66 



REPORT — 1853. 



durability ; but so far as regards strength, it is infinitely superior to that of 

 copper, as may be seen by the following 



Summary of Results. 



On the above data, it will be found that the iron stay and copper plate 

 (not riveted) have little more than one-half the strength of those where both 

 are of iron; that iron stays screwed and riveted into iron plates are to iron 

 stays screwed and riveted into copper plates as 1000 : 856; and that copper 

 stays screwed and riveted into copper plates of the same dimensions, have only 

 about one-half the strength of those where both the staj's and plates are of iron. 

 These are facts in connexion with the construction of locomotive, marine, 

 and other description of boilers having flat surfaces, which may safely be 

 relied upon, and that more particularly when exposed to severe strain, or 

 the elastic force of high-pressure steam. 



Provisional Report on the Theory of Determinants. 

 By J. J. Sylvester, F.R.S. 



I TRUST that I may stand acquitted of any want of respect to the British 

 Association, in having failed to be ready with the Report which last year 

 they did me the honour of confiding to me, on the Theory of Determi- 

 nants. A circumstance has occurred since the last meeting, which seems 

 to render such report less necessary or useful than at that time it appeared 

 to be, as I have been informed that a complete compendium of all the methods 

 and results of this theory is shortly forthcoming from the hands of a fellow- 

 countryman, Mr. Spottiswoode, in the journal of M. Crelle, which is access- 

 ible to the whole mathematical world. This and the pressure on my mind 

 attendant upon multifarious occupations and numerous original researches, 

 may, I hope, serve as a sufficient apology for being unprepared with the 

 report. The much vaster subject of Invariants, which includes the theory of 

 Determinants as its simplest case, has at present no chronicler or editor ; and 

 if the Association would think it desirable that a summary of the progress 

 so far made in it should be collected, and be not unwilling to commit to my 

 charge the execution of it, 1 should have pleasure in accepting the task, pro- 

 vided the period for its completion were previously understood to be not 

 necessarily limited to the period of a single year from the present time. 



26 Lincoln's Inn Fields, September 3, 1853. 



