•  
  •  
 

Document Type

Research

Abstract

The theory of Amsler's polar planimeter, as commonly given, leads to the expression A= L h, where A is the area circumscribed, L is the length of the tracer arm, and h is the net distance of translation of the tracer arm in a direction perpendicular to its length. However, it can be shown that the area may also be given by A = L 2, where ∅ is the net angle through which the tracer arm has rotated about either of its ends. But as the tracer point passes around the area A, the tracer arm does not, in general, rotate simply about one end. At any particular instant it rotates about some point which may be situated anywhere along its length. However, about whatever single point the arm may be rotating, such rotation can be resolved into two simultaneous rotations about the two ends. Therefore for purposes of analysis we may consider that the tracer arm rotates only about the ends, and we may express the area in terms of that rotation, as already stated.

Publication Date

1926

Journal Title

Proceedings of the Iowa Academy of Science

Volume

33

Issue

1

First Page

250

Last Page

251

Copyright

© Copyright 1926 by the Iowa Academy of Science, Inc.

Language

en

File Format

application/pdf

Share

COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.