1821.] Mr. Adams on the perpetual Renewal of Leases. 307 



and because by this course I should myself, as I have stated, 

 avoid being obliged to attack the works and refute the notions 

 of many respectable individuals. From my first principle, I 

 have proceeded entirely by what appears to me to be strict 

 mathematical induction. The communication is, therefore, to 

 be considered mathematical, and can hence be refuted only by 

 showing that the principles are false, among which, to give 

 every advantage to its opponents, I will reckon the postulata ; 

 by mathematically refuting the inductions, or by showing that 

 the results do not agree numerically with the phenomena they 

 profess to explain. To avoid metaphysical difficulties, the prin- 

 ciples maybe passed over by the admission of a simple axiom in 

 philosophy ; namely, that it is impossible, by correct reasoning 

 from false principles to bring out true conclusions ; and hence 

 the attempts at refutation may be confined to the mathematics 

 and the results. To any respectable efforts of this kind, I shall 

 be happy to pay every attention ; but I hope the testimonies in 

 the extracts I have given in this letter, and the extent of my 

 researches in that paper, and the one I am now publishing in the 

 Annals, will be admitted a sufficient proof that I have not thought 

 lightly on the subject ; and, therefore, 1 trust, the world will not 

 henceforward require that I should reply to every one who 

 chooses to publish his undemonstrated opinions. 



I am, dear Sir, yours truly, 



J. Hekapath. 



Article XIII. 



On the perpetual Renewal of Leases. By Mr. James Adams. 

 (To the Editor of the Annals of Philosophy.) 



SIR, Stonchouse, near Plymouth, July 9, 1821. 



The insertion of the following problem and solution in the 

 Annals of Philosophy, when convenient, will oblige 



Your humble servant, 



James Adams. 



Problem. — A copyhold estate depending upon three of the 

 best lives that could be found is granted on condition that the 

 lessee and his successors, whenever a life may drop, shall be 



iiuuestiu Physica est. Nos proprietatem Fluidorum ex ejusmodi particulis constantium 

 mathematice demonstravimus, ut philosophic ausam pntbeanius qua;stionem illam trac- 

 tandi."— (Principia, lib. 2. Schol. Prop. 23.) 



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