PHILOSOPHICAL SOCIETY OF WASHINGTON. 121 



These represent values of the two arguments. The lines of the third 

 set are curved, and each one represents a value of the correction. 

 In use, the straight lines representing the values of the two argu- 

 ments are traced to their intersection, and from the relation of this 

 point of intersection to the curved lines the correction is deduced. 



This method is theoretically applicable to the tabulation of any 

 quantity which is the function of two variables, but is practically 

 useful only when the quantity to be determined is either expressible 

 by a small number of digits, or else is subject to only a small range 

 of variation. 



A second graphic table was exhibited, having for its object the 

 computation of altitude from horizontal distances and vertical 

 angles as data. On this, successive values of computed altitude are 

 indicated by parallel, equidistant, straight lines. Vertical angles 

 are indicated by the directions of lines radiating from a poiut, but 

 the intervals of these lines are not equal. Distances are measur- 

 able along these radial lines, but are not indicated in the drawing. 

 The scale of distances is identical with that of the map, including 

 the points whose altitudes are to be computed. The lines are drawn 

 on tracing-linen. 



For the use of this table it is postulated that the points whose 

 altitudes are to be computed are correctly placed upon a map, and 

 that the same map indicates a point from which the elevation or 

 depression angles of the various points were measured. The trans- 

 parent linen bearing the table is placed over the map and con- 

 nected with it by a pin passing through the common origin of the 

 radial lines, and also through the indicated position of the station 

 from which the angles were measured. About this point as a centre 

 the table is then moved until the radial line, indicating the vertical 

 angle of one of the points, is brought immediately over the repre- 

 sentation of that point upon the map, The position of that point 

 among the parallel lines then indicates the desired altitude. 



The use of this device is limited to a special case, but that case 

 is one of frequent recurrence in the preparation of contour maps, 

 and it is hoped that the device will lead to an economy of time. 



The principle involved in the application of a transparent graphic 

 table permits of the extension of the graphic table to cases involv- 

 ing three arguments. Two sets of lines could be drawn on a lower 

 sheet, and two other sets on an upper transparent sheet, and these 



