1837.] Captain Kater's Altitude and Azimuth Instrument. 141 





DIFFERENCE OF LONGITUDE. 





30' 



i° r 



lo 30' 



2o 0' 



2 6 30' 



3o 0' 



5o 



1" 



3" | 



6" 



11" 



17" 



24" 



10 



1 



5 



12 



21 



34 



48 



15 



2 



8 



18 



31 



49 



70 



20 



2 



10 



23 



40 



63 



91 



25 





12 



27 



48 



75 



108 



30 



I 



14 



31 



54 



85 



122 



By using a table of this kind, the error may be corrected without any 

 additional trouble, or wasting time in the niceties of the computation 

 by the formula; if it is ever necessary to undertake a survey of any 

 extent with the small circle, or to use inferior instruments, when others 

 cannot be procured. 



In sketching in a hilly country, like those which are common among 

 the mountainous tracts of India, when it is difficult, and sometimes 

 impossible, to ascend to the summit of hills, from the impenetrable 

 jungle which generally clothes the sides, the circle becomes a very 

 useful instrument, from the facility with which azimuths of the 

 sun or moon may be taken with it ; by which means an azimuthal trian- 

 gulation may be carried on, with as much readiness as with a circum- 

 ferentor, but with infinitely greater exactness. 



In using the circle in this way the subjoined diagram will explain 

 the method of operation. 



Let A (PI. 4 fig. 4) be the plan of a camp, from whence the hill 

 stations D and C can be seen. Let B be a little hill from where D and 

 C can also be seen. Let the distance A B be assumed as a base, and 

 the distance guessed by the perambulator. Let the latitude be 

 exactly ascertained at A, and also the angles BAG and BAD 

 be measured from A, and also the angle between B and the sun's cen- 

 tre. Let the angles ABD and ABC be observed from B, then with 

 the base A B the distance D C may be computed. From E, another 

 camp beyond the range of hills D C, let the angle DECbe measured, 

 and also the angle between the sun and one of the stations D or C. Then, 

 if M express the meridian, the angle M E C being Known, the angle M C 

 E is also known, from the azimuth atE, and also the angle M C D from the 

 azimuth at A, and, the distance D C being given, the triangle DEC may 

 be computed. Again if F is another camp, separated from F by another 

 range of hills, but from D and C can be seen, D E and C E can be 

 computed in the same manner, and from E and F more points as G &c. 



