NOTES ei7 



here and there there is some crumbHng of the rocks, some 

 landshp, some Httle ravine, some Uttle rivage, some more 

 gentle slope where the feet may hold ; and there it is that the 

 man of sense endeavours to ascend. He tries, and he may 

 be foiled ; but, if he succeeds, he makes an advance. Nature 

 is infinite. We can rise only step by step. The people who 

 talk about pure science think that they can jump vast dis- 

 tances — with the result that they generally remain where they 

 are. We can say that the true investigator takes the most 

 promising opportunity offered to him, irrespective of the 

 question whether his success will lead to immediately useful 

 results or not ; but he always knows this — that, whatever 

 new result he may obtain, it is almost certain to be a key which 

 will open new treasures of nature for the benefit of men in 

 general. For example, when Faraday investigated electricity, 

 do we think that he had no vision within him as to the large 

 practical results which might follow his work ? He did not talk 

 of these practical results at the moment because before his work 

 was done he could not specify them ; but he knew that know- 

 ledge brings power, and that power enhances prosperity. 

 Another example is that of Darwin. He saw his opportunity 

 in our ignorance of the reason why different species of living 

 things exist ; and he studied the matter and gave us the Theory 

 of Evolution, True, this was a piece of pure science ; but it 

 was not a piece of useless science. It added to the dignity 

 and the honour of human intelligence. It was therefore useful. 

 There are many people, in this country especially, who may be 

 called the fatuitists— fatuitists in science, art, and politics — 

 who talk, but never achieve anything, except perhaps mischief- 

 making. Those who have themselves made no advances in 

 science too often belong to this school. They write most of the 

 textbooks, sit on most of our committees, preside over many 

 of our societies, and reap many of the rewards ; but let them 

 allow the man with the genuine passion for investigation to 

 choose his subject for himself. 



De Moivre's Theorem (Sir R. Ross) 



I will be very much obliged to any of our mathiematical readers who will 

 be so kind as to inform me where I can find any record of the following 

 proposition — which shows that De Moivre's famous theorem connected with 

 complex numbers is only a particular case of the iteration — that is, the opera- 

 tive involution — of a real algebraic function of which one of the parameters 

 is reduced to zero. I have known the proposition for many years, and 

 indeed indicated it in my paper on " Operative Involution " in Science 

 Progress, No. 50, p. 288, October 1918, in some examples at the end, 

 and in No. 51, p. 486, January 1919, last example; but I have searched in 

 vain for it through my books — even in the works of Hamilton, Tait, and 

 Joly on quaternions, on which subject it has an important bearing. 



