SKETCH OF PROFESSOR H. A. NEWTON. 843 



planted seed there, hoping for fruit. How much such ill-directed 

 thought has been spent on the theory of numbers, on higher equa- 

 tions, on the theory of the tides, etc., which, if rightly expended on 

 some untrodden though humble field of the science, might have really 

 added to human knowledge ! And yet hardly any science can show, 

 on the whole, a more steady progress, year by year, for the last fifty 

 years, or a larger and healthier growth, than the science of quantity. 

 Here, too, as in every other science, the larger the field that has been 

 acquired, the larger its boundary-line from which laborers may work 

 out into the region beyond. An individual may wisely neglect one 

 science, in order to work in another. But a nation may not. For the 

 healthy growth of all, each science should be fostered in due propor- 

 tion. But the mathematics has such relations with other branches 

 that neglect of it must work in time wider injury, I believe, than neg- 

 lect of any other branch." 



The view expressed in the last sentence of this extract was sus- 

 tained by the citations of instances and ways in which the questions 

 of quantity and proportion have to be dealt with at some stage in 

 almost every branch of scientific investigation. 



Of the value of mathematics as an instrument of research in other 

 departments of knowledge, he says : "Again I argue from a natural 

 law of succession of the steps of discovery in the exact sciences we 

 first see differences in things apparently alike, or likeness in things 

 apparently diverse, or we find a new mode of action, or some new rela- 

 tion, supposed to be that of cause and effect, or we discover some other 

 new fact or quality. We frame hypotheses, measure the quantities in- 

 volved, and discuss by mathematics the relations of those quantities. 

 The proof or the disproof of the hypotheses most frequently depends 

 upon the agreement or discordance of the quantities. To discover the 

 new facts and qualities has sometimes been thought to be higher work 

 than to discuss quantities, and perhaps it is. But at least quantitative 

 analysis follows qualitative. It is after we have learned what hind, 

 that we begin to ask how much f " 



Professor Newton is a member of several other learned societies 

 in this country ; he is a member of the Publication Committee of the 

 Connecticut Academy of Sciences ; is a trustee of the Winchester 

 Observatory ; and is the author, in Professor Kingsley's " History of 

 Yale College," of the sketch of Professor Alexander Metcalf Fisher, 

 one of his predecessors in the chair of Mathematics, who died by 

 shipwreck at an early age ; and of the account of Winchester 

 Observatory. 



