452 Mr. Hennessy on the Importance of an Adequate Definition 



Mr. Hopkins walls himself up, as I have elsewhere said, in an 

 imaginary line of demarcation, and fails of candying his specu- 

 lations out to their legitimate conclusion. lie breaks up the 

 Weald, but docs not dispose of the materials. Does he leave 

 them to be disposed of by the gentle means of erosion, by sea- 

 boards or under-currents, or by atmospheric wear ? The erosion 

 by sea-boards it cannot be, for there are no beaches ; there are 

 lacerated escarpments, but there are no cliffs; there are chasms 

 and ravines, but these do not bear the marks of having been 

 " fiords '' or estuaries ; and there are bare rocks, but these have 

 no stratified beds with their attendant fossils at their feet, nor 

 are accompanied by any of the other ordinary signs of sea-beds. 

 [To be continued.] 



LVIII. On the Importance of an Adequate Definition in developing 

 the Theory of Parallel Lines, By J. P. Hennessy* 



PROFESSOR STEVELLY'S criticism, in the last Number 

 of the Philosophical Magazine, on a paper of mine 

 which was published nearly four years ago, raises two distinct 

 questions. It raises, in the first place, a question as to the 

 logical value of the reasoning in my paper. On this I do not 

 think it necessary to offer any observations. To do so, would be 

 to approach too close to what every man of science must wish 

 to avoid, — a personal discussion. I am quite certain that a 

 discussion of such a nature could have no claims whatever to 

 occupy the valuable space of the Philosophical Magazine. I 

 trust, therefore, that Mr. Stevelly will not feel I am treating 

 him with any discourtesy if I allow all the assertions as to 

 ''defective logic and incorrect reasoning" to pass by unan- 

 swered f. 



But the position taken by Mr. Stevelly raises another and 

 more important question. It brings forward the very point on 

 which, in my opinion, the Theory of Parallels will be found to 

 depend. This is, the question as to the sort of definition we are 

 at liberty to employ. 



* Communicated by the Author. 



t With regard to the opinion I may happen to entertain as to the details 

 of his demonstration, Mr. Stevelly observes, — " I am much gratified that 

 Mr. Hennessy does not profess to have detected any defect in the chain of 

 reasoning on which the nroofs are founded." For fear of misapprehen- 

 sion, I may remark that 1 did not oflfer any opinion on that subject, for a 

 very simple reason. "When I had pointed out that the whole principle of 

 Mr. Stevelly's method was taken — inadvertently I am sure — from a French 

 geometer, it did not appear necessary to go any further. The minor details 

 of a " New Method," which was thus deprived of all claim to originality, 

 could hardly be expected to command much attention. 



