May 21, 1874] 



NA TURE 



43 



intercourse of different branches of the human race ? 

 That nations should think or feel exactly in unison is no 

 more to be expected than that individuals of the same 

 family should possess identical tastes and habits ; but as 

 in the smaller, so in the larger groups, these distinctive 

 characters may and ought to exist apart from every un- 

 kind jealousy or envious bitterness. There had been far 

 too much of this in past days, and we hail with pleasure 

 the appearance of this friendly book, which has evidently 

 been drawn up in a truly kind and gtnial spirit. 



If it puts us somewhat to shame, that the Assistant- 

 Astronomers of the Paris Observatory should be telling us 

 what goes on at our own doors, we have only ourselves to 

 thank for the omission, and them for the way in which 

 they have supplied it. The plan they have adopted is an 

 excellent one ; and as to its execution there is very much 

 to praise. A history of English observatories and their 

 work could not be otherwise than somewhat unequal in 

 its execution ; it would probably be so to some extent 

 even in native hands ; to a foreigner, who must, generally 

 speaking, depend upon communicated information, the 

 difficulty would be insuperable ; and to this cause wc 

 may evidently refer the omission of some finely appointed 

 private observatories, such as those of the Rev. H. C. 

 Key, with its 18-inch silvered speculum, of Mr. Bird, the 

 Rev. E. L. Bcnhon, Capt. Noble, Mr. Neijon, lilr. Biines, 

 and many others. It is, in fact, in these private 

 " telescope-houses " that England is so rich, as was 

 formerly remarked in substance to the present writer 

 by M. Leon Foucault, and it is through their work that 

 much of the physical astronomy of the day has been 

 advanced to its present position. But this is exactly what 

 would escape the notice of any but ourselves, and even 

 the generality of ourselves ; and in this respect there is, 

 of course, a good deal of deficiency in the work which 

 cannot well be blamed. But great pains have evidently 

 been taken to insure correctness, and to impart knowledge 

 which to many among ourselves will have all the interest 

 of novelty ; and this has been done, for the most part, as 

 far as we can judge, in a very satisfactory way. 



The French language is now so generally understood 

 among us that a translation is perhaps rot required ; but 

 should it be undertaken, or should the authors, as we hope, 

 be encouraged to send fonh another impression, we would 

 request permission to offer a few suggestions. The Bed- 

 ford Cat.alogue, which has had so marked an influence on 

 English astronomy, would well come in for a share of 

 notice : the names of the opticians, whose work is de- 

 scribed — which are seldom given, and perhaps not aUva\ s 

 correctly — might be supplied with advantage; several 

 orthographical slips, and one considerable error in the 

 little map, might be rectified. With these improvements, 

 and some difference in the arrangement and appropri- 

 ation of the very pretty illustrations, this charming little 

 Tolume, even now greatly to be commended, would meet 

 our expectations in every way. T. W. W. 



LETTERS TO THE EDITOR 



[ The Editor does not hold himself resfonsible /or opinions expressed 

 liy his corres/oiidetils. No notice is taken 0/ anonymous 

 commiiniciilions.'] 



Quantitative Relations of Cause and Effect 

 After Mr. Spencer has implied that he will not himself con- 

 tinue the controversy further, Mr. Haywarel, in his last letter. 



has confused the issues by misstating Mr. Spencer's position. In 

 the circumstances, perhaps, it will not be improper for me, as 

 one familiar with Mr. Spencer's psychological doctrines, to 

 rectify Mr. Ilayward's error and explain that which he mioap- 

 prehends. 



The cue may be taken from an experience described in Mr. 

 Spencer's " Principles of Psychology" (§ 46S, note), where it is 

 shown that when with one hand we pull the other, we have in 

 the feeling of tension produced in the limb pulled a measure of the 

 reaction that is equivalent to the action of the other limb. 

 Both terms of the relation of cause ar,d effect are in tl.is case 

 present to consciousness as muscular tensions, wliich are our 

 symbols of forces in general. While no motion is produced they 

 are felt to be equal, so far as the sensations can serve to measure 

 equality ; and when excels of tension is fel lin the one am, 

 motion is experienced in the other. Here, as in the examples 

 about to be given, the relation between cause and effect, tlioutih 

 numerically indefinite, is definite in the respect that every add'- 

 tional increment of cause produces an additional increment of 

 (ffect ; and it is out of this and similar experiences that the idea 

 of the relation of proportionality grows and becomes organic 



A child, when biting its food, discovers that the harder he 

 bites the deeper is the indentation; in other words, that the 

 more force applied, the greater the effect. If he tears an object 

 with his teeth, he finds that the more he pulls the more the thing 

 yields. Let him press against something so't, as his own person, 

 or his clothes, or a lump of clay, and he sees that the part or object 

 pressed yields little or much, according to the amount of t'.e 

 muscular strain. He can bend a stick, the more completely ti e 

 more force he applies. Any elastic object, as a piece of india- 

 rubber, or a catapult, can be stretched the farther the harde: he 

 pulls. If he tries to push a small body, there is little resistance 

 and it is easy to move ; but he finds that a big body presents 

 greater resistance and is harder to move. The experience is pre- 

 cisely similar if he attempts to lift a big body and a little one ; 

 or if he raises a limb, with or without any object attached to it. 

 He throws a stone : if it is hght, little exerti )n propels it a con- 

 siderable distance; if vir/ heavy, great exertion only a shcrt 

 distance. So, also, if he jumps, a slight effort raises him to a 

 short height, a greater efToit to a greater height. By blowing 

 with his muuth he sees that he can move small objects, or the 

 surface oi his morning's milk, gently or violently according as the 

 blast is weak or strong. And it is the same with sounds : with 

 a slight s'rain on the vocal organs he produces a murmur ; wiili 

 great strain he can raise a shout. 



The experiences these propositions record all implicate the 

 same consciousness — the notion of proportionality between forje 

 applied and result produced ; and it is out of this latent con- 

 sciousness that the axiom of the perfect quantitative equivalence 

 of the relations between cause and effect is evolved. To shew 

 how rigorous, how irreversible, this consciousness becomes, take 

 a boy and suggest to him the following statements : — Can he not 

 break a string he has, by pulling? tell liim to double it, and then 

 he will break it. He cannot hend or break a i)articular stick : 

 let him make less effort and he will succeed. He is unable to 

 raise a heavy weight : teli him he errs by Using too much force. He 

 can't push over a small chest : he will find it easier to up: et a 

 larger one. By blowing hard he canno: move a given object : if 

 he blows lightly he will move it. By great exeition he cannot 

 make himself audible at a distance: but he v\ ill make himself 

 heard with less exertion at a gr ater distance. Tell him to do all 

 or any of these, and of course he fails. The [iropositions are un- 

 thinkable, and their unthicikableness shows that the consciousness 

 which yields them is irreversible. These, then, are pieconcep- 

 tions, pioperly so called, which haveyrown unconsciously out of 

 the earliest experi>nces, beginning with those of the sucking in- 

 fant, are perpetually confirmed by hesh experiences, and have at 

 last become organised in the mental structure. 



It is not, however, any such experiences which Mr. Hay ward 

 adduces to exemplily organic preconceptions. He asserts that 

 his "principal 'exemplificaticn of unconsciously-formed precon- 

 cepiions' was of Mr. .Spencer's own choosing, namely, New- 

 ton's ' Second Law of Motion.' " This is an error : Mr. Spencer 

 gave fio examples of unconsciously- formed preconceptions. If 

 Mr. Hayward will refer to Mr. Spencer's letter in Nature, 

 vol. ix. p. 462, he will find that Mr. Spencer has described the 

 unconsciously-fcrmed notion of the relation between cause and 

 effect in general term=, and wiiliout example or illustration. In 

 his last letter he simply named the relation between muscular 

 tensions and their effects. Probably he expected Mr. Hayward 

 to seize his meaning without any specific example. 



