ANNUAL OF SCIENTIFIC DISCOVERY. 



yond the simple arithmetical ratio. I am quite prepared to admit the possi- 

 bility of an amount of error having crept into these figures, in spite of my 

 precautions ; indeed, I have on that account been anxious to multiply obser- 

 vations in order to obtain most trustworthy results. But I cannot admit the 

 possibility of error having accumulated to such an extent as to entirely over- 

 lay and conceal the operation of the law of the squares, if in reality that law 

 had any bearing on the results. Taking 83 miles as our unit of distance, we 

 have a series of 1, 2, 3, 6, and 12. Taking 166 miles as our unit, we have 

 then a series of 1, 3, and 6. Taking 249 miles, we have still a series of 1, 2, 

 and 4, in very long distances. Yet even under these circumstances, and 

 with these facilities, I cannot find a trace of the operation of that law." 

 The author then examined the evidence of the law of the squares, as shown 

 by the value of a current taken in submarine or subterranean wires at 

 different distances from the generator thereof, . which he showed were strongly 

 corroborative of the previous results. He next examined the question of the 

 size of the conducting wire; and he had the opportunity of testing" the appli- 

 cation of the law, as enunciated by Prof. Thomson last year. The results, far 

 from confirming the law, are strikingly opposed to it. The fact of trebling 

 the size of the conductor augmented the amount of retardation to nearly 

 double that observed in the single wire. The author, however, looked for 

 the experimentum crucis in the limit to the rapidity and distinctness of 

 utterance attainable in the relative distances of 500 and 1,020 miles. 350 

 and 270 were the actual number of distinct signals recorded in equal times 

 through these two lengths respectively. These figures have no relation to 

 the squares of the distance. "Now, if the law of the squares be held to be 

 good in its application to submarine circuits, and if the deductions as to the 

 necessary size of the wire, based upon that law, can be proved to be valid 

 also, we are driven to the inevitable conclusion that submarine cables of 

 certain length, to be successful, must be constructed in accordance with these 

 principles. And what does this involve ? In the case of the Transatlantic 

 line, whose estimated length will be no less than 2,500 miles, it would 

 necessitate the use, for a single conductor only, of a cable so large and 

 ponderous, as that probably no ship except Mr. Scott Eussell's leviathan 

 could carry it, so unwieldy in the manufacture, that its perfect insulation 

 would be a matter almost of practical impossibility, and so expensive, from 

 the amount of materials employed, and the very laborious and critical nature 

 of the processes required in making and laying it out, that the thing would 

 be abandoned as being practically and commercially impossible. If, on the 

 other hand, the law of the squares be proved to be inapplicable to the trans- 

 mission of signals by submarine wires, whether with reference to the amount 

 of retardation observable in them, the rapidity of utterance to be obtained, or 

 the size of conductor required for the purpose, then we may shortly expect to 

 see a cable not much exceeding one ton per mile, containing three, four, or 

 five conductors, stretched from shore to shore, and uniting us to our Transat- 

 lantic brethren, at an expense of less than one-fourth that of the large one 

 above mentioned, able to carry four or five times the number of messages, 

 and therefore yielding about twenty times as much return in proportion to 



