PRESIDENTIAL ADDRESS. 427 



The great drawback to the sextant for survey work is that it is impossible 

 to take accurate rounds of horizontal angles with it, since, unless the points are 

 all on the same level, the angles must be too large. It is essentially a naviga- 

 tor's instrument, and nowadays has been almost entirely superseded by the 

 theodolite for land-surveying. 



As regards the longitude, the difficulty was always to obtain a steady rate 

 for the chronometer, owing principally to the unavoidable oscillations and con- 

 cussions met with in transit. Formerly it was customary to observe lunar dis- 

 tances for getting the Greenwich mean time instead of trusting to the chrono- 

 meters, but these, even with the utmost care, are very unsatisfactory. 



In more recent years the occultation of a star method of finding the Green- 

 wich mean time superseded almost entirely the lunar distance, but all of these 

 so-called ' absolute ' methods of finding longitude are fast becoming out of date 

 since the more general introduction of triangulation and wireless telegraphy. 



Heights of land were usually obtained by the boiling-point thermometer or 

 aneroid. 



This then was the usual equipment of the pioneer. With such an outfit the 

 greater part of the first mapping of Africa and other regions of the world was 

 carried out, with results that were more or less reliable according to the skill 

 of the explorer and the time and opportunities at his disposal. 



In recent years considerable improvement has been made in the instruments 

 and methods of the geographical surveyor : the introduction of the Invar tape 

 for the measuring of the baselines, the more general application of triangulation, 

 the substitution of the theodolite for the sextant, the use of the plane-table for 

 filling in the topographical details of the survey, the application of wireless 

 telegraphy to the determination of longitudes, these and other improvements 

 have all tended to greater accuracy and efficiency in geographical and topo- 

 graphical mapping, so that in many respects the rough approximate methods of 

 the earlier explorers are fast being superseded by instruments and methods 

 more in keeping with modern requirements in map-making. 



Still, the principle underlying all surveying is the same, and the whole 

 subject really amounts to the best and most accurate methods of measurement 

 with a view to representing on a plane, on a greatly reduced scale, the leading 

 features of a certain area of the earth's surface in their relatively correct 

 positions ; and so it resolves itself into geometrical problems of similar angles 

 and proportional distances. This being the case, it is clear that it becomes in 

 the main a question of correct angular and linear measurements, and all the 

 improvements in survey methods have had for their object the increased accuracy 

 of accomplishing this, together with greater facility for computing the results. 



What we do now is exactly what was attempted by the early Greek 

 geometricians and others in ancient times, only we have far more accurate instru- 

 ments. If, for instance, we compare our modern micrometer theodolite with 

 the old scaph of the Greeks the contrast is striking, although both had the same 

 object in view as regards taking altitudes of heavenly bodies. Many of the old 

 instruments, in spite of their great size, were extremely rough, and the angles 

 could only be read with approximation or to a great extent by estimation, while 

 the theodolite, which is now generally used on geographical surveys, although it 

 has circles of only five inches in diameter, can, by means of the micrometers, 

 be read to 2" of arc, or even to 1" by careful estimation. This, when one 

 comes to. think of it, is a triumph of refinement, since it really means that 

 we can measure to within about g^j^^jg part of an inch, which is the space 

 occupied by 1" on the arc of a circle of five inches diameter. At least this is 

 the theoretical accura.cy, but in practice there are, of course, errors in sighting, 

 setting the micrometer wires, and those arising from other sources which have 

 to be taken into consideration. 



The continued striving after greater accuracy of measurement applies not only 

 to angular measuring instruments, but to' linear distance measurement as well ; 

 and the improvements in apparatus for this purpose, could we follow them in 

 detail, would be most interesting. From the rough methods that would suggest 

 themselves naturally to early intelligent men, and some of which I referred to 

 in the earlier part of this address, to the modern baseline apparatus, and accu- 

 rately computed sides of a geodetic triangulation, is a far cry. and the advance 



