394 Progress in Science. [July, 



Feet. Inches. 



Width inside the enclosing walls .. .. .. 211 6 



Length .. 311 6 



Depth from the top of the walls to the stringers 



in the floor of the dock .. 17 i| 



Depth from the level of ordinary high water to 



the top of the stringers . . . . . . . . 13 o 



Depth from the level of ordinary low water to the 



top of the stringers .. .. .. .. no 



The material selected for the wall of the basin was Santorin beton, com- 

 posed of Santorin earth, a volcanic product from the Greek island of San- 

 torino, and lime paste, in the proportion of 7 to 2, forming the hydraulic 

 mortar; to this was added 7 parts of broken stone, the mixture being made 

 into a conical heap, and tempered by exposure in the open air from one to 

 three days, when it was ready for use. Of this beton extensive wharves and 

 moles had already been constructed at Trieste, Fiume, and Pold, and as it had 

 been found durable and efficient, was moderate in cost, and obtainable in any 

 quantity, it was considered that no better material could be determined upon 

 for the walls of the Pold basin. 



Propellers. — On the 18th of April a paper was read at a meeting of the Institu- 

 tion of Civil Engineers, by Sir C. F. Knowles, Bart., M.A., F.R.S., " On the Archi- 

 medean Screw Propeller, or Helix of Maximum Work." In considering the 

 defects of existing screw propellers, the author was led to propose to himself the 

 problem, "What is the form of the surface of the screw propeller of which the 

 work done is the greatest possible ? " Referring the required surfaces to three 

 rectangular co-ordinates, x,y, and z, one in the axis of rotation, the other two in 

 the plane of rotation, the author first obtained a general expression for the 

 total " work done" by the blade in propelling the ship, in the form of a double 

 integral in terms of the co-ordinates x and y, and of the partial differentials of 

 z with respect to each of them, of the speed of rotation of the blade, and 

 lastly, of the speed of the ship. As this integral was to be a maximum for all 

 points of the surface sought, it must be treated by the known methods of the 

 calculus of variations. This done, an equation of condition was obtained, 

 which, by the performance of the operations indicated by the symbols, led to 

 an equation involving two factors, each factor being a partial differential 

 equation between the three co-ordinates of the surface. The first of these 

 being integrated gave for its solution the whole family of ordinary helices 

 which were the surfaces of least work. The second factor was the differential 

 equation of the required surface, the treatment of which was given in the 

 paper in extenso. It led at once,- and very simply, to an equation analogous to 



that of the common helix (tan. 9= atan ' a \ viz., tan. *0 = a tan> 2a . From 



this it was at once deducible that the surface of the blade at the axis cut the 

 plane of rotation at an angle of 45 , while the common helix cut it at go , and 

 therefore acted powerfully in the dead water to propel the ship, just where the 

 common helix had no propelling power. It was proposed to call this surface 

 the hemi-helix, or hemi-angular helix. The paper then proceeded to determine 

 the pressure of this blade upon the vessel in the direction of the keel, and 

 thence the whole circumstances of the ship's motion. 



Civil Engineering. — The Kistnah Viaduct, now in course of construction in 

 connection with the Great Indian Peninsula Railway, consists of 36 spans 

 of 100 feet clear at the top of the columns, and is 3848. feet long from centre 

 to centre of the end columns, which are built into the abutments. The piers 

 are arranged for carrying a double line of railway, although at present girders 

 for a single line only are erected. The section of the river is irregular, 

 the height of the piers varying from 34 feet to 76 feet 6 inches from base 

 of pier to rail level. The river bottom is hard rock, into which the cylinders 

 of the piers are sunk, and to which they are securely bolted. The piers each 

 consist of two columns formed of wrought-iron cylinders, averaging 10 feet in 



