Hence, when the distance between the aerials is constant, the minimum working energy varies as the fourth power of the height of either aerial, but when the lengths of the aerials are constant, the energy caught up by the receiving aerial must vary inversely as the square of the distance D between the aerials. Hence, if we call _e_ this minimum working energy, _e_ must vary as 1/D^{2} when L is constant, or as L^4 when D is constant, and since _e_ is a constant quantity for any given arrangements of receiver and transmitter, it follows that when the height of aerial and distance vary, the ratio L^4/D^2 is constant, or, in other words, D^2 varies as L^4 or D varies as L^2--_i.e._, distance varies as the square of the height of the aerial, which is Marconi's Law. The curve, therefore, connecting height of aerial with sending distance for given arrangements is a portion of a parabola. Otherwise, the law may be stated in the form L = _a_[\sq]{D}, where _a_ is a numerical coefficient. If L and D are both measured in metres, then, for recent Marconi apparatus as used on ships, _a_ = 0·15 roughly. (See a report on experiments made for the Italian Navy, 1900-1901, by Captain Quintino Bonomo--"Telegrafia senza fili," Rome, 1902.) This law, however, must not be used without discretion. After Mr. Marconi had transmitted signals across the British Channel, some people, forgetting that a little knowledge is a dangerous thing, predicted that aerials a thousand feet in height would be required to signal across the Atlantic, but Mr. Marconi has made such improvements of late years in the receiving arrangements that he has been able to receive signals over three thousand miles in 1903 with aerials only thirty-three per cent. longer than those which, in 1899, he employed to cover twenty miles across the English Channel. [Illustration: FIG. 15.--ALTERNATING-CURRENT DOUBLE-TRANSFORMATION POWER PLANT FOR GENERATING ELECTRIC WAVES (Fleming). _a_, alternator; H_{1}H_{2}, choking coil; K, signalling key; T, step-up transformer; S_{1}S_{2} spark-gap; C_{1}C_{2} condensers; T_{1}T_{2}, oscillation transformers; A, aerial; E, earthplate.]