172 REPORT— 1860. 



cubic law of reciprocity. If ( £-1 ) =1, it will follow from those theorems that 



(Ei\ = I. But if ( ^i J =p, or p 2 , they do not determine whether ( & ) = P> 

 \pj* \PJ* a ' \PJ* 



or p 2 . It is remarkable that these theorems, "forma genuina qua inventa 

 sunt," may be obtained by applying the criteria for the resolubility or irreso- 

 lubility of cubic congruences (art. 67) to the congruence r 3 — 3\r — XM=0, 

 mod q (art. 43), which, by virtue of M. Kummer's theorem (art. 44), is re- 

 soluble or irresoluble according as q is or is not a cubic residue of X. 



On the Performance of Steam- Vessels, the Functions of the Screiv, and 

 the Relations of its Diameter and Pitch to the Form of the Vessel. 

 By Vice-Admiral Moorsom. 



(A communication ordered to be printed among the Reports.) 



In this the fourth paper which I now lay before the British Association, it 

 may be desirable to recapitulate the points I have brought into issue, and for 

 the determination of which, data, only to be obtained by experiments, are 

 still wanting, viz. — 



1. There is no agreed method by which the resistance of a ship may be 

 calculated under given conditions of wind and sea. 



2. The known methods are empirical, approximate only, and imply smooth 

 water and no wind. 



3. The relations in which power and speed stand to form and to size are 

 comparatively unknown. 



4. The relations in which the direct and resultant thrust stand to each 

 other in any given screw, and how affected by the resislance of the ship, are 

 undetermined. 



In order to resolve these questions, specific experiments are needed, and 

 none have yet been attempted in such manner as to lead to any satisfactory 

 result. 



The Steam Ship Performance Committee of the British Association have 

 pressed upon successive First Lords of the Admiralty, the great value to the 

 public service which must ensue if the following measures were taken, viz. — 



1. To determine, by specific experiment, the resistance, under given con- 

 ditions, of certain vessels, as types; and, at the same time, to measure the 

 thrust of the screw. 



2. To record the trials of the Queen's ships, so that the performance in 

 smooth water may be compared with the performance at sea, both being re- 

 corded in a tabular form, comprising particulars, to indicate the characteris- 

 tics of the vessel, of the engine, of the screw, and of the boiler. 



Hitherto nothing has come of these representations. 



In the paper read last year at Aberdeen, I showed, in the case of Lord 

 Dufferin's yacht 'Erminia,' how the absence of admitted laws of resistance 

 interfered with the adjustment of her screw, and how, therefore, as a matter 

 of precaution, a screw was provided capable of a thrust beyond what the 

 vessel required. 



1 also showed, in the case of the Duke of Sutherland's yacht ' Undine,' how 

 her screw, from being too near the surface of the water, lost a large portion 

 of the thrust due to its size and proportions. In other words, a screw capa- 

 ble of giving out a resultant thrust in sea water of 5022 lbs., at a speed of 



