CHAP. IV.] 



OVAL AND MELOID. 



91 



NOTE. 



THE two following series of propositions concerning the 

 Ovals belong to this period, and afford an illustration of 

 Maxwell's mode of working in those early days. See above, 

 p. 87. The only alterations made, with the exception of 

 corrections of obvious slips of the pen, consist in a sparing 

 insertion of stops. The MS., as will be seen by the facsimile 

 at p. 104, has almost no punctuation. 



I. OVAL. 



Definition 1. If a point move in such a manner that m times its 

 distance from one point, together with n 

 times its distance from another point, may 

 be equal to a constant quantity, it will 

 describe a curve called an Oval. 



Definition 2. The two points are 

 called the foci, and the numbers signified 

 by m and n are called the powers of the 

 foci. 



Definition 3. The line joining the 

 foci is called the axis. 



PROPOSITION 1 PROBLEM. 



To describe an oval with given foci, 

 given multiples, and given constant quantity. 



Let A and B be the given foci, 3 and 



2 the multiples, and EF the constant quantity, it is required to 

 describe an oval. At A and B erect two infinitely small cylinders. 

 Take a perfectly flexible and iiiextensible thread, without breadth 

 or thickness, equal to EF ; wind it round the focal cylinders and 

 another movable cylinder C, so that the number of plies between 

 A and C may be equal to m, that is 3, and the number between 

 B and C equal to n or 2. Now move C in such a manner that 

 the thread may be quite tight, and an oval will be described by 

 the point. 



