Although not mentioned in this article, much of the credit for the success of the NAA test transmissions actually belonged to Dr. Harold Arnold, of AT&T's Western Electric Co. Arnold had taken the original, crudely designed, Audion, and found that greatly increasing the tube's vacuum resulted in a much higher level of performance.
The Electrical Experimenter, November, 1915, page 321:

Wireless  Telephony  Now  From  Washington  to  Honolulu
THE most wonderful feat in wireless telephony was accomplished on the night of Sept. 29 last, when the human voice was projected through the ether from Washington, D. C., to Honolulu, a distance of 4,900 miles!
    Only a few hours earlier wireless telephonic communication had been established between New York City and San Francisco, a distance of 2,500 miles, which was heralded as an epochal innovation.
    Secretary of the Navy Daniels has announced the successful transmission of wireless telephone messages from the United States naval radio station at Arlington to the naval radio station at Mare Island, Cal., a distance of about 2,500 miles. All that was necessary to carry on this transcontinental wireless telephone conversation, he said, was to connect the receiver and transmitter apparatus of the special telephone outfit with the radio apparatus and send the message. Washington to Honolulu
    Captain W. H. G. Bullard, U. S. N., who is in charge of the Arlington station, and other officers of the navy conversed with officers of the navy on duty at the Mare Island yard in San Francisco.
    The demonstration was the result of experiments that have been in progress for some time, and their success is expected to have a revolutionary influence on communication between American naval vessels and shore stations. By means of this perfected apparatus, which probably will be installed at all naval radio stations, it is expected that officers of the navy on land will be able to carry on wireless telephone conversation with officers at sea. Captain Bullard stated that the apparatus had been perfected to the point where a person on shore might carry on a long distance wireless telephone conversation with a friend on a transatlantic liner in mid-ocean, whenever shore station and liner were equipped with the necessary apparatus. In his formal announcement, Secretary Daniels said:
    "I am pleased to announce the successful outcome of experiments which have been carried on for the last few months by the American Telephone & Telegraph Company and the Western Electric Company in co-operation with radio stations under the jurisdiction of the Navy Department by which long-distance wireless telephony has been made possible.
    "Speech has been successfully transmitted from the Arlington radio station to the radio station at Mare Island, Cal., and there successfully received, thus making possible conversation without wires over a distance of approximately 2,500 miles, the first time this great distance has been covered by wireless telephony. In the first experiments the voice was successfully transmitted by radio to Mare Island from Arlington, the return answers and communication being made over the transcontinental land telephone line. This was successfully accomplished in the presence of officials and engineers of the Western Electric Company, a representative of the Signal Corps of the army, representatives of the technical and operating departments of the Navy Department and a few other interested parties.
    "After this successful demonstration, conversation originating in New York City was transmitted over the land wire to Arlington, there automatically connected to the radio transmitter which carried the voice to Mare Island, where it was clearly and distinctly received, and answers and other conversation were from there transmitted over the transcontinental line to the originating office in New York.
    "The conversation was carried on by the president of the American Telephone & Telegraph Company, Mr. Vail; the vice-president, Mr. Bethell, and Mr. Waterbury, one of the directors, while at Mare Island were officials of the Navy Department, John J. Carty, chief engineer of the American Telephone & Telegraph Company, and representatives of the Western Electric Company.
    "Every official taking part in this demonstration is enthusiastic about the results and the possibility of developing this system as an extension of the telephone system to ships at sea. The fact that the voices can be started on a land wire and automatically transmitted to a voice radio transmitter holds out hope that persons should readily be put in touch by telephone with others at sea through some central transmitting station.
    "The use of such long distance wireless telephone communications in naval or military operations is still in an undeveloped state, but it is expected valuable use can be made of the wonderful demonstration; but aside from such considerations the department and its officials feel proud that they have been interested co-operators in the first practical development of this last march in the wonderful science of radio communication."
coverage map
    The space through which the oral message was sent to Hawaii is greater than that between New York and London, New York and Paris, greater even than from New York City to the North Pole!
    From New York to London is 3,740 miles; to Paris, 4,020; to Berlin, 4,385; to Bremen, 4,235; to Antwerp, 4,000, and to the North Pole, 3,435 miles.
    Owing to the lack of adequate sending apparatus at Honolulu it was impossible to communicate back to Washington, but a cablegram announced the fact that the message had been received and distinctly heard.
    The account of the successful experiment was given out by James D. Ellsworth, of the American Telephone & Telegraph Company. He said in part:
    "Wireless telephony from the Atlantic seaboard to Hawaii, a distance of 4,600 miles, is an accomplished fact. By the special wireless telephone developments which have been made by the engineers of the American Telephone & Telegraph Company and of the Western Electric Company (which concern made all the apparatus for this remarkable long distance test, including the vacuum tubes), speech was transmitted from Washington to a wireless station near Honolulu. If anything further was needed to show the wonderful capacity of these new discoveries by the engineers of the Bell system, this last triumph, coming but a few hours after Mr. Vail, the president of the company, had talked by wireless from Washington to Mr. Carty, its chief engineer, located at Mare Island, is conclusive.
    "That transatlantic wireless telephone communication is assured as soon as the disturbed condition in Europe will permit of tests from this country to there, is obvious when it is remembered that all scientists agree on the fact that it is much more difficult to send wireless telephone communications across land than across water. This wireless telephone message from Washington to Hawaii had to pass over the whole of the United States--a distance of 2,500 miles--before it encountered better wireless conditions which exist when sending over large bodies of water. For the purpose of this test the sending was done from the navy wireless station at Arlington, just outside of Washington. The receiving was done on a small wireless antenna specially erected for the purpose by the engineers of the telephone company, which, by permission of the naval authorities, was located at the naval station at Pearl Harbor, Hawaii.
    "The message at Honolulu was received by Lloyd Espenchied, an engineer of the American Telephone & Telegraph Company, who had been sent there by Mr. J. J. Carty, its chief engineer, to take charge of the observations, the successful results of which we are now able to report.
    "Another interesting feature of the tests was that, in a practical way, the ability to connect wireless telephone systems with wire telephone systems was shown. You have no doubt noted that Mr. Vail in his talk used a wire circuit from New York to Washington. At Washington, by the special means invented and developed by the engineers of this company, the wires were connected to our special wireless apparatus and to the navy's mighty wireless tower, where the message went wirelessly to its destination."
    The exact apparatus used in this phenomenal test of the wireless telephone is being kept a secret owing to patent reasons.