7o 



DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



to make different systems of curves simultaneously visible in their true mutual 

 position, as if they had been drawn upon the same sheet of paper. Certain measures 

 must be taken to attain this. 



We have found it most convenient to draw the different charts upon sheets of 

 semi-transparent paper, and to have at hand a special drawing-board. This board 

 consists of a sheet of glass with a wooden frame and has a contrivance for producing 

 illumination from below. This illumination is obtained most easily by an incan- 

 descent electric lamp. The sheets of paper should cover the glass completely. 

 They can be fixed to the wooden frame by drawing-pins. The paper should be 

 sufficiently transparent, or the illumination sufficiently strong, to allow us to have 

 at least three sheets simultaneously upon the board, two containing given systems of 

 curves and a third upon which the derived curves are drawn. The plates accom- 

 panying this book have been printed upon paper which we have found convenient 

 for this kind of work. 



147. Graphical Algebra with One Variable. Let a be a scalar function repre- 

 sented by a chart of equiscalar curves. These curves are to be drawn for what we 

 shall call "integer values" of the scalar, using the expression in a widened sense 

 as a shortened expression for "integer values multiplied by a positive or negative 

 power of 10." By a suitable change of units they will get integer values in the 

 common sense of the word. It is required to find the equiscalar curves which 

 represent in the same way the field of another scalar 



(a) <P = /(<*) 



In this case a curve a = const, will also be a curve <p = const. But the curves which 

 represent integer values of a will as a rule not coincide with those which represent 

 integer values of <p. 



The discontinuous method of finding the curves for integer values of <p will be 

 this : by direct calculation to find the values of <p in a certain number of points, and 

 then to interpolate between them the points where <p has integer values. These 

 points will give the placing of the curves for integer values of <p between those for 

 integer values of a. 



But we can give a continuous method of solving the same problem : We then 

 solve equation (a) with respect to the known variable a, 



(b) a = F(tp) 



and construct an auxiliary table in which the values of a are tabulated for integer 

 values of the argument (p. Thus 



Table E. Table-scheme for graphical algebra with one variable. 



