III. AREA. 77 



moved so far upwards or downwards until the curve line meets in three com- 

 niensurably described points of the scale. The number indicated gives the 

 radius of the curve in centimeters, if the curve is drawn in its natural size. 



If, however, the drawing of which the radius of the curve is to be deter- 

 mined is, as is usually the case, on a reduced scale, the radius indicated must 

 be multiplied with the proportional number of the reduced scale. 



For example, if the drawing should be to the scale of -^^ of the natural 

 size, and the curve radius on the curve scale is indicated with 52 5 cm., the 

 actual radius of the curve will be 52 '5 x 2,500 = 131,250 cm., or 1,3 12* 5 meters; 

 or, should the drawing be to the scale of -gfa, and the curve scale indicates 

 43 cm., the radius of the curve will be 43 x 500 = 21,500 cm., or 215 meters. 



The curve scale can likewise be used as a reduction scale of every other 

 measure which is to be calculated in meter measure, as the radius in meters 

 can always be read directly, no matter in what scale the drawing is made. 



This is a great saving of labour, which is very much facilitated if, as often 

 is the case, old maps and drawings are to be made use of. 



In using the curve scale it will sometimes happen that the curve to be 

 ascertained does not exactly meet the line drawn on the scale, but will fall 

 between two lines. In this case the smaller division can, as the radii are 

 marked progressively by 0'5 cm., be easily estimated by eye after a little 

 practice. 



For example, the curve of the radius of 1,110 meters, at a proportionate 

 scale of ^ 5 1 6 6 ., lies between 88 5 and 89 * of the curve scale, and amounts to 

 nearly 88 -9. 



As, however, in most cases, round numbers, without fractions, are chosen 

 for the radii, the radius can always be determined with the greatest accuracy, 



109 3 a. Ellipsometer. 



Before the eyepiece of the glass, a double refracting prism is made to turn 

 until a wire, moving perpendicularly to the principal section of the prism. 

 passes through the two intersecting points of the two reflections of the ellipse. 

 An index shows at the moment the position of the prism. 



Graphometer of Botti. 



The Royal Institute of " Studii Superiorly Florence. 



III. MEASUREMENT OF AREA. * 



316. Amsler's Flanimeter, for calculating with perfect 

 accuracy the areas of plans, maps, or other plane surfaces, in 

 square inches and metrical measure. Elliott Brothers. 



317. Folarplanimeter. Ott and Coradi, Kcmpten, Baviera. 



By means of the polarplanimeter the superficial contents of any kind of 

 figures drawn on paper, no matter what their outline may be, can be ascer^ 

 tained by mere tracing more exactly and quickly than by any other method. 



The inventors of this instrument are respectively J. Amsler, Schaffhausen, 

 and Ch. Starke, Vienna. Ott and Coradi's construction is a combination 

 of both, embracing the excellences of each. It differs from Amsler's instru- 

 ment by the pole (axis) of the instrument not being formed by an inserted 

 point of a needle, but by a steel ball embedded in a metal cylinder, thus 



