366 PERSONAL PREPARATION FOR RESEARCH. 



be the fifteenth birthday of the Quaternions. The 

 started into life, or light, full-grown, on the 1 6th Octol 

 1843, as I was walking with Lady Hamilton to Dublin, 

 and came up to Brougham Bridge. That is to say, I then 

 and there felt the galvanic circuit of thoughjb closed, and 

 the sparks which fell from it were the fundamental 

 equations between I, J, K ; exactly such as I have used 

 them ever since. I pulled out, on the spot, a pocket-book,, 

 which still exists, and made an entry, on which, at the 

 very moment, I felt that it might be worth my while to 

 expend the labour of at least ten (or it might be fifteen) 

 years to come. But then it is fair to say that this was 

 because I felt a problem to have been at that moment 

 solved, an intellectual ivant relieved, which had haunted 

 me for at least fifteen years before.' l 



Hypotheses are more varied than the truths of science ; 

 for every single new truth of science discovered by means 

 of research, many hypotheses have been imagined. They 

 are devised by various different methods ; they are often 

 suggested by comparison and analogy of facts and general 

 truths, by generalising upon them, by inferring causes, 

 necessary conditions, and coincidences. Every investi- 

 gator, in forming hypotheses, constructs such only as 

 are consistent with his views of nature ; but he perceives 

 nature as through a glass, darkly : consequently a very 

 large proportion of his speculations are unsuccessful, i.e., 

 they yield either negative or unsatisfactory results when 

 tested by experiment or observation. Many of the un- 

 successful hypotheses are intrinsically erroneous ; others 

 may not have succeeded because they were not tested in 

 a suitable manner, or, if they were suitably tested, the 

 results were either of a kind which was not suspected, or 

 were so minute that they were not perceived. 

 1 North British Review, vol. xiv. p. 57. 



