4 Report on the Magnetic Survey. [No. 1. 



This map, in the scale of three inches to two miles, proportion 

 1 : 42240, was sent to Capt. Thuillier, Surveyor General's Office, 

 Calcutta, where, through the kind assistance of Capt. Thuillier, 

 copies are now being made which will be added to the next report. 



We chiefly used a portable levelling instrument, consisting of a 

 divided wheel and a diopter for tracing the level lines from 500 ft. to 

 500 ft. vertical distance; with these measurments were combined 

 the determination of the inclinations of slopes by a very sensible 

 Clinometer. 



As the latter process gives very material assistance in cases 

 where every point is not accessible (from want of roads as well as 

 particularly from the luxuriant vegetation), I may mention in a few 

 words how we proceeded to deduce from the inclinations the form 

 of the lines required. The horizontal projection (P) of a unit of 

 vertical height [500 ft. in the present case] varies with the inclina- 

 tion (I) of the surface, being the cotangent of the angle of inclina- 

 tion multiplied by the height taken as the standard (P = cot* 

 I. % 500.) 



Beginning therefore at a point whose height was measured and 

 coincided with the full multiple of 500 ft., the projection in the 

 map of the next point 500 ft. higher can be deduced from the for- 

 mula above mentioned. 



"We calculated a table containing, in inches and its decimal frac- 

 tions from degree to degree, the values of P reduced to the propor- 

 tion of 1 : 42240 of which I give a few numbers as an example. 



Angle of declivity. 





Horizontal distance of two 



degrees. 



Log cot* 



contour lines in the plan, 

 inches. 







CO 



CO 



10 



0.7537 



0.806 



20 



0.4389 



0.390 



30 



0.2386 



0.203 



40 



0.0762 



0.169 



50 



9.9238 



0.11& 



The points with which the steps from 500 ft. to 500 ft. coincided 

 being thus found on the different slopes, their combination gives the 

 equi-distant contour lines as an immediate result. 



We left Darjiling August 19th to go by boat to the foot of the 



