VII what would happen if these differential equations were the sole consideration. The result is represented in the frontispiece. The extensive researches of V. Bjerknes and his School are pervaded by the idea of using the differential equations for all that they are worth. But whereas Prof. Bjerknes mostly employs graphs, I have thought it better to proceed by way of numerical tables. The reason for this is that a previous comparison of the two methods, in dealing with differential equations, had convinced me that the arithmetical procedure is the more exact and the more powerful in coping with otherwise awkward equations.
Graphical methods are sometimes elegant when the problem involves irregularly curved boundaries.
But the atmospheric boundary, at the earth, nearly coincides with one of the coordinate surfaces, so that graphs would have no advantage over arithmetic in that respect. It has been customary to regard line-squalls and other marked discontinuities as curious exceptions to the otherwise smoothly gradated distribution of the atmosphere. But in the last two years Prof. V. Bjerknes and his collaborators J. Bjerknes, H. Solberg and T. Bergeron at Bergen have enunciated the view, based on detailed observation, that discontinuities are the vital organs supplying the energy to cyclones. For such purposes graphs have a special facility which numerical tables lack. So probably the most thorough treatment will be reached by tabulating quantities numerically, where they vary continuously, and by drawing a line on the table where there is a discontinuity.