FIELDS OF PRESSURE AND MASS IN THE ATMOSPHERE. 91 



63. Arithmetical and Graphic Methods of Adding and Subtracting Scalar 

 Fields. Let a x and a 2 be scalar quantities of the same kind, say both temperatures, 

 both pressures, or both heights above sea-level. From the fields a t and a 2 we shall 

 often have to deduce the field of their sum 



For the solution of this problem two methods offer themselves. 



(A) Arithtnetical method. We may form arithmetically the sum (a), likewise 

 the difference (&), at a certain number of points. The numbers representing these 

 sums or differences are noted in the plane, and the equiscalar curves drawn accord- 

 ing to the method mentioned in the preceding article. 



This method will be especially convenient when the values of both quantities 

 a, and a 2 are observed at the same points. The sums or differences used in draw- 

 ing the chart can then be derived directly from the observed quantities. 



(B) Graphic method. The curves are supposed to be drawn for the same 

 interval in the field of a, as in that of a. 2 . Superimposed upon each other, the 

 curves divide the plane into a set of curvilinear parallelograms. We can then draw 

 two sets of diagonal curves, and it will easily be verified that the one set represents 

 the field of the sum a x -{-a 2 , and the other that of the difference a x <x 2 . 



This graphic method of forming the sum or difference of two scalar fields is 

 most convenient, and will be much used below. It will generally prove prac- 

 ticable to draw the curves of the different systems on different papers laid upon 

 each other. Transparent paper may be used, or, more conveniently, common 

 paper placed on a sheet of glass and strongly illuminated from below. 



The arithmetical and the graphic methods supplement each other in a valuable 

 manner. The latter gives both systems of diagonal curves sharply, if the two sets 

 of originally given curves cut each other at nearly right angles. But if the angles 

 approach o or 180 , only the one system, that containing the long diagonals of the 

 parallelograms, will be sharply defined. The other, that containing the short diag- 

 onals, will be very indeterminate, greatly varying with small errors in the course ot 

 the originally given curves. This second set is therefore obtained better by the 

 arithmetical method, especially if the arithmetical sums or differences can be formed 

 from originally measured and not from interpolated values of the two scalar quan- 

 tities a x and <xj. 



64. Charts of Absolute and of Mutual Topography of Isobaric Surfaces. 



The synoptic representations of the fields of pressure and ot mass are worked out 

 on charts containing the situation of the stations from which the observations have 

 been made. 



On a chart of this description we can mark the height of a certain isobaric surface 

 above each station. Then, by aid of these heights, we draw, as explained in section 

 62, a topographic chart showing the configuration of the isobaric surface. In this 



