book in the Van Nostrand Science Series; and in 1913 he produced a second edition of it with a few revisions and the addition of four folding plates.

In that treatise he draws the conclusion that "the critical span at which the suspension bridge becomes economically superior to the cantilever bridge is 1,670 feet." His calculations were made for a structure carrying four steam railway tracks between trusses and two exterior sidewalks on the lower deck, and a roadway with electric railway tracks between trusses on the upper deck, the total live load for the trusses being 18,000 pounds per linear foot, of which 12,000 pounds were for the steam railways. His profile shows bare bed rock, which, under the approaches, is approximately horizontal and a few feet above extreme high-water level. He figured his cantilever structures for main openings of 1,000 feet, 1,500 feet, and 2,000 feet, and his suspension bridges for main openings of 1,500 feet, 2,250 feet, and 3,000 feet.

While recognizing the value of Dr. Steinman's work and giving him due credit for his laudable energy and ambition, the author doubted the correctness of the main conclusion just mentioned, and in "Bridge Engineering" he wrote concerning it as follows:

"In order to evolve a mathematical demonstration of the problem, he (Dr. Steinman) had to make numerous assumptions more or less approximately correct. Without checking all of his mathematical work, it is evident that the professor has made as fair a comparison as he could; but his assumptions were so numerous and approximate that his conclusions must be taken with a liberal allowance for variation. ...

"All these facts affect materially the question at issue, and it is probable that, if the changes implied were incorporated, the span length for equal cost found by the investigator would be considerably greater."

For a number of years the author has had the desire to settle this economic question; but the amount of labor involved had always appeared appalling. In truth, it was so, because Dr. Steinman spent most of his spare time for two years in making the computations for his investigation.

It is true that the author could easily have figured the weights of metal and the costs thereof for cantilever bridges by employing the diagrams which he prepared for his papers on "Nickel Steel for Bridges,"* and "The Possibilities in Bridge Construction by the Use of High-Alloy Steels,"* most of which diagrams were published in these papers; but not until after he had written Chapter XXVII of "Bridge Engineering" did he possess any quick method of computing the weights of metal and the costs of suspension bridges. In that chapter are presented for the first time a number of formulae, from which, in conjunction with the numerous diagrams in Chapter LV of the same treatise, can be found quite readily the approximate weights of metal for all portions of suspension bridges.

In April, 1918, for the first time since the issuing of his book, the author found leisure to make the contemplated economic investigations. They

* Published in the Transactions of the American Society of Civil Engineers.