On the Angle of Dock Gates and the Bee's Cell. 437 



surface at v.'hich the diffraction takes place) with the actual inci- 

 dent ray. This assumption, though plausible at first sight, is 

 altogether precarious ; and since in the particular case of diffrac- 

 tion in one and the same medium it leads to a result at variance 

 with that of a rigorous investigation, it cannot be admitted. 

 • M. Eisenlohr^s formula agrees no doubt very well with M. 

 Holtzmann's experiments; but then it must be recollected that 

 the formula contains a disposable constant, whereby such an 

 agreement can in good measure be brought about. But in 

 agreeing with these experiments, it is necessarily at variance 

 with mine, in passing to which it is not allowable to change the 

 value of the disposable constant. I can no more ignore the 

 unifoi'm result of my own experiments, than I am disposed to 

 dispute the accuracy of M. Holtzmann's, made under different 

 experimental circumstances. Whether the circumstances of his 

 experiments or of mine made the nearer approach to the sim- 

 plicity assumed in theory, or whether in both there did not exist 

 experimental conditions sensibly influencing the result, but of 

 such a nature that it would be impracticable to take account of 

 them in theory, is a question which at present I think it would 

 be premature to discuss. I still adhere to the opinion I formerly 

 expressed*, that the whole question must be subjected to a 

 thorouglily searching experimental investigation before physical 

 conclusions can safely be drawn from the phsenomena. 



LXV. On the Angle of Dock Gates and the Bee's Cell. By 

 Charles M. Willich, Actuai-y, University Life Assurance 

 Society. 



To the Editors of the Philosophical Magazine and Journal. 

 Gentlemen, 



THE question as to the proper angle at which dock gates 

 should be placed so that the timber employed should yield 

 the most favourable result, has often been discussed by mathe- 

 maticians, and determined as a problem of maxima and minima. 

 The angle has been found to be 109° 28' 16". 



A patient consideration of the properties of the cube and its 

 partition, has led me to the fact that the geometrical solid formed 

 by the union of two cubes, being a dodecaliedroa with twelve 

 rhomboidal faces, produces angles affording the greatest amount 

 of resistance. 



The obtuse aii^le on the face of this dodecahedron produced 

 by the union of two cubes as above mentioned, is the precise 

 angle which affords the greatest resistance to water pressure 'u\ 

 a dock gate. 



* Phil. Mag. Ser. 4. vol. xiii. p. 151). 



