516 REPORT — 1894. 



' roll ' of the ordinary wheel, and can therefore be used in its place to 

 measure an area. 



Amsler describes, in the paper quoted, a planimeter of this kind ; but 

 instead of making the knife-edge wheel slide along the bar CD, he makes 

 the bar slide across the rod QT, fixing at each end a knife-edge wheel. 



Just as in Amsler's Polar-planimeter the axis of the recording wheel 

 must be parallel to the rod, so the axis of the knife edge wheel must be 

 perpendicular to it. If it deviates from it by an angle i, and if S 

 denotes the sliding, W the rolling of the wheel, then the area will be 



SZ sin £+W^ cos e 



In the Hine- Robertson planimeter the point Q is not guided in a circle 

 but along a straight line. The whole instrument is small, and is contained 

 in a box seven by eleven inches. At the bottom of the box, along one 

 edge, a strip of metal is fastened with a V-groove in it. In this the one 

 end Q of the rod slides. The paper with the indicator-diagram, for which 

 the instrument is meant to be used, is clamped to the bottom and every- 

 thing ready. The wheel slides, as described, along the bar, which is so 

 graduated that the wheel is set to zero when pushed towards the rod as far 

 as it will go. The instrument is therefore very handy ; but it has one 

 fault — the axis of the wheel is not perpendicular to QT. 



The rod is at the end towards Q bent to a curve, and only the piece in 

 CT, whei'e C is the point of junction with the bar carrying the wheel, is 

 straight. This bar, which should be perpendicular to QT, is so to CT, and 

 makes with QT an angle £=10^ nearly. If it gives, nevertheless, good 

 results this must be due to the fact that the errors nearly cancel each other. 



If the instrument be so placed that CT is parallel to the v-groove, 

 and the line over which CT lies be marked on the paper, then the error 

 will be positive when the tracer is on the one side of this line, negative 

 when on the other. As from the very dimensions of the instrument this line 

 will almost always cross the indicator-diagram, such cancelling of the 

 errors will be explained. But there seems to be no reason why the axis 

 of the wheel should not have its proper position. 



The Prytz or Hatchet Planimeter. 



This planimeter belongs geometrically to Type III., but the recording 

 apparatus is altogether different from Amsler's. It is curious in its sim- 



FiG. 11. 



ZJ.. 



plicity, consisting simply of a single rod of metal, without any wheel or 

 other movable part. For the ultimate reading an ordinary scale is used. 



A metal rod is bent as in fig. 14. At T it ends in a point which 

 serves as tracer. At Q it is flattened to a knife-edge, whose plane passes 

 through T. This is placed in a vertical plane with T and Q resting on the 

 paper. 



