July 2, 1888.] 



♦ KNOWLEDGE ♦ 



199 



While this is proceeding we shall gradually drop those 

 industries which demand the greatest supply of coal in pro- 

 portion to value of result. Thus our blast furnace.?, and 

 other smelting furnaces, will be blown out. We shall cease 

 to make crude pig iron and other crude metal, the cost of 

 which chiefly depends on that of coal and ore, but not being 

 addicted to the misdirection of industry by legislative inter- 

 ference, we shall develop our industries in the direction of 

 higher elaborations of the raw material. One ton of watch 

 springs demands more industiy and has higher value than 

 a thousand tons of pig iron, while the pig iron demands 

 five hundred times as mucli coal for its production. There- 

 fore by the aid of unfettered natural selection, and the sur- 

 vival of the fittest, the blast furnaces will be blown out, and 

 an evolution of those industries demanding more labour, 

 more skill, and more intelligence, and less fuel, will proceed, 

 provided we retain those energies which at the proper time 

 brought our coal to the surface, and created the steam-engine 

 to pump the pits when more powerful pumps were needed, 

 and also created railways and locomotives to carrj- it through- 

 out the land when such carriage was demanded. 



I have alwaj's regarded, and frequently described, the 

 notion that our manufacturing supremacy depends on our 

 coal supplies as a gi-oss popular failacv, and one which at 

 the present day may be very mischievous if it induces us to 

 lean upon such a rotten staff. The sooner we understand 

 that any physical advantage in coal supply we ever 

 possessed has already gone, the better for our future pro- 

 gress. It is not desirable that we should continue to be the 

 coal-cellar of the world, nor that we should depend on the 

 coarser industries that are so voracious of fuel. 



Our old form of " manufacturing supremacy " is becoming 

 a national curse. We import more than a million of eggs 

 daily, and corresponding quantities of butter, cheese, fruit, 

 and other agricultural produce. We obtain these in exchange 

 for factory products, for goods that are hatefully produced at 

 the cost of national degeneracy by the crowding of millions of 

 miserable wretches into the slums of manufacturing towns, 

 where their unhealthy work and surroundings c;\use them 

 to produce stunted, scrofulous, and vicious offspring. At 

 the same time we are extending the big fixctoiy and steam- 

 engine system of work to our agriculture, and thereby con- 

 verting into a prairie a country that should be a garden. 

 Farming is becoming one of the lost arts in England, our 

 so-called farmers being mere graziers, wholesale manu- 

 facturers of mere beef and mutton. 



Coal worship has promoted the exaggerated use of grossness 

 in everything ; big mechanical work done by big engines in 

 big factories, producing big incomes at one end and big union 

 workhouses at the other. Let us endeavour to supersede 

 these by small farms highly worked by peasant proprietors, 

 and small workshops belonging to highly skilled and artistic 

 artisans, with good wages all round. 



King Coal must be dethroned, and with him will go his 

 grovelling money-grubbing courtiers, to be replaced by a 

 commonwealth of individual industrial skill and intelligence 

 naturally fitting a small island densely populated, and with 

 a climate so moderate in all directions that a full day's work 

 may be done on any day throughout the year. 



Let other nations do the big things, the tall work, and 

 the coarse work — let us do the best. But we cannot step 

 into this position at once. This progress, like that of our 

 coal exhaustion, with which it is intimately connected, must 

 be gradual and endless. Instead of relying on coal or iron 

 ores or any other physical advantages, we must prepare for 

 their declining supply by developing more reliable and 

 enduring sources of prosperity — the intelligence of all the 

 people, especially the workers. A rich man can afford 

 to be a fool, and the nation can afford to let him play the 



fool provided he is a harmless fool ; but not so with the 

 industrial millions. They must be highly educated in order 

 to do the higher work demanded under the new conditions. 

 They determine the progress of the nation, whether it has 

 little coal, or much coal, or no coal. If we understand this 

 and act upon it, the gi'adual exhaustion of our coal supplies 

 will be a national blessing. We shall have fewer flunkey- 

 feeding millionaues — or, better still, none ; and fewer 

 paupers — or, better still, none ; but the nation will be 

 enriched by consisting mainly of skilful and intelligent 

 wealth-producers suflicientlj' well paid to obtain rational 

 comfort, but not sufficiently to become sensual sybarites. 



EASY STUDY IN THE DIFFERENTIAL 

 CALCULUS. 



SCTGGESTED BY TUE "S.iTUEDAY REVIEW." 



X my " Easy Lessons in the Differential Cal- 

 culus," written specially for beginners, and 

 rather to show them how well woith studying 

 the Calculus is than as a treatise on that im- 

 portant pait of mathematics, I explain in 

 Lesson I. and illustiate by an example what is 

 meant by " ditferentiation," and in Lesson II. 

 what is meant by " integration." The particular example 

 selected is the fall of a body under the action of gravit}-, 

 £0 that in these two short lessons I cons-ider only the differ- 

 ential coefficient of the familiar expression " , representing 



the space fallen through in time t under gravity. In 

 Lesson III. (only four pages in length) I take another 

 simple expres-ion {ay—y'), for diflerentiation, "before pro- 

 ceeding to obtain the diflerential coefficients of various 

 familiar functions." At this very early stiige, before I had 

 given the differential coeffi-cients of anii of tlie simjjle func- 

 tions (attended to in Lessons IV. and Y.), I thought it well 

 to show how even the pre-elementarj' matter already dealt 

 with could be used in solving a familiar problem or two. 

 Having only the differential coefficient of (« y — y'-) available 

 for the purpose, I was naturall}- somewhat limited in my 

 choice, especially as I had barely begun to show the rela- 

 tions between differential coefficients and the increments or 

 decrements of variable quantities. I selected two cases 

 which involved the expression (ay — y-) or y{fi—y); the 

 first related to the recfcmgle between two lines of length, 

 y and {a — y), the problem being the determination of the 

 value of y, in order that the rectangle represented in area 

 by y{a — y) might be a maximum. Every geometrician 

 knows the problem and its answer, and half-a-dozen ways of 

 solving it. Every algebraist knows what value of y makes 

 the expression {a y—y'-) a maximum, and how to prove that 

 this happens. But of course the illustration of the special 

 point I was considering would be none the worse for the 

 familiar character of the problem dealt with — perhaps rather 

 the better. The point to be illustrated was the way in 

 which the differential calculus can be applied to probleins, 

 which, dealt with geometrically or algebraically, require 

 usually some special device planned to meet each case as it 

 arises, which is true even for these very simple cases. 



However, the Saturday Review has thought it fair to 

 treat as follows this simple illustration, given at the very 

 beginning of my subject, before I had dealt with the 

 simplest of the diflerential coefficients, and specially de- 

 scribed as merely a preliminary example of the method of 

 using the diflerential calculus : — 



Lesson III. is headed " Illustrations of the Use of the Calculus " 

 [the reviewer might have noticed, had he cared to be honest, that 



