20* Prof. Moseley's Reply to Mr. Earnshaw. 



from the tendency of the opposite semiarch to motion, and is 

 just equal to that tendency. It; is therefore equal to the least 

 force which would support that semiarch, and therefore to 

 the least force which would support the first-mentioned semi- 

 arch ; or it is a minimum subject to the conditions, and 

 therefore the pressure upon the abutment is also a minimum. 

 And the positions of the resultants of the pressures upon the 

 different points of the key and abutments, as well as the mag- 

 nitudes of those resultants, are subject to this law*. 



Here, then, we have verified another application of the 

 principle of least pressure, and it is shown to constitute a 

 most important element in the true theory of the arch, deter- 

 mining the position of its line of pressure, and thence all the 

 conditions of its equilibrium. 



I have now answered the objections of Mr. Earnshaw at 

 considerable length ; and I beg in conclusion to assure him 

 of the respect which I feel to be due to any observations 

 which he may think fit to make on subjects connected with 

 the science of mechanics, and of the pleasure which I shall 

 have in answering any other inquiries which may suggest them- 

 selves to him on the subject at issue between us. The ques- 

 tion of statical resistance is beset with difficulties. Those which 

 Mr. Earnshaw has suggested are by no means the only, 

 nor even the greatest difficulties which have occurred to me, 

 and which I have carefully considered. It will, however, give 

 me great pleasure to know that, so far as these are concerned, 

 the explanations I have given, appear to that gentleman satis- 

 factory. In the mean time I beg leave to state, that it is my 

 intention on some early occasion (should my other occupations 

 permit it,) to resume the discussion of the subject, and to endea- 

 vour to apply the theory of statical resistances to some of that 

 vast variety of practical questions which depend upon it. 



I have the honour to be, 



Gentlemen, yours, &c. 

 King's College, London, H. MosELEY. 



February 8, 1834. 



* It is evident, that an infinite number of different forces might be ap- 

 plied at an infinite number of different points of the keystone, each of 

 which would support the semiarch ; of these one only is that which viiMjitst 

 sustain it. 1 have discussed this subject fully in a paper read before the 

 Cambridge Philosophical Society during the last term. 



