detailed plots of the country in the im- 
 mediate vicinity, profile drawings of the 
 
81 
 
 more distant regions are made. Then, 
 by lines of sight, which shall be intersect- 
 ed by other rays from other topographical 
 or triangulation stations, the most 
 prominent features within a radius of 
 twenty or thirty kilometres are crossed, 
 and, as a precaution, angles are also read 
 to all eminent points visible at a greater 
 distance, even to the horizon, as they 
 may come into use in some future di- 
 lemma in map-drawing. 
 
 While the site of the topographical 
 station should be as elevated and marked 
 as possible, yet any hill, however humble 
 and inconspicuous, or even the level sur- 
 face of a plain, may serve this purpose? 
 provided that there be three triangula- 
 tion stations, or other known points, visi- 
 ble, and there is any useful information 
 to be gained by lingering here. A few 
 hours are usually enough for its occupa- 
 tion, and the route between points of 
 triangulation should be marked at regu- 
 lar intervals by the monuments of these 
 stations. It is a good plan for the en- 
 gineer to make a practice of diverging 
 
82 
 
 from his route at some point in each 
 day's odometric survey, and, ascending 
 a suitable eminence close at hand, make 
 a topographical station there. As far as 
 a general rule can be given for the oc- 
 currence of mountain stations, it is advis- 
 able for the party to advance by linear 
 survey every second day, remaining in 
 camp on each alternate day, while the 
 engineer ascends some peak in the vicin- 
 ity for the purpose of establishing a 
 topographical or triangulation station 
 there. 
 
 The - large triangulation theodolite 
 should be used in the more important 
 topographical stations, or those which 
 may possibly be treated as points in a 
 secondary triangulation, but, for the sake 
 of convenience, the small route transit 
 must be made to suffice for those which 
 are made in the course of the daily 
 march. 
 
 THE ODOMETRIC, OR MEANDER SURVEY.* 
 
 The meander survey is useful as an 
 
 * Note to the Portuguese Edition. This term, which is 
 now firmly grounded in the technical language of 
 
83 
 
 adjunct to the triangulation, filling up 
 its skeleton with that 'detailed informa- 
 tion which alone can give practical and 
 popular value to a map. It determines 
 the courses of valleys and streams, the 
 routes of roads and trails, the peripheries 
 
 geographical surveying in the United States, is a mis- 
 nomer, and therefore, in introducing a corresponding 
 one into the Portuguese, it will be well to adopt some 
 more appropriate expression. For this reason " odomet- 
 ric survey" will be used to designate line surveys in 
 which the odometer takes part, and "route survey" 
 (caminhamento) as a general term, to include not only the 
 above, but also those in which distances are determined 
 by time, by the chain where that method is employed, or 
 by paces, whether of man or horse, and whether re- 
 corded by the pedometer or by direct counting. 
 
 As the meander survey is understood, where this ex- 
 pression is used, it is simply any survpy following a zig- 
 zag line, whose angles in general, are alternately salient 
 and re-entrant, as the line accommodates itself to the 
 route of travel. But this word " meander," having been 
 derived from the river of the same name, in ancient 
 Phrygia, which was celebrated for its winding, sinuous 
 course, literally means "abounding in curves." It will 
 thus be seen that the more a survey approaches to a true 
 meander, the farther it departs from the first principles 
 of accurate linear surveying, which dictate that it shall 
 consist of straight lines and angles only. Since it is al- 
 ways to be regretted when a survey is confined to a true 
 meand*er line, as for instance, in tracing the course of a 
 road along and up the Fide of a mountain range, so it is 
 also a matter of regret that this word should have been 
 introduced into the language of engineering, apparently 
 sanctioning a faulty survey. 
 
84 
 
 of lakes and basins, and the distances 
 between springs of water, villages, areas 
 of pasture, fords of rivers, and other 
 points of interest to the future traveler. 
 Finally, it is a commendable occupation 
 for the engineer while on his way from 
 one mountain station to the next, and, 
 since it occasions no delay in the general 
 progress of the work, as the engineer 
 can, as a rule, meander as much road as 
 his pack-train can travel in one day, its 
 results are net gain to the survey. 
 
 In the theoretical journey of this kind, 
 the engineer would follow the edge of 
 the dividing ridge from one station to 
 the next, from which lofty promenade 
 he could see the earth like an extended 
 scroll beneath his feet, and make a sur- 
 vey that would be exhaustive and 
 complete. But in the real, hard prac- 
 tice, he finds this path an impracticable 
 one, for it is broken by precipices and 
 blocked by abutments often a hundred 
 metres or more in height. His easiest 
 route of travel is by the side of flowing 
 water, whose tendency it is to erode aft- 
 
85 
 
 rupt cliffs and soften steep gradients 
 into an average and even slope. Be- 
 sides, along the streams there are trails 
 made by the wild animals which come 
 here for drink and covert, and by the 
 people of the country who come hither 
 to hunt and fish. Therefore, if the* de- 
 tour be not too great, the most expedi- 
 ent route from mountain to mountain, is 
 down one valley and up another, and 
 the geographer who traverses a valley 
 without taking some sort of a survey of 
 it, is culpably negligent of his duty. 
 On the other hand, if in a block of 
 mountains the pre-eminent peaks be oc- 
 cupied, and the streams which emanate 
 therefrom be meandered, nothing more 
 is needed for a most excellent geograph- 
 ical map of that country. 
 
 THE MEANDER TRANSIT. 
 
 It is supposed that all transportation 
 of outfit, and all travel, even in the me- 
 ander survey, is accomplished on the 
 backs of horses or mules. Riding in 
 the saddle, the surveyor can devote but 
 
86 
 
 one hand to the grasp and protection of 
 his instrument, the feet of whose tripod 
 rest in a holster attached to the left 
 stirrup. To facilitate his secure- hold, 
 the members of the tripod are thirds of 
 a cylinder, which fold into the smallest 
 possible compass, and are easily held in 
 the grip of one hand. 
 
 The instrumental part of the meander 
 transit is neat, solid, and compactly 
 constructed. Its graduated limb is of 
 small diameter, and its horizontal ver- 
 nier reads to minutes only, which is all 
 very well, since no smaller divisions can 
 be plotted on the map. This graduation 
 is used in the occupation of topograph- 
 ical stations, at those meander stations 
 where the view is extended enough to 
 make it profitable to linger an hour or 
 so in the accumulation of notes and 
 sketches, and at all those which are 
 three-point stations as well. But in the 
 general survey, not the vernier-plate, 
 but the compass needle, is used, on ac- 
 count of its greater convenience. The 
 compass box is graduated, from zero at 
 
8V 
 
 the north, around by the left to 360 at 
 the north again, so that a reading of 90 
 corresponds to magnetic east, and 270 
 to west. The field records are kept 
 in this manner, and in the office the de- 
 clination of the needle is first applied to 
 each bearing^ after which it is reduced 
 to its true direction, preparatory to the 
 plotting. 
 
 THE ODOMETEB. 
 
 The distances from station to station 
 of the meander are measured by the 
 odometer, an implement of survey which, 
 in some of its forms, has been long in 
 use in Europe, and has of late years re- 
 ceived especial attention and improve- 
 ments in the reconnoissances and other 
 geographical surveys carried on by the 
 War Department of the United States 
 of North America. In this service it 
 has been adapted to the severe condi- 
 tions of travel in a new country. It has 
 been strengthened so as to withstand 
 any shock or fall to which it may be 
 subject. The recording apparatus is 
 
88 
 
 made so compact and simple that there 
 is no danger of disarrangement there. 
 Instead of the old laborious process of 
 pushing it by hand, the wheel has been 
 fitted with shafts, so as to be drawn by 
 a mule, and so efficient is the method of 
 attachment that the odometer can follow 
 any route, however rough, precipitous, 
 or narrow, that will admit of the passage 
 of a pack-mule. 
 
 In its simplest and best form the 
 odometer vehicle is a solitary wheel, a 
 little more than a meter in diameter, or 
 about the size of a light carriage- wheel. 
 It is strongly constructed of the best 
 material, and is braced by opposite in- 
 clinations of alternate spokes, so as to be 
 uninjured by the heaviest jars and col- 
 lisions. A pair of shafts are attached to 
 it, and into these a strong and steady 
 mule is firmly harnessed by straps from 
 above and underneath. The vehicle is 
 close in the rear of the animal, and the 
 shafts are made short and heavy, and in 
 this manner the wheel is preserved in a 
 plumb or upright position as it runs, not 
 
89 
 
 swaying from side to side. The length 
 of the circumference of the wheel being 
 accurately known and the number of 
 revolutions being recorded by the at- 
 tached apparatus, it is a simple matter 
 to learn the distance between any two 
 points. 
 
 The recording instrument hangs in a 
 cylindrical box which is strapped to the 
 wheel. It consists of a mechanical com- 
 bination attached to a heavy block of 
 metal, whose center of gravity is at one 
 side of the axis to which it is suspended. 
 As it is free to revolve upon this axis it 
 always maintains a vertical position, 
 while its box turns with the wheel, and 
 the apparatus scores the number of 
 revolutions, of which it is capable of re- 
 cording 9900, or a distance of about 
 forty kilometers, when it begins anew. 
 
 USEFULNESS OF THE ODOMETEK. 
 
 This detailed description of the odo- 
 meter is in accordance with the promise, 
 made in the early part of this article, to 
 dwell upon the novel features of this 
 
90 
 
 work, even to the exclusion and apparent 
 neglect of others, already well-known, 
 which are really of greater importance. 
 Still it would be difficult to over-esti- 
 mate the usefulness and practical value 
 of this instrument. It requires but little 
 technical knowledge to use it and to 
 conduct the meander survey which ac- 
 companies it, and any person educated 
 in the simplest rudiments of surveying 
 is competent for this kind of work. 
 
 For this reason every party of scien- 
 tific exploration and reconnoissance, 
 every preliminary survey for railways, 
 and every marching body of troops 
 should consider its outfit incomplete 
 without the implements of an odometric 
 survey. Aside from the mass of notes 
 and sketches that would be accumulated 
 by them, and the itinerary maps that 
 would result, in the item of distances 
 alone the country would be more than 
 repaid for the cost of these surveys. As 
 a means of mensuration the odometer 
 will determine distances en route, as the 
 wagon travels, more truthfully than the 
 
91 
 
 chain itself. These, being published, 
 are of profit, not only to the ordinary 
 traveler, but also to the general govern- 
 ment, whose agents and officials, in one 
 capacity or another, are constantly pas- 
 sing to and fro. 
 
 ERRORS OF THE ODOMETRIC SURVEY. 
 
 is there any very great error in 
 the ordinary surveys which the odome- 
 ter is likely to be called upon to perform. 
 Having the geographical positions of 
 two towns forty kilometres apart, they 
 may be connected by an odometric sur- 
 vey, the plot of which can be adjusted 
 between these two positions so that no 
 intermediate points will be appreciably 
 out of place on a map of the usual scale. 
 Since this is a map for practical use and 
 for the public good, it fulfills its pur- 
 pose as well as if its distances had been 
 measured by the most refined methods. 
 
 The great objection to its use is the 
 tendency towards the accumulation of 
 error in an odometric meander, and the 
 farther it is from the known point which 
 
92 
 
 is its origin, the greater is the probable 
 error of any position determined by it. 
 Therefore, in a prolonged journey, or in 
 a general survey of the country, the 
 odoraetric position should frequently be 
 verified, or checked and rectified, by con- 
 nection with known points. This can be 
 accomplished by making a station at 
 some point on a railway, boundary, or 
 other line of accurate survey ; by astro- 
 nomical observation, which, however, if 
 taken with a sextant, is often less relia- 
 ble than the meander itself; or by mak- 
 ing a meander station dependent upon 
 the accompanying triangulation, by 
 means of the three-point problem. The 
 last method, which is by far the most 
 reliable, will be explained further on. 
 
 ERROR OF DIRECTION. 
 
 The meander is affected by error of 
 two kinds, of direction, and of distance. 
 The former, in its most serious nature, is 
 incurred in the survey of a tortuous val- 
 ley, whose general course must be ac- 
 cepted, or in crossing a timbered coun- 
 
93 
 
 try, or a pathless plain, where the sur- 
 veyor is in a constant state of uncer- 
 tainty as to whither he is to go, or, tak- 
 ing a back-sight, as to whence he has 
 come. Sometimes the engineer is 
 obliged to keep his eye on the sun and 
 get a general idea of the course from 
 that. Or, in traversing a dense forest, 
 he may find himself compelled to resort 
 to the paradox of sighting upon a sound; 
 that is, he allows the pack-train to keep 
 a certain distance in advance, and from 
 time to time he directs his telescope to 
 the tinkling of the bell which is carried by 
 the horse that leads the train. It must 
 be confessed that these make-shifts are 
 loose methods of survey, but they are 
 better than none, since they give the 
 prominent directions and the distances 
 between streams, divides, etc., and 
 months afterwards, when the engineer 
 comes to make the map and lay down 
 upon it the trail of that day's march, he 
 will find the poorest and most incom- 
 plete notes more reliable than his present 
 memory and judgment. 
 
94 
 
 Even under the most favorable cir- 
 cumstances it will seldom be possible to 
 direct the telescope with greater pre- 
 cision than to the nearest degree, nor, as 
 a consequence, will it ever be worth 
 while to record any fraction of a revolu- 
 tion in the odometer. A road does not 
 usually change direction by an abrupt 
 angle, but by a gradual curve, and the 
 bearing is made approximately tangent 
 to that curve. Or, in the survey of a 
 stream, it is not known on which side 
 the trail will run at some point a kilo- 
 metre in advance, and so the approxi- 
 mate center of the valley is accepted. 
 But if there should be a solitary tree, 
 bush, house, rock, or other prominent 
 object fortunately situated for a station, 
 the course will be made closely tangent 
 to that, a reading of instruments will be 
 taken upon arriving there, and, going on 
 to the next station, the engineer will 
 take a back-sight to the same point. In 
 general the system of back-sights will 
 be found more satisfactory than that of 
 foresights, as it is easier, on a strange 
 
95 
 
 route, to tell whence you have corne than 
 to decide where you are going. 
 
 ERROR OF DISTANCE. 
 
 This error of direction, it will be seen, 
 is thrown by the law of chance alter- 
 nately to the right and left of the true 
 line, and so has a tendency in its elements 
 towards mutual compensation, and in a 
 measure it corrects itself. But not so 
 the error of distance, which is always 
 plus, and cumulatively so. The test of 
 the odometer wheel, by which its num- 
 ber of revolutions per kilometre is ascer- 
 tained, is made upon a level surface and 
 along a staked alignment, giving a re- 
 sult almost absolutely correct. In prac- 
 tice, however, the vehicle climbs acclivi- 
 ties of every grade, tacks hither and 
 thither as it follows the trail up the 
 mountain, winds incessantly in its route 
 through the forest, and is disturbed by 
 frequent jolts and collisions along the 
 rocky floor of the canon. In a theo- 
 retical traverse the straight line between 
 any two stations is determined, but in an 
 
96 
 
 odometer survey the measuring imple- 
 ment usually follows a beaten path, and 
 the route distance, by road or trail, is 
 rarely the shortest distance between two 
 points. Hence an "overrun" in its 
 record, which can only be remedied, and 
 that approximately, by the judgment of 
 the surveyor, who is taught by experience 
 to estimate very closely the surplus in a 
 given run, and who applies a correction 
 accordingly. 
 
 Still, to such perfection has the odo- 
 meter survey been brought, that it is a 
 common occurrence for a skilled worker 
 to meander a closed circuit of. one hun- 
 dred kilometres, and plotting the route, 
 to find the plot also close within a small 
 fraction of a kilometre. Even this error, 
 being judiciously distributed in the pro- 
 cess of adjustment, different weights 
 being assigned to different runs, accord- 
 ing to their probable accuracy," may be 
 reduced so as to be practically imper- 
 ceptible. 
 
 OCCURRENCE OF MEANDER STATIONS. 
 
 No general rule can be given for the 
 
97 
 
 frequency of meander stations, but in 
 ordinary country they will average per- 
 haps one to the kilometre. In this all 
 will depend upon local circumstances 
 and exigencies. In the survey of a long 
 and hidden valley, affording no opportu- 
 nity for checks, especial care must be 
 taken to preserve the integrity of the 
 meander, and the stations must be espe- 
 cially frequent; but in a survey by a 
 direct line across the plain two or three 
 stations a day may be sufficient. In a 
 winding path up a mountain side a 
 dozen stations may be necessary if there 
 are no chances for checks; but if the 
 ends of the trail, at the top and bottom 
 of the mountain, can be located by the 
 three-point problem, the intermediate 
 route can be neglected, being, at most, 
 sketched in by the eye. 
 
 There are two considerations to govern 
 the occurrence of stations; first, to pre- 
 serve the continued accuracy of the sur- 
 vey, and second, to note the local 
 geographical features which may be 
 encountered. For y the latter purpose 
 
98 
 
 stations will be made at the center of 
 every village, at every country-house of 
 importance, at the crossing and diverg- 
 ence of streams, roads and trails, at the 
 opening of a valley, at the foot and 
 summit of a mountain, and at the 
 many other geographical vantage- 
 grounds which the practical engineer 
 will know how to select. But in this, as 
 in the other departments of the survey, 
 too punctilious zeal may defeat its own 
 interests by causing delay, and the sur- 
 veyor who is too scrupulously exact in 
 the forenoon may have to virtually 
 abandon his task in the afternoon, in 
 order to reach a suitable camping-ground 
 by night. 
 
 SCOPE OF THE MEANDER SURVEY. 
 
 The zone of country considered from 
 a meander line may extend to the 
 farthest visible point, as a series of sights 
 upon a mountain even twenty-five kilo- 
 metres away will give its position to a 
 close approximation; but its principal in- 
 tent is the preparation of a narrow route 
 
map, the areas encompassed by whose 
 windings will be filled in from the topo- 
 graphical stations. Since, from its nature 
 and narrow scope, it is fuller and takes 
 cognizance of objects more minute than 
 can be noticed in the other systems, in 
 this the engineer is liable to a charge of 
 partiality, reproved in the early part of 
 this article. But this is not partiality in 
 one field at the cost of neglect in 
 another, and the greater excellence of 
 this work is so much clear gain. More- 
 over, since the meander is usually by 
 way of roads of frequent travel, and 
 since a map is useful, and should be ex- 
 cellent, exactly in proportion to the num- 
 ber of people who are guided by it, it is 
 well that the meander plot should excel 
 in completeness those almost inaccessible 
 parts which will never be seen except by 
 the hunter or bandit. 
 
 MAKESHIFTS IN THE SURVEY. 
 
 In a forced march of forty kilometres 
 or more, the meteorologist and odometer 
 recorder, the safe carriage of whose im- 
 
100 
 
 plements requires a slow and steady gait, 
 may proceed at a walk after taking their 
 readings at a meander station, which task 
 will occupy them but a few minutes, 
 while the surveyor lingers behind to make 
 the necessary sketches and observations, 
 and then, riding at gallop, overtakes his 
 comrades before the next station is 
 reached. Many such shifts as this are 
 known to the practical and energetic 
 geographer, who learns to emancipate 
 himself from too close dependence on the 
 text-books of surveying, some of whose 
 rules are very common-place and pedan- 
 tic, and brings into play his powers of 
 ingenuity and invention, to adapt himself 
 to the peculiar circumstances by which 
 he may be surrounded. If he finds him- 
 self alone, out on some trip of hasty 
 reconnoissance, or on some hunting ex- 
 cursion on which he could not carry both 
 rifle and transit, he draws from his watch 
 pocket an aneroid, and from his saddle- 
 bags a pocket compass or an altazimuth, 
 and his equipment for survey is com- 
 plete; as for distances, he can estimate 
 
101 
 
 them, or determine them by the time 
 they take, calculating at the rate of five 
 kilometres an hour, or, better still, by 
 counting the steps of his horse and allow- 
 ing six hundred double paces for a kilo- 
 metre. 
 
 In a geological survey of Brazil very 
 much of the travel and exploration is 
 necessarily done by water, as the outcrop 
 of the various formations is most favora- 
 bly shown upon the banks of the rivers, 
 along which there is frequently no passa- 
 ble route by land. Here the stadia may 
 be used, provided there are two or more 
 boats in the party, or, in the less import- 
 ant instances, the methods of obtaining 
 distances by estimation or by time would 
 have to suffice. In either case the sur- 
 veyor should lose no opportunity to 
 emerge from the trough of the stream, 
 or to ascend some eminence, and insure 
 his position by observations upon three 
 or more known points. Should these be 
 wanting, he should resort to the sextant 
 and to its use in astronomical determina- 
 tions. 
 
102 
 
 Since the attention of the geologist is 
 in great- part absorbed in the duties pe- 
 culiar to his profession, he cannot usually 
 carry any but the lightest and most con- 
 venient implements of survey, and since 
 these are amply sufficient for his geologi- 
 cal notes of dip, strike, trend, etc., it is a 
 matter of expediency to make them an- 
 swer for his geographical work as well. 
 With the engineer, however, there rarely 
 comes a necessity for being separated 
 from his portable transit, which admits 
 of being firmly set on its tripod, and from 
 which angles, either horizontal or verti- 
 cal, may be accurately read to the near- 
 est minute. And in the general geo- 
 graphical plan it is wise to deprecate as 
 far as possible the employment of unreli- 
 able pocket instruments, or of the devices 
 for learning distances that have been de- 
 tailed above. Since nothing is to be 
 gained in time by their use, and very 
 much may be lost in accuracy, the engi- 
 neer should teach himself to consider that 
 any method less complete than that of 
 the portable transit and odometer is but 
 
103 
 
 a temporary expedient and makeshift, 
 serving an excellent purpose when all 
 other means fail, but not to be relied 
 upon as a permanent constituent of the 
 survey. 
 
 CO-OPERATION OF THE TRIANGULATION 
 AND MEANDER. 
 
 While the meander survey is an ex- 
 cellent apprenticeship for the young en- 
 gineer, it should not be despised, as an 
 occupation, by even the director of the 
 triangulation. Humble as it is, it per- 
 forms a task in the geographical plan 
 which no system of triangulation can be 
 relied upon to perform in a rapid work 
 of this nature. It enables the survey to 
 reach any point, however remote and se- 
 cluded, and to determine its positions; it 
 makes the map complete in all of the 
 details which are so useful to the trav- 
 eler; and as an agent in what we may 
 call the practical or economical branch 
 of geography it is without an equal. 
 
 It is dependent upon the triangulation, 
 it is true, but then the dependence is 
 
104 
 
 mutual. The full benefit of either can 
 only be secured through the co-opera- 
 tion of the two. As without the trian- 
 gulation the map is unreliable, so with- 
 out the meander it is incomplete. To 
 use a homely illustration, the triangula- 
 tion may be compared to the framework 
 of the dwelling, and the meander to the 
 intermediate filling of wall or other sub- 
 stance which makes the house habitable, 
 and is a shelter to the inmates. This 
 frame, if its lines are true and its angles 
 correct, is a beautiful thing for the arti- 
 san to contemplate, but without its com- 
 pletion of walls and furniture, it is of no 
 real benefit to the world. In the same 
 manner a bare triangulation scheme may 
 be an interesting study to the geographer 
 himself, but to the traveling public and 
 the people at large, it possesses neither 
 interest nor value. On the other hand, 
 as the frame of the house is an absolute 
 necessity to it, securing and sustaining it 
 in its proper proportions, so is the trian- 
 gulation the rigid frame work of the 
 map and the skeleton to which the use- 
 ful data of the meander are attached. 
 
105 
 
 CHECKS BY THE THREE-POINT PROBLEM. 
 
 Since the meander is from its very 
 nature so hasty and loose, the system of 
 frequent checks can alone make it relia- 
 ble, and at intervals of every few kilo- 
 metres, and especially at the crossing* of 
 divides and other eminences from which 
 there is a broad scope of country visible, 
 connection should be made with the 
 triangulation. Each of these stations 
 then becomes a new initial point, at 
 which the survey begins afresh and the 
 error again begins to accumulate. 
 
 This rectification is accomplished by 
 the use of the three-point problem, a 
 geodetic determination which, as a 
 means of locating topographical stations, 
 and as a connecting link between the 
 meander and the triangulation, is of the 
 highest importance in geographical sur- 
 veying. Having three triangulation sta- 
 tions in sight, and favorably situated, it 
 is possible for the observer to determine 
 his position in a few minutes of time 
 and by the simple operation of reading 
 the two angles included by those three 
 
106 
 
 stations. From these and the data per- 
 tinent to the triangulation stations he 
 can compute his distance from them, and 
 hence his present latitude and longitude. 
 Or, plotting these angles from any cen- 
 ter on a piece of tracing cloth, he can 
 lay this upon the projected map and 
 swing it around until each of the three 
 plotted rays covers its proper triangula- 
 tion point, when this center will indicate 
 the position of the three-point station, as 
 it is called. For this graphic determina- 
 tion not only three points, but four, and 
 even more, if they are visible, should be 
 observed, as a greater number facilitate 
 the operation and insure the accuracy 
 of the result. 
 
 This method of trilinear determinations 
 cannot be introduced too often. A 
 three- point station in the streets of a 
 settlement, at the forks of a road, or at 
 the end of a mountain range, will locate 
 these important places, and in camp, 
 even in the center of a broad and vacant 
 plain, there is no more profitable man- 
 ner in which the engineer can spend his 
 
107 
 
 leisure time, before or after dinner, than 
 by making a three-point station there 
 and determining his position. Every 
 camp thus fixed is a new and reliable 
 origin at which the meander of the next 
 morning will begin. 
 
 A SURVEY BY THREE-POINT STATIONS 
 ALONE. 
 
 In some cases a successful meander 
 may be carried on by three-point sta- 
 tions alone, when all other means would 
 fail. Take, for instance, the rugged 
 shores of a lake or bay, which are inac- 
 cessible except to a man on foot or in a 
 boat. In the mountains on the other 
 side of the water a series of triangula- 
 tion stations stand up in full view. By 
 means of these the engineer, working 
 his way, transit in hand, from bay to 
 bay, and from point to point, along the 
 water's edge, makes three-point stations 
 at all prominent changes of curvature, 
 and, sketching in the intermediate shore, 
 he determines its line by tangents and 
 intersections, and thus secures a good 
 
108 
 
 survey of the coast. If there are islands 
 out in the water they may be surveyed 
 in the same way. 
 
 If the engineer was confronted with a 
 piece of geography like the bay and 
 islands of Rio de Janeiro, and if there 
 were no roads along the beach to make 
 direct linear measurements feasible, he 
 could extend his triangulation to include 
 all of the prominent peaks in the vicinity, 
 and then, by means of three-point sta- 
 tions, he could rapidly trace in the shore- 
 line. As the surroundings of Rio are so 
 broken and irregular, the triangulation 
 points could be made so numerous that 
 it would be difficult to find a spot on the 
 beach of mainland or island so secluded 
 that some three of these stations would 
 not be visible from there. 
 
 THE MEANDER PLOT. 
 
 Every three-point station, as well as 
 every other meander station, should par- 
 take more or less of the nature of a regu- 
 lar topographical station; that is, contour 
 sketches should be kept constantly on 
 
109 
 
 the plotted page as it progresses, and a 
 continuous panorama of profile views, 
 drawn in a separate portion of the book, 
 should accompany the survey, so that, 
 as some geographical features are left in 
 the rear, others may be introduced in 
 advance. 
 
 As from one topographical station to 
 its neighbor, so every distance from one 
 meander station to the next should be 
 considered a base to be used in the loca- 
 tion of points useful in the structure of 
 the map. The longer this base, the more 
 distant may be the range of these views. 
 In case several meander stations inter- 
 vene between one observation and the 
 following, this total intermediate dis- 
 tance becomes what is called a broken 
 base, but it is none the less useful for all 
 of that. The above considerations will 
 influence the engineer in his choice of 
 stations, which will always be situated in 
 such positions as may offer the best ad- 
 vantages for the accumulation of what- 
 ever information he most needs. 
 
110 
 
 THE DECLINATION OF THE COMPASS 
 NEEDLE. 
 
 The variation of the compass needle, 
 or, more properly, its declination, will be 
 carefully watched throughout the sur- 
 vey, and determinations of its angle will 
 be made from time to time; these will be 
 more than usually frequent wherever 
 there is suspicion of some attraction im- 
 mediately local, arising from the presence 
 of magnetite or other ore of iron, basaltic 
 rock, or other disturbing influence. These 
 determinations are important, not only 
 in the reduction of the meander notes 
 taken in this vicinity, but also for the 
 practical use, both present and future, 
 of the country at large. In addition, their 
 results will aid the general cause of sci- 
 ence in its investigation of the laws of 
 terrestrial magnetism, and in tracing the 
 course of isogonic lines around the world. 
 
 At every triangulation, topographical, 
 and three-point station, the observer 
 will note the direction of magnetic 
 north, as indicated by the pointing of 
 the compass needle. If his instrument 
 
Ill 
 
 has a double movement in azimuth, as 
 all should have, it is well, for the sake of 
 convenience, to first set the zero of the 
 graduated limb upon the same point of 
 the vernier plate, by the upper motion, 
 and then, by means of the lower move- 
 ment, bring the north end of the needle 
 to the zero of its circle. His initial 
 entry in his note-book will then be 
 " Magnetic North, 00' 00"." This 
 direction of the telescope being referred 
 to some line proceeding from here, 
 whose true azimuth will be found by 
 subsequent computation, the magnetic 
 azimuth or declination of the needle at 
 that place will be determined; it will 
 simply be the difference between the true 
 azimuth of the line, reckoned from the 
 north point of the horizon, and its ap- 
 parent azimuth, or the vernier reading 
 which he enters in his notes. 
 
 BY DIRECT ASTRONOMICAL OBSERVATION. 
 
 The declination of the needle will also 
 be determined directly by astronomical 
 observation in the evening at camp. For 
 
112 
 
 this purpose the engineer will select such 
 nights, clear and still, as may appear to 
 him most favorable, and such camping 
 places as may most urgently require this 
 information. A star as near as possible 
 to the pole will be chosen, as, from its 
 greater declination, an error in the lati- 
 tude of the observer's place, and, from 
 its slower motion, an error in the time 
 of the observation, will result in less 
 serious errors in the azimuth; and the 
 smaller the polar distance of the star, the 
 more convenient will be the observation 
 and the computations which follow, and 
 the more exact is the result likely to be. 
 In the northern hemisphere a Ursce Mi- 
 noris, or Polaris, is almost always used, 
 as it is at present only about 1 20' from 
 the pole, and it possesses the additional 
 advantage of a brilliancy of the second 
 order. But south of the equator there 
 are no available stars so favorably situ- 
 ated as this. The most southern one of 
 any considerable size is ft Hydri, of the 
 third magnitude, whose polar distance is 
 a little more than twelve degrees. 
 
113 
 
 This would have to be accepted in a 
 survey of this nature in preference to 
 any of the less brilliant stars of greater 
 declination, as the observations would 
 have to be made frequently by engineers 
 of little astronomical experience, and 
 with instruments not especially adapted 
 to this kind of work. Indeed, it might 
 be necessary at times to use the small 
 meander transit for that purpose; arid it 
 is seldom that the telescopes of even the 
 theodolites for triangulation, as now con- 
 structed, are provided with the hollow 
 rotation axis requisite for a proper illu- 
 mination of the diaphragm, without 
 which it is difficult to see both cross- 
 hair and star, unless the latter is of con- 
 spicuous magnitude. 
 
 Knowing, at least approximately, the 
 latitude of the place, and also the decli- 
 nation of the star and its hour angle at 
 the time of observation, its azimuth 
 angle from the south point can be com- 
 puted. But as the hour angle depends 
 upon the local time at that place, and 
 there is great room for error there, the 
 
114 
 
 observer, unless he has full confidence in 
 his ability to make an accurate time-de- 
 termination, should find the approximate 
 minute of the star's greatest elongation, 
 and follow it with the transit thread 
 until it reaches the dead point in its 
 azimuth motion, where it seems to stop 
 a few moments between its advance and 
 retrogression. Then, being at its 
 greatest elongation, the sine of its azi. 
 muth angle is equal to the cosine of its 
 declination divided by the cosine of the 
 latitude of the place. 
 
 Should the star Hydri not arrive at 
 its east or west point at a convenient 
 hour, as at certain seasons of the year it 
 will not, the star Canopus, differing in 
 right ascension about six hours, or a 
 Trianguli Australis, of about sixteen 
 hours greater right ascension, may be 
 employed. These are respectively of the 
 first and second magnitude, and hence 
 are very well adapted to this purpose, 
 but, owing to their greater polar dis- 
 tances, it would be necessary, in their use, 
 for the observer to be especially sure of 
 the correctness of his latitude. 
 
115 
 
 The sun is not usually available for 
 determinations of azimuth or time, as 
 the engineer is generally upon the march 
 throughout the day. The use of a star, 
 however, admits of greater precision in 
 the observations, while the resulting 
 computations are less complicated, and, 
 in the case of an azimuth determination, 
 a south star is doubly convenient from 
 the fact that its two daily elongations 
 always come above the horizon, and 
 whichever one occurs most opportunely 
 may be used; or it may be possible at 
 times to observe both, in which case it 
 becomes unnecessary for the engineer to 
 know his latitude. The same difficulty 
 of latitude, may also be avoided by the 
 method of equal altitudes of a star, taken 
 at several hours before and after its 
 meridian passage; the middle point be- 
 tween the two corresponding azimuths 
 will be upon the meridian. 
 
 THE METEOROLOGIST AND HIS INSTRU- 
 MENTS. 
 
 In all of his travels the meteorologist 
 will be the constant companion of the 
 
116 
 
 engineer, so as to be prepared to take 
 observations at any point that the latter 
 may designate. At the beginning of the 
 field season he will be furnished with, at 
 least, two complete sets of meteorological 
 instruments, to be carried by himself and 
 by others who may be appointed to as- 
 sist him. Each set will be composed of 
 a cistern barometer, an aneroid, maxi- 
 mum and minimum thermometers, pocket 
 thermometers, and a psychrometer, con- 
 sisting of two similar thermometers, one 
 with its bulb capable of being moistened 
 by the capillary attraction of a loose cord 
 of cotton filaments leading to it from a 
 cup of water, and the other dry, as in the 
 ordinary instrument. 
 
 Prior to taking the field he will com- 
 pare these barometers by a series of 
 readings extending through several days, 
 with some standard barometer whose er- 
 ror is known, in order to obtain the in- 
 strumental errors of the instruments at 
 hand. Throughout the season, also, he 
 will lose no opportunity for comparisons 
 with any reliable barometers that may 
 
117 
 
 be encountered, as well as for frequent 
 comparisons between these two. In this 
 manner the time of any possible disloca- 
 tion of the scale, or other source of error, 
 will be determined. 
 
 As in the rough and rapid travel of a 
 geographical survey, there is great lia- 
 bility to break the fragile glass tube 
 which contains the heavy mercurial col- 
 umn, an extra supply of barometer tubes 
 and mercury should be transported with 
 the party, and also an assortment of 
 tools and material for the filling, boiling, 
 and fitting of a fresh tube. This is a 
 delicate and difficult task, but it is one 
 in which every meteorologist should be 
 proficient. As full instructions for the 
 use and repair of meteorological instru- 
 ments have already been prepared by 
 the Commission, it is needless to repeat 
 them here. 
 
 METEOROLOGICAL OBSERVATIONS. 
 
 At every station of the survey, the 
 meteorologist will read from his instru- 
 ments the data from which the elevation 
 
118 
 
 of that point may be subsequently com- 
 puted. Nothing more is then needed 
 for the precise determination of that 
 station's position. The engineer has fixed 
 it in latitude and longitude; the mete- 
 orologist, in its altitude above sea-level. 
 The meteorological data will be more or 
 less comprehensive and will be read from 
 instruments more or less reliable, accord- 
 ing to the geographical importance of 
 the place at which they are taken. The 
 more frequent the readings, and the 
 more prolonged the series, the more 
 trustworthy will the resulting mean be, 
 and the less liable to be materially 
 affected by errors of observation, and 
 by those erratic fluctuations to which the 
 barometer is subject, owing to the con- 
 stantly varying atmospheric currents and 
 other disturbing physical conditions to 
 which it is exposed, and whose effect 
 cannot be entirely eliminated by any 
 formulas that it is possible to devise. 
 
 Beginning at the point of outfit, 
 which, on account of the work of pre- 
 paration and the measurement of the 
 
119 
 
 base-line, may be occupied some weeks 
 or a month, hourly readings will be taken 
 throughout the day and night for as 
 long a time as possible. The cistern 
 barometers will be read, as the height of 
 the mercurial column is the basis upon 
 which all barometrical determinations 
 rest. The attached thermometer will 
 be read, to learn the temperature of the 
 mercury, and hence what correction 
 must be applied to reduce it to the 
 freezing point, at which all barometrical 
 heights are compared. The isolated 
 thermometer will give the temperature 
 of the surrounding atmosphere, to be 
 used in determining the mean tempera- 
 ture of the stratum of air intermediate 
 between this and the reference station. 
 And the psychrometer will reveal the 
 amount of aqueous vapor in the atmos- 
 phere, and the influence of its pressure 
 upon the height of the column of mercu- 
 ry. In addition to these, note will also 
 be taken of the direction and force of the 
 wind, the condition of the sky, the proxi- 
 mity of storms, and other atmospherical 
 
120 
 
 phenomena, as this information may 
 give the key to some abnormal baro- 
 metric oscillation which would otherwise 
 have to remain unexplained. 
 
 HORARY AND ABNORMAL OSCILLATIONS. 
 
 The hourly observations will be con- 
 tinued throughout the day and night for 
 the purpose of determining the amount 
 of the horary oscillation at that place. 
 This horary oscillation is a somewhat 
 regular rise and fall of the barometer, 
 occupying a period of twenty-four hours. 
 The range of this fluctuation in some 
 parts of the world is so great, that its 
 effect upon the mercurial column may 
 equal that which would be produced by 
 a change of fifty meters in altitude. It 
 is such that, if the successive heights of 
 the column be represented graphically 
 by a curve, this curve will show two 
 daily maxima and minima, occurring at 
 intervals of about six hours, the morning 
 maximum being attained at about ten 
 o'clock A. M. This horary curve, as it 
 is called, varies with the latitude, alti- 
 
121 
 
 tade, and climate of a place, as well as 
 with the different portions of the year. 
 The value of the horary variation for 
 any hour of the day is revealed by a 
 study of the prolonged series of observa- 
 tions at that place, and may be assumed 
 to be the same for all observations taken 
 in the vicinity of that station and in the 
 same season of the year. 
 
 The barometer is also influenced by 
 the abnormal oscillation, apparently re- 
 sulting from the progress of great atmos- 
 pheric waves across the country, affect- 
 ing the mercurial column by a gradual 
 rise of several days, followed by a period 
 of subsidence of about an equal duration. 
 The effect of this disturbance can be 
 eliminated, approximately, by taking the 
 difference of the barometric readings at 
 the beginning and ending of any one day 
 of its rise or fall, and considering this as 
 its amount for that twenty four hours, a 
 proportional part of which will be its 
 value for one hour. 
 
122 
 
 DETERMINATION OF HEIGHTS. 
 
 To obtain the altitude of the first 
 station of the survey, a mean of the cor- 
 rected heights of the mercurial column 
 is compared with a corresponding mean 
 of the same hours of the same days at 
 some permanent station, whose elevation 
 above the sea is definitely known, as, for 
 instance, the Imperial Observatory at 
 Rio de Janeiro. This, by a process of 
 computation, gives their difference of 
 altitude, and hence the total elevation of 
 the point in question. 
 
 Now, making this point of outfit a 
 reference station, at which an observer is 
 left with meteorological instruments to 
 be read at stated intervals throughout the 
 day, the party takes the field, and the 
 traveling meteorologist reads a series of 
 barometrical and other observations at 
 the first camp and at all others to which 
 they may come during the season. 
 These will be compared, as before, with 
 synchronous* observations at the refer- 
 
 * It is well to distinguish between the meanings, as now 
 understood, of the two words " synchronous " and " sim- 
 
123 
 
 ence station, and the differences of alti- 
 tude will be calculated. At every topo- 
 graphical station, and station of import- 
 ance along the meander survey, such as 
 villages, f azendas, mines, mountain passes, 
 divides, etc., and at all other points that 
 may be designated by the engineer, the 
 meteorologist will read the cistern baro- 
 meter, the watch, the thermometer, and 
 the psychrometer, and, for the purposes 
 of comparison, the aneroid barometer as 
 well. These isolated observations will 
 also be referred to the main barometrical 
 station at a distance. 
 
 But, on the occasion of the ascent of 
 a mountain peak from a fixed camp, bet- 
 ter results will be obtained by consider- 
 
 ultaneous." The term " simultaneous " is applied to ob- 
 servations which are made at the same absolute instant 
 of time, as, for instance, upon the occultations and 
 eclipses of the heavenly bodies. Synchronous observa- 
 tions are taken at the same hour of the day, local time, 
 irrespective of the difference of longitude between the 
 two stations. Therefore, observations can be both sim- 
 ultaneous and synchronous only when the observers are 
 upon the same meridian. The word " simultaneous " 
 belongs especially to the province of astronomy, whilst 
 " synchronous " is most frequently used in connection 
 with the phenomena of physical geography. 
 
124 
 
 ing the camp a reference station in the 
 determination of the altitude of the 
 mountain. This ascent will necessitate 
 the occupancy of the neighboring camp 
 for two nights and a day at least, and 
 perhaps longer, while the peak may be 
 occupied only a portion of a day, during 
 which time, however, there will be cor- 
 responding hourly observations at camp 
 and mountain-top. Hence the altitude 
 of the mountain will be most truthfully 
 ascertained by referring it, by these syn- 
 chronous observations, to the camp, and 
 then the camp, in a similar manner, to 
 the distant reference station. 
 
 HORARY CURVES AND REFERENCE STA- 
 TIONS. 
 
 Whenever the party, or a portion of 
 it, remains stationary in camp for a few 
 days at a time, hourly observations day 
 and night will be taken to determine the 
 horary curve at that place; the longer 
 the series, the better will be the result. 
 Since the horary variations are constantly 
 changing with altitude, country and cli- 
 
125 
 
 mate, it is important to have as frequent 
 determinations of them as can practicably 
 be made, so that no very great distance 
 may intervene between the place where 
 a table of horary corrections is construct- 
 ed and the place where it is used. 
 
 For a similar reason it may be deemed 
 necessary to establish and sustain a sec- 
 ond meteorological reference station, if 
 the field of the season's survey should be 
 a wide one, or if it should vary greatly 
 in the atmospherical condition of differ- 
 ent portions of its area. No comprehen- 
 sive rule can be given to govern the num- 
 ber of these reference stations; all must 
 depend upon the judgment of the direc- 
 tor of the survey, and the resources at 
 his command. In general, the farther 
 the place of an observation from its 
 reference station, the less reliable will be 
 its result. But, as an exception, let us 
 take the example of a broad inland plain, 
 separated from the sea and its influences 
 by a wall of mountains, within which, 
 upon the plain, the reference station is 
 situated. In this case it may be more 
 
326 
 
 justifiable to refer to this station a point 
 on the plain, five hundred kilometres dis- 
 tant, than one just over the mountains, 
 only one hundred kilometres away. This 
 is owing to the widely different climatic 
 circumstances of inland and sea-coast, 
 resulting in meteorological conditions so 
 dissimilar that equal amounts of pressure 
 cannot be relied upon as an indication of 
 equal thickness of the atmospheric enve- 
 lope. 
 
 THE ANEROID BAROMETER. 
 
 At the many stations of the meander 
 survey that are comparatively unimport- 
 ant, and that are occupied for a few min- 
 utes only, it will suffice for the meteoro- 
 logist to read only his aneroid, watch, 
 and thermometer. Although the aneroid 
 is not a reliable instrument, yet it serves 
 an excellent purpose where rapid and ap- 
 proximate work is sufficient. Since its 
 principal use is in obtaining profiles of 
 the meander routes, which will enable 
 the engineer to properly distribute the 
 contour lines upon his map, and since, 
 
127 
 
 farther, the error of an aneroid will rare- 
 ly exceed the vertical distance between 
 two of these contours, the resulting inac- 
 curacy upon the plot will be quite inap- 
 preciable. 
 
 The aneroid is to the cistern barometer 
 what the meander is to the triangulation, 
 that is, a means of filling in, which, 
 while costing but little extra effort, 
 is productive of very valuable results. 
 The engineer who rejects the meander 
 and the aneroid, because they are not 
 rigidly exact in their functions, will find 
 himself reduced to the necessity of 
 tracing in the roads and streams of his 
 map, locating many of the villages, cross- 
 roads, etc., and drawing in the contours 
 from his judgment and memory alone; 
 and it is safe to say that the conjectures 
 of the most able and trained topographi- 
 cal intellect are by far less reliable than 
 the figures of those humble instruments, 
 the aneroid and odometer, when judi- 
 ciously used. 
 
 At every camp the aneroids are com- 
 pared with the cistern barometer, their 
 
128 
 
 scales are adjusted in compensation for 
 any error that may have crept in, and 
 the vertical element of the survey starts 
 from a new and true datum plane when 
 the march is resumed. At the end of 
 the day's journey, also, they are imme- 
 diately compared again, and the error 
 accumulated throughout the day is 
 noted, and, by a process of distribution 
 along the day's profile, may be reduced 
 to a minimum. Before and after every 
 side trip, reconnoissance, or ascent of 
 mountain, the aneroid is compared with 
 the mercurial barometer, and thus, by a 
 continual and careful watch over it, it 
 may be relied upon to give results not 
 seriously in error. But if left to itself 
 and unchecked for any great length of 
 time, or for any great distance of journey, 
 or great change in altitude, this fickle in- 
 strument may continue to go astray, by 
 a shifting of its scale, exhaustion of its 
 spring, or from other causes, until its 
 readings are hundreds of metres too 
 high or too low. Even then, however, 
 it may be of use to the geographer in 
 
129 
 
 drawing in the relief of the country, as 
 the discrepancy is usually of gradual 
 growth, and the relative altitudes during 
 the progress of the survey, as, for in- 
 stance, the height of a bluff above the 
 neighboring valley, are sufficiently exact 
 to be of much assistance to him in his 
 plotting. 
 
 BAROMETRICAL RESULTS. 
 
 As to the reliability of altitudes de- 
 termined by the cistern barometer, evi- 
 dences and opinions differ, but those per- 
 sons who are most thoroughly informed 
 are generally the most lenient in their 
 acceptation of results. Colonel Wil- 
 liamson, of the United States Army, who 
 has probably given more intelligent 
 study to the barometer than any other 
 man, has compiled a table of the maxi- 
 mum errors which occur in numerous 
 series of observations taken both in North 
 America and Europe. Among these are 
 many that exceed fifty meters in amount, 
 and he assumes that the barometer under 
 similar circumstances will be liable to 
 
130 
 
 equal errors elsewhere. These, however, 
 are not to be considered as representing 
 the probable error of barometrical re- 
 sults; they are rather the extreme limits 
 of probable error, and may be taken as 
 the error to which the barometer is liable 
 under certain rare and very unfavorable 
 conditions. While exact truth concern- 
 ing altitudes is something which no 
 barometer can be expected to tell, and 
 while it is never safe to guarantee the 
 accuracy of such a determination, even 
 within many meters, yet when baro- 
 metrical work is prosecuted judiciously 
 and systematically, as it would be in this 
 survey, and based upon formulas which 
 represent the latest and most complete 
 knowledge of meteorology, its tendency 
 is to give results that are seldom more 
 than a few meters wrong. 
 
 It is often difficult for the popular 
 mind to comprehend how an error of 
 meters may be inevitable in some of the 
 processes of barometric hypsometry. 
 Since the scale of a barometer may be 
 read to a thousandth of an inch, and that 
 
131 
 
 amount of variation is supposed to cor- 
 respond to a change of one foot in alti- 
 tude, it would naturally be thought 
 possible to determine the elevation of a 
 place to the nearest foot. But this diffi- 
 culty will be better understood when it 
 is remembered that the barometrical 
 measurement of the difference of altitude 
 between two places depends upon the 
 determination of the weights of a column 
 of atmosphere at each of these stations; 
 that this atmosphere is in a state of con- 
 stant change and perturbation, its press- 
 ure being modified by variations of heat 
 and cold, storm and calm, and the 
 absence and presence of moisture through- 
 out different portions of its extent; and 
 that, while some of these conditions are 
 quite unknown to the observer, those 
 that are apparent to him can be but in- 
 completely compensated for. There- 
 fore, since barometric hypsometry is not 
 one of the exact sciences, but is affected 
 by every change in the wind and 
 weather, any determination of altitude 
 that is true within a meter is as much 
 
132 
 
 a source of surprise as of gratification to 
 the meteorologist, who will be obliged 
 to confess that this closeness could 
 scarcely be possible without some coin- 
 cidence and accidental equilibrium in 
 the disturbing influences to which the 
 barometer is subject. 
 
 DIFFICULTIES IN BAROMETRIC 
 HYPSOMETRY. 
 
 At times men of little experience may 
 have to be accepted as meteorologists. 
 They work, perhaps, under the embar- 
 rassments of exposure, fatigue, and a 
 lack of appreciation of the responsibilities 
 that rest upon them. It may be long 
 before they can be taught to regard 
 those niceties of barometrical work with- 
 out which it cannot be truly successful; 
 although there is but little hope of 
 determining an altitude to the single 
 foot, yet they have to learn that this is 
 no reason for neglecting that thousandth 
 of an inch which corresponds to a foot. 
 Their instruments may be out of order, 
 owing to the hardships of travel to which 
 
133 
 
 they are exposed; the readings may have 
 to be referred to a distant station of very 
 dissimilar physical surroundings; or they 
 may have been taken upon the top of a 
 lofty mountain, in a belt of the atmos- 
 phere with meteorological phenomena 
 quite different from those properties of 
 the lower strata of the air, for which 
 our formulas were framed. 
 
 These are some of the sources of error 
 which may have conspired to vitiate 
 those results which are fifty meters or 
 more at fault. In Brazil, however, it is 
 hardly necessary to anticipate discrepan- 
 cies so great as this, since it is a country 
 in which no very great change of alti- 
 tude is possible, violent and phenomenal 
 storms are not frequent, and the atmos- 
 phere is of comparatively steady tem- 
 perature, and not liable to sudden transi- 
 tions from one extreme to the other. 
 
 BAROMETRIC FORMULAS. 
 
 Even if the observations have been 
 made under the most favorable condi- 
 tions of atmosphere, elevation and loca- 
 
134 
 
 tion, and are perfect as far as human in- 
 telligence can make them so, that is, free 
 from all personal and instrumental er- 
 rors, there yet remains a consideration 
 which may materially affect the com- 
 pleted altitude. The same observations, 
 reduced by different formulas, will give 
 results in some cases widely different, 
 the discrepancy between the returns of 
 two well-authorized methods of compu- 
 tation frequently amounting to the sum 
 of the real errors of both; this is ex- 
 emplified in the following determination 
 of the height of Corcovado, in which one 
 system of reduction gives an altitude 
 above the true one, and the other places 
 it too low. 
 
 The barometric formula is composed 
 of several terms, each of which is a com- 
 bination of some physical constants, such 
 as the relative weight of air and mercury, 
 or the variation of gravity with latitude, 
 and some of the barometrical data, as 
 the temperature or moisture of the at- 
 mosphere. Of these formulas, there are 
 two general classes, based upon the equa- 
 
135 
 
 tions of Laplace and Bessel. Not only 
 do they differ in those constant quanti- 
 ties upon which all barometrical determ- 
 inations must depend, but also in the 
 presence or absence of an entire term, as 
 the formula of Bessel has a separate fac- 
 tor as a correction for the humidity of 
 ,the air, while Laplace includes the in- 
 fluence of the aqueous vapor with that 
 of temperature. 
 
 Thus it will be seen that the formula 
 of Laplace is more convenient, while that 
 of Bessel is more complete. The scien- 
 tific world has found it difficult to choose 
 between them, and while Delcros, Guyot> 
 and others have accepted the formula of 
 Laplace, that of Bessel has been adopted 
 by Plantamour, Williamson, and others. 
 But it is admitted, even by those who 
 are in favor of the former method, that 
 the constants in use in Bessel's formula, 
 as modified by the more recent arrange- 
 ment of Plantamour, are later and more 
 reliable than those accepted by Laplace, 
 and there is also a prevalent opinion 
 among scientists that some accuracy has 
 
136 
 
 been sacrificed to convenience in La- 
 place's method, a concession which it may 
 sometimes be justifiable to make in the 
 application of a formula, but never in 
 its construction. 
 
 The advocates of each system have 
 published examples showing the close 
 accordance of their results with altitudes 
 determined trigonometrically or by spirit- 
 level. But as the number of these re- 
 markable coincidences is about equal on 
 each side, and as in each instance the 
 observations would have given results 
 considerably wrong by the application of 
 the other formula, they prove simply two 
 things; first, that they are coincidences, 
 and that to certain cases the method of La- 
 place is more applicable, while to others 
 that of Plantamour will yield better re- 
 turns; and second 3 that it is quite impos- 
 sible to devise any formula that will 
 yield an accurate solution of all problems 
 in the barometrical measurement of 
 heights. 
 
 Since there seems to be a preponder- 
 ance of evidence and a growing disposi- 
 
137 
 
 tion in favor of Plantamour's formula, it 
 has already been adopted by the Geo- 
 logical Commission as a basis for its 
 barometrical work, and its several terms 
 have been developed into tables for the 
 convenient computation of altitudes. 
 After the preparation of those tables and 
 as a test example with which to prove 
 their efficacy, the height of Corcovado 
 Peak was determined barometrically 
 with the following results: 
 
 Metres. 
 
 Altitude of Corcovado, by tables of the 
 commission, based upon Planta- 
 mour's formula 705 .84 
 
 By Laplace's formula 702.15 
 
 Determined by triangulation 704.74 
 
 Metres. 
 
 Error by Plantamour's formula +1.10 
 
 " Laplace's " 2.59 
 
 Discrepancy between the two 3.69 
 
 The foregoing is a very creditable and 
 satisfactory barometrical result, and is 
 one more argument in favor of the use 
 of Plantamour's complete formula. 
 
 ALTITUDES BY VERTICAL ANGLES. 
 
 As a supplement to the barometric 
 
138 
 
 hypsometry, every theodolite, whether 
 for meanders or triangulation, is fitted 
 with a vertical circle, from which to read 
 the angles of elevation and depression of 
 those points which are located by inter- 
 sections, in order to compute the heights 
 of the same. From this angle and the 
 horizontal distance between any two 
 peaks, their apparent difference of alti- 
 tude is obtained by a trigonometrical 
 calculation, and then a correction is ap- 
 plied for earth's curvature and refrac- 
 tion. In the field these angles are 
 recorded as plus or minus, according as 
 the objective point is above or below the 
 observer's station, whose altitude is in- 
 variably determined by barometric read- 
 ings. 
 
 In this manner the heights of hund- 
 reds of points throughout the field of 
 survey are found with an accuracy 
 nearly equal to that of the peak from 
 which the angle is taken. Indeed, a 
 mean altitude derived from the three 
 angles of elevation, read from three 
 different triangulation stations, will give 
 
139 
 
 the altitude of the point of intersection 
 with less probable error than that of 
 either of the mountains from which it 
 was derived. 
 
 METEOROLOGY IN THE SOUTHERN HEMI- 
 SPHERE. 
 
 Brazil stands almost alone as a great 
 civilized country lying in the Southern 
 hemisphere. It is comprehensive in its 
 latitude, reaching from north of the 
 equator far into the south temperate 
 zone. From this unique and favorable 
 position upon the earth's surface, as well 
 as from the liberal patronage bestowed 
 by its government upon the de- 
 velopment of science, it needs no 
 prophetic eye to see that this em- 
 pire is destined to become one of the 
 busiest and most fruitful fields of scien- 
 tific research. Especially is this the case 
 in the investigation of those great ques- 
 tions concerning the terrestial shape and 
 dimensions, and those others, still more 
 numerous, which from the form of the 
 earth, or from other and unknown 
 
140 
 
 causes, vary with geographical position. 
 Important among the latter is the science 
 of meteorology, whose general laws are 
 not the same all the world over, but 
 which are largely influenced by latitude 
 and by proximity to either pole. 
 
 The following extract from Colonel 
 Williamson's valuable treatise on the 
 barometer and its uses, will illustrate 
 the absence and the need of meteorologi- 
 cal observations south of the equator: 
 
 " It has been determined by actual ob- 
 servations, and confirmed by theory, that 
 the sea-level pressure varies in different 
 latitudes by a definite law, modified in 
 practice by local peculiarities of climate. 
 It has been found that the mean baro- 
 metric pressure is less in the immediate 
 vicinity of the equator, and it increases 
 towards the north to -between latitude 
 30 and 35 where it is greatest. It then 
 gradually decreases to about latitude 60 , 
 and from there towards the north pole 
 there is a slight increase. In the south- 
 ern hemisphere, where the observations 
 have been less numerous, the mean 
 
141 
 
 pressure seems to increase to between 
 20 and 30 of south latitude, when it 
 gradually decreases to about 42, and 
 then commences a remarkable fall, so 
 that towards the south pole, the mean 
 pressure is said to be less than 29 
 inches."* 
 
 In the table of mean heights of the 
 barometer at the sea-level, given in 
 various works on meteorology, there are 
 but two stations south of the equator; 
 these are Rio de Janeiro and the Cape of 
 Good Hope. In north latitude, however, 
 the list comprises more than thirty 
 places at which this determination has 
 been satisfactorily accomplished, by 
 years of observations, and these are 
 favorably situated at intervals between 
 the equator and the pole. 
 
 Again, while the horary oscillation in 
 the atmospheric pressure is greatest 
 near the equator, and diminishes thence 
 each way to the poles, the abnormal 
 oscillation is least in regions of small 
 
 * T36.6 millimetres. 
 
142 
 
 latitude, and increases with the distance 
 from the equator. As the latter is 
 the more incomprehensible and less 
 regular of the two, and consequently the 
 greater source of error, it would appear 
 that, in general, barometrical work would 
 be most reliable in tropical regions, and 
 hence this system of hypsometry would 
 be especially applicable to Brazil. And, 
 in addition to their immediate and prac- 
 tical use in the construction of maps, the 
 meteorological results of a survey of the 
 proposed nature, taken at low and high 
 altitudes, at the sea-coast and in the 
 remote inland, with permanent stations 
 at intervals where long series of obser- 
 vations would be accumulated, would 
 form a basis upon which to establish the 
 general laws of barometric fluctuation 
 throughout this vast portion of the 
 Southern hemisphere. 
 
 CONTINGENCIES IN THE SURVEY. 
 
 The foregoing are the general divi- 
 sions and some of the novel features of 
 the geographer's work in the field. 
 
143 
 
 While these are sufficient to carry the 
 survey across any ordinary country, cer- 
 tain districts may be encountered in 
 which these methods may not be easily 
 applicable. It is impossible, in a paper 
 of this nature and length, to foresee and 
 provide for all of the emergencies that 
 may arise; it is necessary for the geog- 
 rapher to first see his territory, and then, 
 if he is a true engineer, he will be able 
 to devise some means of survey which 
 will be competent to meet the difficulties, 
 however great they may be. 
 
 For instance, it may be asked how a 
 survey based upon triangulation can be 
 carried across the smooth and unbroken 
 table-lands of a country. The answer 
 will be that the plains are not usually so 
 broad that they cannot be spanned by 
 the length of a triangle-side ; and, 
 furthermore, if there are no eminences 
 that can be used for triangulation points, 
 so much less is there need for this system 
 of survey. Over the smooth plain it is 
 possible to travel in straight lines, such 
 being the usual character of roads in a 
 
144 
 
 level country, and since a meander by 
 direct routes is reliable, the survey can 
 proceed from one known point to the 
 next with comparative accuracy, tracing 
 in the rivers, lakes, and. other geographi- 
 cal features as it goes. As a rough, 
 mountainous country is*its own remedy, 
 furnishing a great number of advantage- 
 ous stations for the survey, so, with the 
 absence of these mountains, vanishes in 
 great part the labors and difficulties of 
 this work. 
 
 THE STADIA, OK TELEMETER. 
 
 Although the stadia, or telemeter pro- 
 cess, is too slow for the general prosecu- 
 tion of a geographical survey, there may 
 be occasional areas in which the previous 
 methods will fail, and this will suffice. 
 The direct linear survey of a river, by 
 this means, has already been mentioned. 
 As another illustration, take the case of 
 a valley as, for instance, the valley of 
 the Amazon which is so broken with 
 lakes, swamps, and the many channels 
 and arms of the river, that its islands 
 
145 
 
 and shores cannot be reached and located 
 by any means of direct measurement; 
 and where, farther, the vegetation is so 
 abundant and dense, that ordinarily no 
 three fixed points are visible from the 
 water's edge. Here the telemeter may 
 be the only instrument by which the re- 
 quired distances may be obtained. The 
 observer, establishing his instrument in 
 open ground, from which triangulation 
 stations can be seen, sends his assistant, 
 in a boat or otherwise, to such points 
 along the water as may be in sight. 
 These he locates by single observations, 
 reading the distances from the rod held 
 by the assistant. Thus the telemeter 
 station is referred to the observer's posi- 
 tion, which, in its turn, can be fixed by 
 means of three- point observations upon 
 the triangulation stations of the border- 
 ing cliffs. 
 
 In this simple and ingenious way of 
 determining distances by single observa- 
 tions, it is necessary that the diaphragm 
 of the telescope of the observer's instru- 
 ment should be fitted with two horizon- 
 
146 
 
 tal cross-wires, and that his assistant 
 should be furnished with a graduated 
 rod, or telemeter. Then looking through 
 the telescope, the projection of the cross- 
 wires upon the rod includes a certain 
 amount of the graduation. This is a 
 chord subtending a certain constant 
 angle in the line of collimation, and, by 
 a principle in geometry, this chord in- 
 creases directly with its distance from 
 the angle which it subtends. 
 
 THE PLANE TABLE. 
 
 With the use of the plane table, there 
 comes so great a temptation to go into 
 the details of the work, to linger over a 
 small area, and to finish the sheets with 
 a topographical completeness, that its too 
 general adoption will be found to retard 
 the progress of a geographical survey. 
 In addition, it is cumbersome in its 
 shape, offering a broad surface of ex- 
 posure, and for that reason is not well 
 fitted for service upon high mountain 
 stations, where the wind is strong and 
 storms are frequent. In its favor, how- 
 
147 
 
 ever, it must be said that this instru- 
 ment has been successfully employed 
 upon the extensive geological and geo- 
 graphical surveys under Major J. W. 
 Powell, of the United States, and that 
 very favorable reports have been made 
 concerning its usefulness. The incon- 
 venience of its shape has been modified 
 in this service, the table being composed 
 of slats hinged together, so that it may 
 be folded into a small compass for the 
 purpose of transportation. 
 
 When, in the course of a work of this 
 nature, there is encountered a district 
 where the importance of the field will 
 justify a minute and laborious survey, 
 the plane-table will serve an excellent 
 purpose there. It is very useful in the 
 mapping of a populous district, the 
 suburbs of a city, a mining region, or in 
 the representation on large scale of a 
 piece of topography which is interesting 
 as a type of geological structure. It is 
 always an easy matter for the geogra- 
 pher to accommodate himself and his 
 methods to detailed surveys like the 
 
148 
 
 above, and it is a mistaken idea to sup- 
 pose that the exploration of a province, 
 unfits an engineer for the topographical 
 delineation of a parish. In all work of 
 engineering there is a constant tendency 
 towards greater accuracy, refinement, 
 and detail, and it is not freedom which 
 the geographer enjoys, in neglecting the 
 minor features of the earth's surface, 
 but rather a necessary restraint that is 
 imposed upon him, to keep him from 
 sacrificing the important to the unim. 
 portant. 
 
 THE OFFICE WORK. 
 
 As for the computations and other 
 reductions of notes which follow a field 
 season of the survey, there is not space 
 to discuss them here, nor is there any 
 special need of such a discussion, as they 
 do not differ materially from those 
 which apply to geodetic work in general. 
 Nor are the duties of the draughting- 
 room greatly distinguished above the 
 customary routine of such office work. 
 This thing only, may be noticed, that 
 
149 
 
 the hand-to-hand struggle which the 
 field engineer constantly sustains with 
 the forces and obstacles of nature blunts 
 the delicacy of his touch, and makes his 
 hand too heavy for the fine drawing 
 necessary in a map finished for publica- 
 tion, and there should be in every office 
 a superior draughtsman who is accus- 
 tomed to the use of no heavier imple- 
 ment than the artist's pen. 
 
 This artistic finish is bought by some 
 sacrifice of accuracy, however, and be- 
 tween the field engineer and the final 
 draughtsman there should be few, if any, 
 middlemen to compile and replot the 
 work, because only the man who has 
 seen the country can reproduce its physi- 
 cal characteristics with truthfulness. 
 In every copy that is subsequently made 
 the face of the land grows more artifi- 
 cial and ideal; each mountain loses its 
 individuality of shape, and assumes a 
 symmetrical regularity which it does 
 not possess in nature; some of the nice- 
 ties of truthful representation are mag- 
 nified into exaggeration, and others are 
 
150 
 
 overlooked and obliterated; the bed of 
 every canon grows broader in each suc- 
 cessive transcript; and the large hills 
 grow larger as the smaller ones dwindle 
 away. As in a popular parlor game, a 
 whispered story, passing current from 
 mouth to mouth throughout the round 
 of a circle, grows strange and distorted 
 beyond recognition, so in the successive 
 reproductions of a map by strange 
 hands, it loses its photographic truth of 
 execution as the idiosyncracies of the 
 various draughtsmen are wrought into 
 the plan. Finally it comes to represent 
 a country that is unnatural in its regu- 
 larity, made not so much by the acci- 
 dents of nature as by the design of 
 man, and moulded by the rules of a uni- 
 form and rigid geometry. 
 
 PLOTTING THE NOTES. 
 
 It is necessary that each engineer 
 shall plot his own notes, as he alone is 
 familiar with their arrangement through- 
 out his books, and only he is able to de- 
 rive the full benefit from them. There- 
 
151 
 
 fore during the office season he will be 
 engaged upon a contour plot of the area 
 which he has surveyed during the pre- 
 ceding half of the year. Here he will 
 collect and compile in graphic shape all 
 of x the information which lies scattered 
 throughout the dozen note and sketch- 
 books which represent his labors in the 
 field. Upon this map fine drawing will 
 not be so essential as truthful representa- 
 tion and the utmost accuracy of position 
 that can be attained from the material 
 at hand; an inaccuracy that is barely 
 apparent upon the paper will correspond 
 to a very large error in the field, and so 
 a moment's oversight in the office may 
 invalidate the scrupulous care of a day's 
 or week's work upon the survey. 
 
 These sheets will be the basis of all 
 the maps of the survey, no matter in 
 what shape they may be published, and 
 hence the urgency of having them correct 
 in all of their positions, statements and 
 figures, and so complete as to include 
 every detail upon the pages of the 
 sketch-books, down to the shape of a 
 
152 
 
 mountain-spur or village, or the presence 
 of a spring of water or dwelling place. 
 As the expense of sustaining an engineer 
 in the field is at least double the cost of 
 his office-work, he should confine himself 
 to what is absolutely necessary in the 
 collection of his notes, and then utilize 
 even the least of these in his subsequent 
 plotting and development of them. 
 
 CONTOUR PLOTS. 
 
 The plots will be constructed in con- 
 tour lines, as that is the only method in 
 which the engineer can give precise ex- 
 pression to his information and impress- 
 ions concerning the heights, slopes, and 
 forms of the country that he has sur- 
 veyed. While a map executed in 
 hachures would be more artistic and 
 more pleasing to the eye, it cannot be 
 made so mathematically invariable in its 
 conveyance of ideas, that is, it cannot be 
 made to convey the same ideas to all 
 persons; the bluff that would seem high 
 to one observer would seem low to 
 another, and the depth of shade that 
 
153 
 
 would represent a steep gradient to one 
 draughtsman would stand for a moderate 
 declivity to another, according to their 
 peculiarities of judgment, or to the 
 different schools of drawing in which 
 they had been educated. The most 
 skilled cartographer, with one of the 
 best of hachure maps before him, would 
 find it difficult to estimate the angle of 
 any mountain slope, or to tell which of 
 two neighboring peaks was the highest, 
 unless their heights were given in figures. 
 In a glance at a contour plot, however, 
 he could count the excess of lines in one 
 of these mountains, and so compute its 
 superior altitude; or note the number of 
 lines in a centimeter of space, and so 
 determine the gradient of the earth's 
 surface there. For this reason the con- 
 tour plot is the only true basis from 
 which subsequent maps can be made; 
 then, no matter how many field engi- 
 neers may contribute to this work, their 
 reports will all come to the compiler and 
 final draughtsman, written in the uniform 
 language of lines at regular vertical in- 
 
154 
 
 tervals. Otherwise, if the plots were in 
 hachures, this draughtsman would find 
 it well-nigh impossible to so assimilate 
 them that his finished map would not 
 reveal traces of the many different hands 
 from which it originated. 
 
 FINAL MAPS. 
 
 Unless the contour lines are so numer- 
 ous and close together as to produce 
 striking contrasts of light and shade as 
 the slope varies, this map has no mean- 
 ing to the popular eye. The ordinary 
 observer sees in it only a maze and con- 
 f vision of lines, of whose design and 
 importance he is ignorant, and so it is of 
 no assistance to him. Therefore, since 
 maps are usually published for the in- 
 formation and guidance of the people at 
 large, it is wise that they should be 
 drawn with hachure shading, which 
 gives a more intelligible but less precise 
 picture of the country. In the construc- 
 tion of this, the contours of the engineer's 
 plot are so many guide-lines to the 
 draughtsman, who graduates the light 
 
155 
 
 and darkness of the shade to accord with 
 the divergence or approach of these 
 wavering lines. 
 
 In addition to these a map in contours 
 may also be issued for the use of engi- 
 neers, the projectors of railways, and, 
 more especially, as a basis of the geo- 
 logical and resource charts, to which 
 this system is peculiarly adapted, as its 
 lines of equal level are of great assist- 
 ance in determining the extent of the 
 various formations, and for depicting 
 those areas of vegetable growth which 
 are bounded by fixed limits of altitude. 
 The dip and strike of a bed of uniform 
 slope being given at any one point of its 
 outcrop, it is an easy matter to trace 
 upon this map its line of reappearance 
 upon the farther side of a mountain- 
 range, or at any other point at which it 
 may be exposed again. Or, by counting 
 the lines of vertical equi-distance, the 
 geologist learns the thickness of the vari- 
 ous strata, the extent of a fault, or any 
 other fact in geological dimensions. 
 
156 
 
 REVIEW OF THIS METHOD OF SURVEY. 
 
 In this paper the writer is at a disad- 
 vantage in appearing to advocate inac- 
 curate methods, and perhaps, at times, 
 actuated by a desire to give a perfectly 
 frank and honest expose of the subject 
 under discussion, he has magnified the 
 amount of inaccuracy to which the 
 operations described in these pages 
 would be liable; at all events he has 
 been very liberal in his allowance for 
 probable error. Indeed, to those who 
 have been in the habit of reading, and 
 believing, barometrical altitudes that are 
 given down to the tenth of a foot, or 
 sextant determinations to the hundredth 
 of a second, it may appear unpardomibly 
 liberal to allow for an error of meters or 
 seconds in these classes of work, and 
 perhaps to some it may seem indicative 
 of professional unfitness in the engineer 
 who would acknowledge the liability of 
 such. But while results like the above 
 are frequently published, their authors 
 would be either sciolists or charlatans if 
 they were to claim that they were abso- 
 
157 
 
 lately reliable down to those small 
 fractions; it is often the custom among 
 the most conscientious and intelligent 
 engineers to make their reports in that 
 elaborated form, since those are the 
 figures at which their computations 
 finally arrived, and hence there are cer- 
 tain weights of probability in their 
 favor. 
 
 In like manner, in the computations of 
 a survey of the proposed nature, it would 
 never be allowable to neglect or throw 
 away any odd figure or fraction, on the 
 plea that it was probably exceeded by 
 the error of the whole. By following 
 this system, not only are habits of accu- 
 racy inculcated and sustained among the 
 assistants of a survey, but the closest 
 possible approximation to the truth is at- 
 tained. 
 
 In the ordinary branches of his profes- 
 sion, habits of rigid precision, at what- 
 ever cost of time and money, are the 
 best recommendations for an engineer. 
 In a geographical survey, however, to 
 enforce this rule beyond .the triangula- 
 
158 
 
 tion, upon which the integrity of the 
 whole depends, and to continue it in full 
 force throughout all of the subordinate 
 branches of the work, would be to make 
 such a survey impossible in Brazil, owing 
 to the enormous expense that would at- 
 tend it. Viewed theoretically, the best 
 of maps, even those produced by the 
 tedious processes of the European topo- 
 graphical surveys, are but approxima- 
 tions to the truth; the question now 
 arises as to how close it is profitable to 
 bring this approximation. Viewed prac- 
 tically, the maps that would result from 
 the proposed system of survey would be 
 seldom, if ever, in error to a perceptible 
 degree, and it would seem that this is 
 the limit of accuracy bayond which this 
 country cannot well afford to go. 
 
 To condemn a method of surveying 
 because it is not absolutely accurate 
 would be to condemn all of the survey 
 of the world, and especially all of the 
 systems of ordinary land surveying, 
 which are so faulty that it is very sel- 
 dom that a purchaser of land does not 
 
159 
 
 get either considerably more or less than 
 he pays for. Still, that has not been 
 deemed sufficient reason why all buying 
 and selling of real estate should cease 
 until its boundaries could be determined 
 by the instrumentality of such rods, com- 
 pensated for temperature or packed in 
 ice, as are used in the measurement of 
 geodetic base-lines. In one respect the 
 proposed system is far superior to the 
 land survey, as it is founded upon the 
 principle of triangulation, which, secur- 
 ing it in its true proportions, prevents 
 any great accumulation of error. In the 
 United States of North America, where 
 surveys of this nature are in active and 
 successful operation, it has been earnestly 
 advocated that the triangulation of the 
 geographical survey should be made the 
 basis of the land survey, the different 
 triangulation stations serving as initial 
 points from which to run the land bound- 
 aries, and it is very probable that, with- 
 in a year or two, this plan will be 
 adopted there. 
 There are different degrees of accu- 
 
160 
 
 racy, each adapted to the end which it is 
 intended to serve; this degree, explained 
 here, is sufficient for the rapid prepara- 
 tion of a very useful and complete 
 geographical map. It would not suffice 
 for the measurement of an arc of the 
 meridian r such as has been proposed for 
 this empire. That is a work in which 
 no error, however small, that is not be- 
 yond the cognizance of the human 
 senses and judgment, can be excused or 
 overlooked. To publish a wrong result 
 here would be not only a national dis- 
 grace, but a misfortune to the whole 
 world, as it is upon the shape and dimen- 
 sions of the earth that many of our 
 geodetic and other scientific formulas 
 rest, while it is from the same source 
 that the world derives its standard unit 
 of length, by which the interests of all 
 civilized people are affected. Or, if 
 Brazil were prepared to enter into that 
 honorable rivalry in geodetic work, in 
 which some of the older nations are en- 
 gaged, each seeking to produce instru- 
 ments, methods, results, discoveries, and 
 
161 
 
 developments that may be in advance of 
 everything hitherto achieved, this sys- 
 tem of survey would not be recom- 
 mended. It is not impossible, however, 
 that, from this as a beginning, there 
 might grow, keeping pace with the gen- 
 eral progress of the country, a geodetic 
 institution that would be equal to the 
 best. 
 
 ORIGIN OF THIS SYSTEM. 
 
 The writer by no means pretends to be 
 the inventor of the combination of 
 methods described in these pages, al- 
 though hitherto there has been but little 
 description of them in print. An effi- 
 cient system of survey cannot be the in- 
 vention of any one man; it must be the 
 outgrowth of years of practical expe- 
 rience, resulting in the gradual accumu- 
 lation of ideas and improvements con- 
 tributed by those who have been en- 
 gaged upon it. This one is the result of 
 a growth of at least a quarter of a cen- 
 tury, and therefore is not open to the 
 serious objection of being new and un- 
 
162 
 
 tried. During that length of time, the 
 enterprise of geographical surveying 
 has been receiving more and more en- 
 couragement from the government of 
 the United States, which has wisely 
 adopted that plan, in connection with 
 geological and other scientific research, 
 as a means of opening and illustrating 
 its vast public territory. 
 
 At the present day there are actively 
 engaged upon this duty in that country 
 three important commissions of survey. 
 That of Dr. F. V. Hayden, geologist in 
 charge, is known throughout the world 
 by its extensive and important work, not 
 only in geology and geography, but in 
 all their kindred sciences as well. A 
 second is under Major J. W. Powell, the 
 intelligent geologist and intrepid ex- 
 plorer who was the first to descend the 
 great canon of the Colorado River. An- 
 other, more strictly geographical in its 
 nature, is under the auspices of the War 
 Department, and is conducted by Lieut. 
 George M. Wheeler, an officer of envia- 
 ble reputation in the United States Corps 
 
163 
 
 of Engineers. While the general plan 
 is much the same throughout these 
 three commissions, it is especially to his 
 former associates, the geographers and 
 officers of the last-named organization, 
 that the writer wishes to acknowledge 
 his indebtedness for whatsoever of value 
 there may be in this paper. 
 
 BRAZIL AND THE UNITED STATES. 
 
 Although, as has been stated hereto- 
 fore, it is not wise for any nation to copy, 
 blindly, and without adaptation to its 
 own peculiar needs, the system of sur- 
 vey employed by any other country, yet 
 it would seem that the processes that are 
 fitted to the United States would require 
 but little modification to be adapted to 
 use in Brazil, so analogous are the two 
 countries in many respects. They have 
 equal amounts of territory as near as 
 may be, but, peopling this territory, 
 there are four times as many inhabitants 
 in the United States as there are in 
 Brazil; thus it would seem that the me- 
 thods that are deemed sufficient for the 
 
164 
 
 former would certainly suffice for the 
 latter. In each country the population 
 diminishes from a thickly-settled sea- 
 coast back into an uncivilized and almost 
 unknown interior. In each of these 
 there is a great amount of wild land 
 which the government is anxious to open 
 to colonization and cultivation. To ex- 
 pose and popularize the natural wealth 
 of this public domain, the U. S. Govern- 
 ment resorted to the plan of scientific 
 surveys, to which the Geological Com- 
 mission of Brazil is very similar in all 
 respects, and so efficiently have they 
 accomplished their purpose that it has 
 become a noticeable fact in the cartog- 
 raphy of the United States that its maps 
 of some of the remote and unsettled dis- 
 tricts of the Rocky Mountains are 
 superior to those of its oldest and richest 
 States, and, therefore, there are now 
 plans on foot looking to the extension of 
 these geographical surveys over the en- 
 tire surface of the country. 
 
 As the American manner of railway- 
 building, more expeditious and involving 
 
165 
 
 less first cost than the European methods, 
 has been found practicable in Brazil, in 
 some instances, in which all other plans 
 would fail, so with this question of geo- 
 graphical surveys, it may prove to be the 
 American system or none. 
 
 RESULTS OF THIS SYSTEM. 
 
 Considering now the results that could 
 be expected from such a geographical 
 survey of Brazil, this question can be 
 best answered by referring to areas sur- 
 veyed in the same manner in the United 
 States. From Lieut. Wheeler's annual 
 report, which the writer has before him, 
 it appears that in six years' continuance 
 of his commission an approximate extent 
 of 800,000 square kilometres has been 
 surveyed. Allowing an average of five 
 parties in the field during that time, the 
 season's work of one engineer reduces 
 itself to about 25,000 square kilometres. 
 Allowing proportional returns from the 
 various other geographical surveys at 
 present in commission, or that have been 
 in existence during the last ten years in 
 
166 
 
 the western portion of the United States, 
 it appears that one-third of the area of 
 that great country has been thus sur- 
 veyed in that period. 
 
 This is at a total expenditure which, 
 while including the cost of all other 
 concomitant scientific labors, to which 
 the geographical work has been in large 
 part incidental and tributary, has never 
 exceeded four hundred contos ($ 200,000) 
 per year. There is probably no other 
 department of public enterprise which 
 has yielded so extensive and valuable re- 
 turns for an equal amount of money. 
 
 AN ESTIMATE FOR ONE SEASON. 
 
 In general, an area of from 10,000 to 
 30,000 square kilometres, varying ac- 
 cording to the geographical nature of 
 the country, is assigned to each party 
 for a season of four, five, or six months, 
 and its ability to satisfactorily cover 
 that district in that time is conceded. 
 To illustrate the possibility of such rapid 
 progress, let us take a typical area of 
 20,000 square kilometres and see what 
 
167 
 
 can be done with it by one party and 
 one geographer in one season's work of 
 six months in duration. Of this time 
 the first month will be consumed in the 
 measurement and development of the 
 base, and in other preparation. Of the 
 remaining period one month more will 
 perhaps be lost in unavoidable delays 
 resulting from storms or other causes. 
 There will then remain four months, 
 which, at twenty-five available days in 
 each, will afford one hundred days for 
 active service in the field. 
 
 Allow one half of these days for the 
 meander survey, and the other half for 
 the occupation of mountain stations. 
 Fifty mountain stations will thus result, 
 and, in addition to these, there will be a 
 topographical station either upon or 
 adjacent to each day's meander. So 
 there are one hundred triangulation and 
 topographical stations distributed at 
 judicious intervals over this territory. 
 That is, there is one for every two 
 hundred square kilometres of ground, or, 
 typically, they are but about fourteen 
 
168 
 
 kilometres apart, and the piece of coun- 
 try to be sketched in contours need not 
 extend more than seven kilometres in 
 each direction; this estimate ignores the 
 meander surveys, to which fifty days of 
 the season will be devoted, and by which 
 these stations will be separated and sur- 
 rounded. 
 
 At twenty-five kilometres a day, a very 
 reasonable allowance, the total distance 
 of meander route will be 1250 kilometres. 
 This distance would reach across our 
 area nine times, cutting it into strips of 
 sixteen kilometres in width. Hence, in 
 order to include the entire country from 
 this survey, the typical zone of each 
 meander would not reach more than 
 eight kilometres on either side of its 
 path; but, since it would be superfluous 
 to sketch from this base the country in 
 the immediate vicinity of the mountain 
 stations, these plots en route need never 
 extend more than four kilometres from 
 the central line. Of course, in practice, 
 these surveys will not be thus distributed 
 in straight lines at equal distances apart, 
 
169 
 
 but will communicate, intersect, and 
 duplicate in every possible way. Still 
 the meander will serve its original pur- 
 pose of penetrating those regions and 
 traversing those border-lands that are 
 remote from the mountain stations, and 
 will trace out the roads, trails, and im- 
 portant streams, whose entire length in 
 this area will not be likely to exceed 
 1250 kilometres. 
 
 Returning to the office at the end of the 
 season, the engineer will have material 
 enough to make a plot of the country on 
 a scale of one centimetre to the kilo- 
 metre (100*000)? or one-half a centimetre 
 to the kilometre (^-oSror)' Or, to put 
 this statement with more precision, he 
 will have so much and so detailed mate- 
 terial,that he will not be able to portray 
 it conveniently and intelligibly on a scale 
 of less than 3-^-^0 o- But when the 
 final draughtsman comes to copy these 
 plots, he may condense them, if it be 
 thought expedient, to proportions of 
 TToVsr* or even smaller. On the other 
 hand, portions of this area may be plot- 
 
170 
 
 ted upon a much larger plan than any 
 here noticed, should such be found nec- 
 essary for the clear and complete geo- 
 graphical and geological representation 
 of the same. 
 
 EUROPEAN SURVEYS. 
 
 Now, in contradistinction to the above 
 showing, let us take up the reports of 
 some European surveys. In Prussia, 
 12,000 square kilometres, a little more or 
 less, are surveyed annually, at a cost of 
 800,000 marks, or, as near as may be, 
 four hundred contos of Brazilian money,* 
 exclusive of the salaries of military as- 
 sistants; notice that in the United States, 
 with a total annual appropriation not 
 greater than this, at least 300,000 square 
 kilometres are geographically surveyed 
 each year, this territory being studied at 
 the same time by the geologist, the 
 chemist and the naturalist. 
 
 Upon the Ordnance Survey of Great 
 Britain there were over 1800 assistants 
 
 * A conto of reis, in Brazil, is equal to about five hun- 
 dred American dollars, or a hundred pounds sterling. 
 
171 
 
 and employes engaged during the year 
 of 1874; the total area surveyed by them 
 was not more than 8,000 square kilome- 
 tres. With the methods in use in Austria 
 an experienced topographer can survey 
 in one field season of six months five 
 hundred square kilometres at the farthest. 
 In Switzerland the topography is in large 
 part done by contract, and it alone, ex- 
 clusive of triangulation and publication, 
 costs 700 or 800 francs per square stunde, 
 or about twenty-two mil reis* per square 
 kilometre. So with the surveys of Italy, 
 Spain, Sweden, and the other European 
 countries of comparatively small extent; 
 they are so slow, detailed, and withal so 
 expensive as to be inapplicable to the 
 great empire of Brazil. 
 
 AX ADVANTAGEOUS DEVELOPMENT. 
 
 So vast is the extent of this empire 
 that the idea of a geographical survey 
 of its territory, as a whole, is an astound- 
 ing one, and is liable, in itself, to forbid 
 all further consideration of the subject. 
 
 * Eleven American dollars. 
 
172 
 
 But this plan does not necessarily imply 
 the regular extension of this survey over 
 the whole country, irrespective of popu- 
 lation and wealth. On the contrary it 
 would devote itself at first to such areas 
 as, from geological or other economical 
 reasons, might most urgently require it, 
 and a region of especial interest to the 
 geologist would be surveyed first and 
 with especial care, to the neglect or even 
 exclusion of those great stretches of 
 country whose structure is unvaried and 
 monotonous. In a few conditions of its 
 plan, as, for instance, in the system 
 adopted in the projection of its maps, it 
 might provide for any possible ultimate 
 extension, but in other respects it could 
 operate with equal facility, in whatever 
 districts might be assigned to it. 
 
 Nor does this plan imply the necessity 
 of any great outlay at the beginning, but 
 would ask to start upon a small scale at 
 first, with a view to gradual growth as it 
 proved itself worthy of encouragement. 
 As the aim of this project would be not 
 only the production of much-needed 
 
173 
 
 maps, but also the introduction of these 
 methods of survey from abroad, and the 
 training of Brazilian engineers in the use 
 of the same, any very extensive initial 
 basis would prove not only embarrassing 
 at first but also probably disastrous in 
 the end. A survey inaugurated upon a 
 grandiose scale is too liable to exhaust 
 the patience and liberality of its official 
 patrons before it can exhibit results ap- 
 parently equivalent to the expenditure 
 that it has caused, and the frequent fate 
 of such enterprises is that they are dis- 
 continued at about the time when, their 
 organization being successfully com- 
 pleted, they are prepared to enter upon 
 an area of efficient and fruitful labor; 
 hence, all of the expense of organization 
 and other preliminaries becomes a total 
 loss to the government. 
 
 On the other hand, some of the rm>st 
 important surveys of the world have 
 arisen from humble beginnings. Such an 
 enterprise educates its own members, the 
 assistant engineer of one season becom- 
 ing the engineer of the next, and so on. 
 
174 
 
 It develops gradually and with a healthy 
 growth, perfecting its own methods, and 
 always experimenting upon a small scale, 
 so that it is never liable to serious disas- 
 ter. And, above all, by its early pro- 
 duction and exhibition of results com- 
 mensurate with its size, and with its 
 cost, which is insignificant at first, it 
 buys the right to be continued, en- 
 couraged and increased from year to 
 year. 
 
 A GEOLOGICAL AND GEOGRAPHICAL SUR- 
 VEY. 
 
 There are two very good arguments 
 for such a geographical survey in connec- 
 tion with the Geological Commission of 
 Brazil ; first, its necessity to the geologi- 
 cal survey, as explained in the early part 
 of this paper; and second, because in 
 sudh a connection it can work most 
 economically and profitably. With a 
 combination of these elements comes 
 much valuable co-operation between the 
 representatives of the various branches 
 of science, and this is constantly acting 
 
175 
 
 to lessen the expense and increase the re- 
 turns of such a survey. For instance, as 
 the meteorologist of the engineering 
 corps, an assistant with some acquaint- 
 ance with geology, could be chosen. As 
 his meteorological duties upon the march 
 would be but light, he could devote 
 much of his time to a geological study 
 of the road, leaving the regular geologist 
 at liberty to go from camp to camp by 
 any other route that he might select. 
 Again, the meteorologist, or even the en- 
 gineer himself, may make strati graphical 
 sketches upon every mountain, and bring 
 specimens of rock from the same, while 
 the geologist is away upon some detour 
 to regions of interest in another direc- 
 tion. 
 
 Or, reversing this illustration, the 
 geologist, whose profession is so closely 
 allied to that of the geographer, is con- 
 stantly making notes of direction, dis- 
 tance, slope, and altitude, which are of 
 the highest importance and use in the 
 construction of a map. These are lost 
 to the world if there is not an accom- 
 
176 
 
 panying geographical survey into whose 
 plots they may be assimilated. 
 
 In witness of the sympathy with 
 which the present members of the Geo- 
 logical Commission regard geographical 
 work, and of their skill in the prosecu- 
 tion of the same, the writer would men- 
 tion their intelligent and extensive sur- 
 veys of the valley of the Amazon, from 
 Monte Alegre westwards, and of its 
 tributary, the Trombetas; of the island 
 of Fernando de Noronha; and of many 
 localities along the Atlantic coast and 
 elsewhere in the empire. These are evi- 
 dences of a willingness and an ability to 
 collect geographical information, which, 
 in themselves, assure the success of a 
 system of geographical surveying in 
 connection with the Geological Commis- 
 sion of Brazil. 
 
* * Any book in this Catalogue sent free by mail, on 
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