470 Intelligence and Miscellaneous Articles. 



may be very imperfectly applicable, like the equilibrium theory of 

 the tides. 



Second Memoir on the Intrinsic Equation of Curves. By the 

 Master of Trinity. 



The intrinsic equation of curves, according to which any curve is 

 expressed by means of an equation between its length (s) and its 

 angle of deflection (<p), may be conveniently used for many purposes. 

 When a curve is so represented, the portion of the length which 

 comes after a cusp must necessarily be taken as negative. This had 

 appeared anomalous to some mathematicians, on the ground that a 

 cusp is in all cases the limit of a loop. To clear up this point, the 

 author adduces two cases. (1 .) The curve of which the equation is 

 s=za<p-{-b sin <p, which is a looped curve when b is less than a, and 

 a cusped curve otherwise. But in this curve it appears that a loop 

 arises from the vanishing of two cusps, and of the intervening nega- 

 tive portion of the arc. (2.) The case of the ordinary trochoid, which 

 is a looped curve when the describing point is exterior to the rolling 

 circle, and becomes a cusped curve (a cycloid) when the point is in 

 the circle. But in this case the length of the trochoid is equal to 

 the length of an elliptical arc, which, in the case of the cycloid, 

 coincides with the major axis, and becomes negative beyond the 

 vertex of the ellipse. Other equations were examined, which give 

 running pattern curves with cusps, cusped curves with infinite diver- 

 ging spirals at the extremities, and sinuous curves with infinite con- 

 verging spirals at the extremities ; and certain integrals which oc- 

 curred in the former memoir on this subject were discussed. 



LXVI. Intelligence and Miscellaneous Articles. 



THE FIRST IDEA OF THE ELECTRIC TELEGRAPH. 



To the Editors of the Philosophical Magazine and Journal. 

 Gentlemen, Sidmouth, Nov. 12, 1850. 



N the Number of the Philosophical Magazine for May, I observe that 

 Professor Maunoir claims for his friend Dr. Odier the first idea 

 of the electric telegraph. I herewith send you a translation from a 

 German work by Schwenter, entitled Delicia Physico -Mathematics > 

 and published in 1636, from which it will appear that the crude idea 

 of the electric telegraph was entertained upwards of a century before 

 the period alluded to by Professor Maunoir. Indeed CErsted's grand 

 discovery was alone wanting to perfect the telegraph in 1636. The 

 idea, in fact, appears to have been entertained prior even to this 

 date, for Schwenter himself quotes from a. previous author. 

 I am, Gentlemen, 



Respectfully yours/ 



N. S. Heineken. 



"How two people might communicate with each other at a distance 

 by means of the magnetic needle : — 



" If Claudius were at Paris and Johannes at Rome, and one wished 



I 



