GRAPHICAL DIFFERENTIATION AND INTEGRATION. 



127 



they are obtained directly, will always have more or less of the oscillating course 

 which is characteristic of curves obtained by a process of graphical differentiation. 

 These oscillations should be carefully reduced. Then all results concerning singular 

 points, etc., which can be obtained by use of the simple scalar addition or subtrac- 

 tion (section 159), must be worked out with the greatest care. The rest of the work 



<f-a.-2i(W) 



fi -a.- 28(36) 



/3-a.z9(j5) 



cp - a.-zs(36) 21M 20M , 



/I2(S2) 



(3- a '30(a) 



/3-<Z -3/(33) 



Fig. ioi. Graphical tables for time-differentiation of a vector-field. 



will then mainly consist in forming the vector-sum of vectors which form angles 

 differing very little from 32. If for this we wish to use graphical tables those of 

 fig. 101 will serve the purpose. But in many cases the method of section 158 seems 

 to be the best in spite of the greater number of separate operations. 



