On some Organic Substances of High Refractive Power. 245 



while to mention them, as they have an interest in connection 

 with this paper. 



If the signs of all the terms of an equation bx + ex 2 + dx? 

 + &c. —y be changed, the curve of course is in no way 

 changed. If the signs of the even powers be changed, the 

 curve is obviously turned round about the origin through two 

 right angles ; but if the sign of the term containing x alone 

 be reversed, the shape of the curve is entirely altered, yet 

 the relation between the new and the old curve is very simple. 



Firstly, they cross at the origin, making there equal angles 

 on either side of the axis of y. Secondly, whatever value of 

 x be taken the tangents of the two curves for that value 

 will cross one another and the axis of y in the same point. 

 This must be so, for the distance of this point from the 



origin =y—x-^-, and in this expression no part of the term 



involving x remains. Fig. 8 shows the series of curves for 

 the particular series of equations 



y = x d + 3x 2 + 2x (1) 



y = z*-3x 2 + 2x (2) 



y=x d + 3x 2 -2x (3) 



y = x 3 -3x 2 -2x (4) 



and shows the intersection of three pairs of tangents in y. 



I should say, in conclusion, that I have brought this 

 machine before the notice of the Physical Society not as a 

 thing which is likely to be of any practical use, but because 

 it has a certain interest, more especially in connection with 

 another machine invented by my friend Mr. Cunynghame, 

 which is really practically valuable, and which he will show 

 this afternoon. (See p. 260.) 



XXXII. Note on some Organic Substances of High Refractive 

 Power. By H. G. Madan, M.A* 



IN the course of some correspondence respecting M. Bert- 

 rand's polarizing-prisms, one of which I had the honour 

 of showing to the Society last summer, I was informed that 

 the cement used was naphthyl-phenyl-ketone dibromide. It 

 was evident, from the theory of the prism, that this substance 

 must have a refractive index at least as high as that of calc- 

 spar for the ordinary ray, viz. 1*658 ; and as so highly re- 

 fractive a cement seemed likely to be of great value for 



* Communicated by the Physical Society : read January 23, 1886. 

 Phil. Mag. S. 5. Vol. 21. No. 130. March 1886. S 



