December 1, 1887.] 



♦ KNOWLEDGE ♦ 



31 



to show off knowledge on matters outside its subject. He 

 says, indeed, that I refer to Newton's geometrical methods, 

 but onl}- to show how cumbersome they are. This, bow- 

 ever, was not my object. I gave an example of Newton's 

 geometrical method of dealing with a particular jiroblem, 

 and of an algebraical method of dealing with the same 

 problem, and touched in passing on their cumbersome 

 nature, in order to impress on the student the value of a 

 method which deals with all such problems in a simple and 

 easy way. 



But my critic shows in an even more marked way his entire 

 misapprehension of my very simple and modest little plan,^ 

 when he asks vrhy I did not deal with the measurement of 

 arcs, since it is about as important as the measurement of 

 areas. If he knew anything about the Calculus, he would 

 be aware that so soon as the student enters on the deter- 

 mination of arcs, he finds himself confronted by problems 

 of much greater difficulty than are involved in the determi- 

 nation of areas. Passing from the circle to the ellipse, 

 which is next in simplicity of character, he finds that the 

 formula for the determination of an elliptic arc does not 

 admit of integration — being, in fact, the .^econd of the three 

 well-known " elliptic integrals " whose discussion by 

 Legendre, Jacobi, and others has taxed the highest powers 

 of ditlerential analysis. 



It will not be thought surprising that a critic who thus 

 misunderstands the whole purpose of the book he criticises 

 should imagine many things which have no existence, and 

 misunderstand whatever can be misunderstood. He says 

 my book is far from justifying " the boast " in the preface, 

 and though the nearest approach to a boast is contained in 

 the sentence, " I have striven in this little work to show at 

 once how and why we want a method of calculation dealing 

 with quantities which vary in value under varying condi- 

 tions, and how such a method of calculation is to be used 

 in practice." Again, I mention that I took up little of the 

 Differential Calculus for my degree examination at Cambridge ; 

 and this clear-minded critic, so keenly conscious of the 

 value of a nice logical perception of minute difTerences, 

 assumes forthwith that I know no more of the Calculus now 

 than I did then. I add that " what I have since learned 

 about higher departments of mathematics " (for the Differen- 

 tial Calculus is quite elementary) "I have studied as occasion 

 required— the only really effective way of studying mathe- 

 matics," and my intensely perceptive critic finds the meaning 

 of this simple statement beyond his utmost jwwers of con- 

 ception. 



When critics of this sort are coarsely rude, we must not 

 blame them as we would others. But we must not, there- 

 fore, refrain from pointing out where they show coarseness 

 or ill manners. My " practical teacher " is not content to 

 criticise and misunderstand ; he is not satisfied to blame as 

 if his ipse dixit alone settled the matter : he adopts the 

 method of the vituperative costermonger, who by his 

 "That's just like (/ojt. Bill," con,veys at once the idea of 

 blame and the suggestion of continued misconduct. The 

 Practical Tmcher, assuming the weekly charge for learning 

 manners not wasted in the case of its writers, ought to know 

 that to describe what a writer says as '■ eminently charac- 

 teristic," with the evidently underlying idea that that is, of 

 itself, to condemn it, is unworthy of a respectable publica- 

 tion, for it is altogether ungentlemanly. "VVe look tor such 

 tricks at Billingsgate, not among decent members of society, 

 or in sedate and well-mannered journals. 



I admit, however, two characteristic peculiarities in my 

 method of teaching, which persons who can recognise 

 minute differences, but fail to see large ones, may recognise 

 as signs of self-conceit. Whenver my own experience has 

 taught me anything, whether it has taught me that I have 



been right, or that I have erred, I always say as much ; and 

 again, when an opinion is based on my own researches only, 

 I point this out — a Saturday Eevieirer or a too confident 

 Practical Teacher says, " It is so and so," and as he does not 

 mention himself, the avei-age mind says, " He is not 

 egotistical, he knows." I prefer to say, " It appears to me, 

 so fiir as my own researches have extended, that the case is 

 so and so," and because I mention myself the average mind 

 says, " This man is an egotist." Which way of speaking is 

 really the more modest, I leave the logical mind to decide. 



AMERICAN UNION AND IRISH DISUNION. 



AM asked by a military correspondent if I can 

 explain how it is that Americans, who fought 

 so hard to maintain union in their own 

 country, show such sympathy with the efforts 

 of the Home Rule party. 



I have never yet met with an American, 

 properly so called, who sympathised in the 

 slightest degree with the followers of Mr. Parnell. There 

 niaij be some Americans who are misled by the clamour of 

 the newspapers, nine-tenths of which owe the bulk of their 

 political articles to Irish writers. And there are certainly 

 many politicians who, in their puUic utterances, cater for the 

 Irish among their constituents. But, from the multitudinous 

 conversations I have had with Americans on the subject of 

 England's difliculties with the Irish, I am convinced their 

 strongest anti-British feeling in this matter amounts to 

 nothing more than a lively sense of amusement that the old 

 country seems likely to be hampered and worried into con- 

 cessions and compromises precisely as the United States 

 have been. That Irish section in America (unfortunately, 

 f^u- the largest) which corresponds v.'ith the present Home 

 Rule party and the old Repealers, plays the same game of 

 disturbance there which the followers of Parnell play here. 

 They practically sell their support to the party which will 

 pay "most for it — and this alike in national politics, in State 

 legislation, and in municipal matters. Iiishmen of this type 

 (most emphatically I do not mean the Irish race) seem 

 incapable of higher or worthier policy. Unfortunately they 

 too often get their way in America ; just as in the old days 

 of corrupt elections, men who were ready to sell their votes, 

 were too often able to secure their price. The only i)roper 

 remedy would be that sets of men guilty of thLs particular 

 form of corruption should be, for a while, deprived of their 

 votes, precisely as corrupt boroughs were in the old times. 



The position of American newspapers in regard to the 

 Irish question is well illustrated by an experience of my 

 own. At the last election but one, when it seemed likely 

 that the Home Rulers would be offered the bribe they had 

 so long hankered for, I chanced, in the course of a letter to 

 the St. Josejih Herald (written from England) to touch on 

 the iniquity that concessions should be made for the sake of 

 a party's votes, and apart (as former action showed) from 

 any reference to the interests of the nation— asking in 

 what this differed, except in scale, from common bribery 

 and corruption. My letter appeared, only through a lucky 

 or unlucky chance in all probability. But immediately the 

 editor was called upon by indignant Irishmen, and told 

 that unless he excluded thenceforth my name from his 

 columns not an Irishman in Missouri would continue to 

 subscribe. As my letters were practically a present to the 

 paper, and only written at the editor's .special request— the 

 paper being of the nonpaying sort— I was no loser, but the 

 reverse, when the editor earned out the wishes of his 

 constituency. But the case illustrated strongly the subser- 



