FROM TONKIN TO INDIA 



sufficient cjuantity of mercury for the artificial horizon, and of keeping it perfectly 

 clean, are further drawbacks when on the march. For the foregoing reasons, I soon 

 gave up using the sextant in favour of the theodolite. Hy land the latter instrument 

 is far handier, and quite as accurate. By always taking double observations of the 

 altitudes — that is to say, with the telescope on the right and again on the left — 

 the errors of coilimation and level are eliminated ; and as it is easy to estimate to 

 i and even to ^ of a division, one can count on being correct to 30". 



I most generally emjjloyed the method of finding the latitude by two circum 

 meridian altitudes without previous calculation. This has the advantage of dispensing 

 completely with the knowledge of absolute values, and it is sufficient to have a 

 good watch with a second hand to mark the exact interval of time between the 

 two observations, which may be taken, immaterially, either before or after noon. 

 The calculation is a little longer than that of latitude deduced from meridian 

 observation ; but the observation is easier and more reliable, the greatest advantage 

 being that one has usually from twenty minutes to forty minutes during which it is 

 possible to take it, instead of being obliged to seize a precise moment, when, as 

 likely as not, the sun may be covered by a cloud. 



On days when we were halted I have sometimes taken a single circummeridian 

 altitude, but on these occasions it was imperative to know exactly the error of the 

 watch, and for that reason to take the observation either two hours before or two 

 hours after midday. From all points of view this method is inferior to the other. 

 Finally, I often employed the pole star, obtaining the true value by some heavenly 

 body immediately before my observation. 



All my altitudes have been invariably observed in the following manner : — Set 

 the telescope so that the sun shall be either a little above or below the observing 

 wires ; then begin to count, taking the time when the sun's disc is tangent to the 

 first thread ; observe successively the time of passing the seven threads of the 

 eye-piece ; read upper and lower vernier : this reading is that which corresponds to 

 the mean of the times noted. If the observation has been made with the telescope 

 on the right, repeat with it on the left, and take the mean. Every altitude thus 

 obtained corresponds in reality to the mean of a series of 7. Those which differ from 

 the mean, and which therefore are useless, can be struck out. When obliged to count 

 for myself, I thought it enough to observe the passage at the ist, 4th, and 7th threads. 

 The latitudes obtained by the theodolite may be considered as, approximately, 

 exact to 30" or 45" ; those of Ssumao, Manhao, Mongtse, etc., being the mean of 

 two or three groups of observations, exact to 1 5" or 30 ". Similarly, those obtained 

 by the sextant are to be regarded as approximately exact to i' to i' 30". Both 

 at Tali-F'ou and at Ssumao I was able to compare my results with tho.se of Francis 

 Gamier, and the discrepancy in neither case amounted to i'. 



Latitudes Nos. 7 and 10 were deduced from 

 Nos. 6 and 9 by the subjoined method, common 

 enough in mountainous countries : — 



Let C B be two points, visible to each other, 

 the latitude of B being ascertained by observa- 

 tion, and its altitude known by barometric 

 readings. The next day being at C, and the 

 state of the atmosphere precluding observation, 

 the latitude of C may be deduced from fixing 

 its position relatively to B. 



For this purpose observe the altitude of C, 

 and take by theodolite the inclination of the .slope CB : 



Let H = altitude of B 

 and let H' = altitude of C, 

 then in the triangle ABC 

 AB = AC cot a = (H' - H) cot a. 



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