96 DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



Let it be required, for instance, to determine the points in which the curve 13 a = 20 

 is cut by the curves <p a = o, 4, 8, 12, . . . and by the curves F = 1, 2, 3, 4, . . . 

 The first draftsman then observes the connected values of A and of B along the curve 

 /3 a = 20, and dictates that it cuts the curve A = 1 in the point where B = B lt the 

 curve A = 2 in the point where B = B 2 , etc. The second draftsman then draws 

 point by point the corresponding curve on the transparent sheet placed upon fig. 78. 

 Then the second draftsman follows the course of the curve which he has drawn, and 

 dictates to the first that it cuts the curve F = 1 at the point where A=A,, the curve 

 F = 2 at the point where A=A 2 . . ., the curve <p a = o at the point where A=A' Q . 

 the curve <p a = 4 at the point where A=A\, . . . . The first draftsman then 

 marks these points on the curve /3 a = 20 on his chart, using different kinds of 

 marks for the curves F = const, and <p a = const., and adding the numerical values 

 of F and <p a. When this is repeated for a sufficient number of curves /8 a = const, 

 we shall get a complete set of points determining the course of the curves F = const, 

 and <p a = const. 



From the set of curves <p a = const, we finally pass, by the graphical addition 

 (<p a) + a = <p, to the curves representing the required angle <p. 



When we compare with the method of section 158, we see that the use of the 

 graphical tables replaces the performance of the separate graphical operations 

 ( 2 )> (3). (4). (5)- Only the simple graphical subtraction(i) and the graphical addi- 

 tion (6) are retained. 



161. Complete Resultantometer. While the method of section 158 required 

 the drawing of four auxiliary systems of curves, besides the fifth and sixth, which 

 represent the result, we succeed by using the graphical tables in arriving at the 

 result by drawing only two auxiliary systems of curves. By introducing a still 

 more complete auxiliary, a complete machine for vector-addition, we can completely 

 avoid the drawing of auxiliary systems of curves. 



Instruments for adding vectors can be constructed in various ways, each having 

 an advantage according to the special form in which the problem presents itself. 

 Fig. 79 shows a convenient construction for our purposes. We draw parallel and 

 equidistant lines on two circular transparent sheets and concentric circles on one 

 of them. The sheets are laid upon each other, so that the upper is free to slide inside 

 the divided brass-ring C, while the lower is mounted in a brass-ring which can slide 

 outside the ring C. This ring contains the divisions o to 63, which represent the 

 angles. When the instrument is to be used on our charts in conical projection, the 

 ring C is attached to the rule R, which passes through the point of convergence of the 

 meridians. (Compare the integration-machine of fig. 62 .) The divisions of the circle 

 C will then always show the true directions relatively to the meridians on the chart. 

 For the practical use of the instrument it will finally be useful to have two screws 

 by which we can attach either of the divided sheets rigidly to the ring C and thus 

 give the lines of the fixed sheet an invariable direction relatively to the meridians of 

 the chart. The two sheets are perforated at the center, in order to make it possible 

 to set marks on the paper underneath by use of a pin or a sharp pencil. All lines are 



