[From the Transactions of the Royal Scottish Society of Arts, VoL IV. Part IV.] 



IX. Description of a New Form of the Platometer, an Instrument for 

 measuring the Areas of Plane Figures drawn on Paper*. 



1. THE measurement of the area of a plane figure on a map or plan is an 

 operation so frequently occurring in practice, that any method by which it may 

 be easily and quickly performed is deserving of attention. A very able expo- 

 sition of the principle of such instruments will be found in the article on 

 Planimeters in the Reports of the Juries of the Great Exhibition, 1851. 



2. In considering the principle of instruments of this kind, it will be most 

 convenient to suppose the area of the figure measured by an imaginary straight 

 line, which, by moving parallel to itself, and at the same 



time altering in length to suit the form of the area, 

 accurately sweeps it out. 



Let AZ be a fixed vertical line, APQZ the boundary 

 of the area, and let a variable horizontal line move 

 parallel to itself from A to Z, so as to have its extremi- 

 ties, P, M, in the curve and in the fixed straight line. 

 Now, suppose the horizontal line (which we shall call the 

 generating line) to move from the position PM to QN t 

 MN being some small quantity, say one inch for distinct- 

 During this movement, the generating line will 



ness. 



have swept out the narrow strip of the surface, PMNQ, 

 which exceeds the portion PMNp by the small triangle PQp. 



But since MN, the breadth of the strip, is one inch, the strip will contain 

 as many square inches as PM is inches long; so that, when the generating 



* Read to the Society, 22nd Jan. 1855. 



