286 M. T. Plateau on the recent Theories of the Constitution of 



right line, that a figure is formed in which the angles at each side 

 are equal to two right angles, is certainly not assuming, either 

 in form or in fact, more than Euclid assumed when defining a 

 square. It has been said that such a definition is imperfect, 

 because we cannot by its aid give a demonstration of the twelfth 

 axiom. This, I think, is another point in which the theory of 

 parallels has been treated unfairly. In the first instance, there 

 is an unwillingness to assume proper premises ; on the other 

 hand, when a full and fair definition is chosen, it is said to be 

 inadequate, because it cannot touch certain propositions which 

 are naturally beyond its reach. The twelfth axiom has, in fact, 

 as much connexion with parallel lines, as the theory of the para- 

 bola has with that of the circle ; yet no one would assert that 

 the definition of a circle was defective because by it we cannot 

 prove, for instance, that " no two right lines in a parabola bisect 

 each other.*' 



Mr. Stevelly appears to think that his demonstration is suited 

 for elementary instruction. I regret that I must also differ with 

 him on this point. As it is merely a matter of opinion, and can- 

 not admit of any proof one way or the other, I do so with extreme 

 diffidence. Perhaps, however, I may venture to remind him, 

 that a distinguished physicist and mathematician like himself is, 

 from the nature of his position, often incapable of forming a very 

 accurate notion as to whether a certain train of reasoning is ele- 

 mentary or otherwise. What may appear very simple to him, 

 may not be so to one whose mental training is of a different 

 character. 

 Jermyn Street, Sept. 3, 1856. 



XXXVII. On the recent Theories of the Constitution of Jets of 

 Liquid issuing from Circular Orifices. By M. T, Plateau*. 



WHEN, in 1849, at the end of the Second Series of my 

 " Experimental and Theoretical Researches on the Figures 

 of Equilibrium,*' &c.t, I published a complete theory of the 

 constitution of jets issuing from circular orifices, and protected 

 from eveiy external influence, I thought that the same would 

 have been immediately adopted, seeing that it was deduced with 

 absolute rigour from the results of accurate experiments, and 

 consequently that it explained all the details and all the laws of 

 the phsenomenon. I was wrong : at the commencement of the 



♦ From the Bulletin de V Academic de Belgique, No. 6. vol. xxiii; com- 

 municated by the Author. 



t M^. de VAcad. de Belgique, vol. xxiii. Scientific Memoirs, vol. v. 

 p. 684. 



