ON PLANIMETERS. 515 



The Lang-Coradi Planimeter. 



Coradi has quite recently constructed a new modification of Amsler's 

 Polar-planimeter which he calls ' Compensations-Polar-planiineter.' Its 

 object is to eliminate the error due to a non-parallelism between the axis of 

 the wheel and the rod QT according to a method due to Herr Lang, a 

 surveyor of Neuwied. The Swiss patent is dated from October 3, 1893. 

 A description of it is published by Lang in the ' Zeitschrift fiir Ver- 

 messungswesen,' 189-1-, Heft 12. 



Lang points out that the error mentioned can be eliminated by going 

 twice round the boundary of the area in the following manner. To fix 

 the idea let the pole O of an ordinary Amsler planimeter be below the 

 curve, the tracer T on it ; then the point Q will be to the right. In this 

 position the tracer is moved round the curve. Then, with the same 

 position of the pole, the planimeter is set so that the point Q comes to the 

 left and the tracer is guided again along the curve. The error in question 

 will be equal but opposite in sign for the two operations, and is therefore 

 eliminated on taking the mean. 



In Amsler's planimeter this second position is not possible. To make 

 it possible Coradi does not connect the rod QT by a hinged joint to the 

 arm OQ, but by a spherical joint. One wheel is placed slightly on one 

 side of the rod near Q, and another supporting wheel is placed on the 

 other side of the rod with its axis perpendicular to the rod. The rod 

 therefore rests with these two wheels at the one end and the tracer at the 

 other end firmly on the paper. At Q the rod has a hole, with a spherical 

 bottom, open at the top. The arm OQ has at Q a tooth projecting down- 

 wards whose spherical end is placed in the hole of the rod. The arm is 

 therefore above the rod, and this requires a new construction of the needle 

 point at O. It consists of a heavy foot having its lower surface in the 

 form of a cylinder whose horizontal edge is perpendicular to OQ. In the 

 middle of this edge is the needle. This arrangement avoids at the same time 

 any obliquity in the axis of the joint at Q. Besides, it is easier handled in 

 taking it in or out of its box, as it consists of two quite separate parts, 

 and thus there is less likelihood of damaging the instrument. 



It seems to be an instrument as carefully thought out as it is 

 executed, and will, most likely, replace the more expensive precision- 

 planimeters. 



The Hine-Robertson Planimeter. 



Within the last few years a new little planimeter has been made by 

 Messrs. Hine & Robertson, of New York, stated to be ' on an entirely new 

 principle.' The principle is however already given by Amsler in his paper 

 of 1856. 



Suppose in an ordinary Amsler planimeter a bar CD fixed rigidly at C 

 to the rod QT and at right angles to it. On this bar let a wheel be 

 mounted so that it can turn about it and also slide along it. Let the 

 rim of this wheel be made with a knife edge ; then the wheel can only roll 

 on the paper, but instead of slipping on the paper it will slide along the 

 bar. If the wheel had a smooth rim and could not move along its axis we 

 should have the arrangement mentioned before (p. 510), when it was pointed 

 out that its slipping would equal the ' roll ' of the ordinary recording wheel. 

 It follows that the displacement of the wheel along the bar equals the 



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