253 Geographical and Topographical Imprcveinenfs. 



equally capable of giving the true shape of any ground abov<t 

 or below water. It may be successfully applied to sea charts, 

 and will prevent much confusion, arising from the tedious 

 method of distinguishing soundings by a multitude of 

 figures. 



Explanalion. 



Suppose a full description is required of any inland in the 

 ocean. First, let an accurate map be laid down in the com- 

 mon way; and let the perpendicular height between the 

 hio'hest point of land and the ocean be di\;ded into any 

 number of equal parts. Suppose these equal divisions are 

 100, ?00, 300, 400 feet above the low-water mark. From 

 the diflercnt points of these several d.ivisions let horizontal 

 lines be run with a good theodolite, and spirit-level an- 

 nexed, all round the island. If the work is well done, each 

 line will end where it began ; and if the bearings and di- 

 stances of these several lines are truly laid down on the 

 map, the crooked courses of them will clearly show the 

 shape. of the ground over which they pass. For example; 

 if any horizontal line passes by the side of a steep hill, it 

 will incline towards the ocean, or approach the next hori- 

 zontal line below it. When the same line crosses a stream 

 of running water or a valley, it will naturally bend up the 

 side of the said stream until it can cross it without losing 

 ' the level ; or, in other words, it will bend towards the centre 

 of the island. Hence, by a little practice, the shape of the 

 several horizontal lines on the map will give as clear an 

 idea to the mind of the shape of any country over which 

 they pass, as a sight of the country itself can convey to the 

 eve. But to obtain a mathematical and true knowledge of 

 tbe altitude and declivity of any part of the country, we 

 have the following proposition : 



As the perpendicular height of any one horizontal line 

 above another is to tlie radius, so is the horizontal di- 

 stance between the horizontal lines measured on the map 

 at any particular place, to the co-tangent of declivity at 

 that place. 



Note: I*^ the horizontal distance between any two hori- 

 zontal lines on the map is equal to the perpendicular height 

 of anv horizontal line above another, the angle of altitude, 

 pr declivity, of any hill will be 4,5 degrees. 



The present improvement, which I beheve to be entirely 

 pew, will be found to possess the following advantages : 



1st. Military men are well acquainted with the many 

 advantages always to be gained from the exact rcftresenta-. 

 ^ion of hisfh orounds. By this method we are able to give 



th? 



