430 



KEPORT — 1892. 



square roots, cubes, cube roots, sines, tangents, and logarithms, are 

 carried out. 



The last five instruments can be obtained from Mr. W. F. Stanley, 

 5 Great Turnstile, London, W.O. 



Planimeteks and Integeators. 



The first recorded idea of the planimeter is attributed to Hermann, of 

 Munich, who worked it out with Lammle. The idea of Hermann's, 

 which was published in 1814, seems to have fallen into oblivion; while 

 in 1827 Oppikofer, of Berne, constructed a planimeter which was called 

 by his name. Professor T. Gonella, of Florence, in 1829 re-invented a 

 similar instrument. Oppikofer's planimeter was accorded a prize at 

 Paris in 183G. Improvements were made by Wettle and Starke in 1849. 

 In England, Sang, Moseley, and others also devised planimeters. All 

 these depended on the principle of recording the area by revolutions of a 

 roller which worked by frictional contact, sometimes on a disc and 

 sometimes on a cone, its distance from the centre of the disc or the apex 

 of the cone being proportional at every distance to the breadth of the 

 figure whose area was to be measured, the revolution of the cone or disc 

 depending at the same time on the length of the figure. 



In 1856 Professor Amsler-LafiTon invented and brought before the 

 world the well-known Amsler planimeter, which has proved up to 

 the present day to be the simplest and best of all such instruments, in 

 spite of ail attempts that have been made to improve upon it and obviate 

 its one or two defects. The action of the Amsler planimeter, as is well 

 known, depends upon the principle that a roller, if moved obliquely across 

 a smooth surface, turns through an amount corresponding to the distance 

 it has moved perpendicular to its axis. Hence the breadth of a figure 

 being measured by the inclination of a bar carrying the roller, and the 

 length by the distance which the wheel moved, the actual turning of the 

 roller gives a record of the area. 



The following measurements made by General Peaucellier, cited by 

 Favaro, give the results of the measurements of a quarter of a circle ten 

 millimetres radius divided into ten segments by parallel ordinates, and 

 show the accuracy of the Amsler planimeter as compared with other 

 methods : — 



Method of chords 

 Simpson's rule . 

 Metiiod of tangents . 

 General Poncelet's rule 

 General Peaucellier's rule 

 Measurements by planimeter 

 Exact area 



Explanations of the action of a planimeter are given in many text- 

 books on mechanics ; a very good account on elementary principles is 

 that of Sir F. J. Bramwell.^ 



By means of a very simple device of two points attached to the 

 Amsler planimeter, the scale of the reading can be adjusted to suit any 



' ' On the Amsler Planimeter,' by F. J. 

 Association. 1872, p. 401 



Bramwell. Report of the British 



