Analysis,Comparision aid Improvement of the Method of Measuring Land Surface Area on Topographical Maps

There are five methods of measuring land surface area on topographical maps.A paper ³ has made a detailed comparision between the complicateness of the various methods;it has,however,not indicated their internal relationships nor made a comparision between the results obtained by the various methods,as to what extent they approach the actual surface area.The author of the present paper attempts to prove by the fundamental formula of area and the principles of approximate calculation the mutual relationships between the various methods;accordingly,derives the non-equality between the values obtained by them and at the same time,compares their merits and defects according to their approximation to the actual area.Furthermore,the author makes a study by elementary method of the closeness of different asymmptotic numeral values to the actual area for ditffterent shapes of surface,which enables us to choose the most reasonable formulae of calculation in practice.Then,the author suggests a graphical method,based on the same principle of he above analysis,which simplifies the calculation work of the most accurate but more complicated Hua Lokeng and Wang Yuan s method.Lastly,based on the same principle,the anthor derives a set of new formulae,which are as accurate as the existed fomulae,but do not require the process of area on topographical maps.Hence they are especially useful in case of having no planimeter.