492 Prof. Sylvester on the Pressure of Earth 



solution ; that is to say, I shall investigate under what conditions 

 the surfaces of "rupture " or "of greatest energy of friction" 

 are or can be planes ; and I shall easily be able to ascertain 

 these conditions, and to prove that when they are satisfied (but 

 not otherwise) the results of the received theory are exact. 



Professor Rankine, in the light in which he appears in a paper 

 published in the Transactions of the Royal Society, is not to be 

 ranked among those whom I have called the followers of Cou- 

 lomb. He is entitled to the merit of having perceived that the 

 received hypothesis rested on no solid foundation, and of having 

 been the first (publicly at least) to assert that the equations of 

 internal equilibrium must be resorted to for the satisfactory dis- 

 cussion of the question ; but, notwithstanding the sincere esteem 

 in which I hold the great abilities of this gentleman, I have been 

 compelled to come to the conclusion, and trust to be able to 

 satisfy himself, that the use he has made of these equations is 

 illusory, and that his results bear upon their very face a demon- 

 strable character of error. 



Under the supposed data, it is, if not obvious, at all events 

 assumed by all writers on the subject, that the equilibrium of 

 every vertical section of the earth, parallel to the side walls, may 

 be determined per se, and that we may treat the question as one 

 regarding space of only two dimensions. I shall therefore, with 

 a view to clearness, treat of the equilibrium of any one such sec- 

 tion ; the molecules, whose equilibrium is to be considered, will 

 be spoken of as bounded by lines instead of planes, and so we 

 shall speak of lines instead of planes of " rupture," and we may 

 thus conform our language to the relations of the figure actually 

 represented upon the paper. 



For the benefit of those to whom the conditions of molecular 

 equilibrium are new, it may be well to indicate briefly how they 

 may be obtained, still keeping within our prescribed framework 

 of two-dimensioned space (although the reader will not expe- 

 rience the slightest difficulty in extending them to space of 

 three dimensions) *. Through any point in the interior of the 



string, whereas, in fact, precisely the contrary effect will take place ; for 

 since downward momentum must result from the impending motion of the 

 cork upwards and the water downwards, part of the weight of the water 

 and cork is spent as downward moving force, and consequently only a 

 portion remains to act as vertical pressure upon the bucket, just as an air- 

 cushion will press with less force than its weight on the seat which bears 

 it, when, in consequence of the air being let out, part of the weight is being 

 expended in lowering the top of the cushion. 



* I have purposely begun with the beginning, because I wish to give per- 

 fect precision to the terms Thrust, Pressure, and Stress, as I shall use them. 

 Some recent authors on mechanics have wished to distinguish force measured 



