CHAP. IV.] ADOLESCENCE 1844 TO 1847. 77 



string of given length passing round three or more fixed 

 pins, and constraining' a tracing point, P. See Fig. 3. 

 Further, the author regards curves of the first kind as con- 

 stituting a particular class of curves of the second kind, two 

 or more foci coinciding in one, a focus in which two strings 

 meet being considered a double focus; when three strings 

 meet a treble focus, etc. 



Professor Forbes observed that the equation to curves 

 of the first class are easily found, having the form 



*Jx + y = a + I ^(x cf + y*, 



which is that of the curve known under the name of the 

 First Oval of Descartes. Mr. Maxwell had already observed 

 that, when one of the foci was at an infinite distance (or 

 the thread moved parallel to itself, and was confined, in 

 respect of length, by the edge of a board), a curve resembling 

 an ellipse was traced ; from which property Professor Forbes 

 was led first to infer the identity of the oval with the 

 Cartesian oval, which is well known to have this property. 

 But the simplest analogy of all is that derived from the 

 method of description, r and / being the radients to any 

 point of the curve from the two foci. 



mr + nr r = constant, 



which, in fact, at once expresses on the undulatory theory of 

 light the optical character of the surface in question, namely, 

 that light diverging from one focus F without the medium, 

 shall be directly convergent at another point / within it ; 

 and in this case the ratio - expresses the index of refraction 

 of the medium. 



If we denote, by the power of either focus, the number of 

 strings leading to it ..by Mr. Maxwell's construction, and if 

 one of the foci be removed to an infinite distance, if the 

 powers of the two foci be equal, the curve is a parabola ; if 

 the power of the nearer focus be greater than the other, the 

 curve is an ellipse ; if the power of the infinitely distant 

 focus be the greater, the curve is a hyperbola. The first case 

 evidently corresponds to the reflection of parallel rays to a 

 focus, the velocity being unchanged after reflection; the 

 second, to the refraction of parallel rays to a focus in a 



