integrating Differential Equations of the First Order. 489 



(3) For the solution of equations of the formXda f Ydy = 0, 



or which mav be reduced to that form. 



(4) To describe curves of the for m £{/(#)} where <f> and /are 



known functions. 



Fig. 2 



Fig. 3. 



As examples of the possible uses of the instrument the 

 following may be given : — 



(1) The templates B, C (fig. 1) are triangular, having 

 angles at B, C respectively, so that cf> (q) — mq, yfr(r) = nr. The 

 curves bb, cc are straight lines, so thntf l (t)=bt, f 2 (t) = ct. 



The differential equation becomes 



(m -|- n) xdx — (mb -f no) {xdt + tdoo) + (mb 2 + nc^tdt — Mda:. 



P describes a series of similar and coaxial ellipses. 



In the particular case when the triangular templates are 



i 



