July si, 1884] 



NA TURE 



3i5 



like the divisions of a polyp community, until now natural 

 history has more than a dozen named branches ; and in 

 physics the divisions are almost as numerous. There are 

 now at least thirty named and bounded sciences ; each 

 name designating a particularly limited field, in which 

 there are able men who work their days out in labour 

 that does not consider the rest of nature as having any 

 relation to their work. 



This progressive division of labour follows a natural 

 law : and it is perhaps fit that science should itself give a 

 capital illustration of the application of this law to forms 

 of thought, as well as to the more concrete things of the 

 world ; but it is an open question whether or no it is ad- 

 vantageous to the best interests of learning. There can 

 be no question that the search for truth of a certain 

 quality is very greatly helped by this principle of divided 

 labour. If a man wish to get the most measurable yield 

 out of the earth in any way, the best thing for him is to 

 stake off a very small claim, tie himself down to it, fer- 

 tilise it highly, till it incessantly, and forget that there are 

 blossoms or fruit beyond his particular patch ; for any 

 moment of consciousness of such impracticable things as 

 grow beyond his field is sure to find expression when he 

 comes to dig his crop, whether his crop in the intellectual 

 field be elements or animals, stars or animalculas. The 

 harvest of things unknown is most easily won in this 

 kitchen-gardening way of work. 



The world needs, or fancies that it needs, this kind of 

 work ; and it is now of a mind to pay more of its various 

 rewards for the least bit of special and peculiar know- 

 ledge than for the widest command of varied learning. 

 In a thousand ways it says to its students, not only as of 

 old, " Study what you most affect," but, "Effect that study 

 altogether, know the least thing that can be known as no 

 one else knows it, and leave the universe to look after 

 itself." 



This is the prescription of our time. We are now pro- 

 ceeding on the unexpressed theory that, because no man 

 can command the details of all science, therefore he shall 

 know only that which he can know in the utmost detail. 

 We seem to be assuming, that, if many separate men 

 each know some bit of the know-able, man in general will 

 in a way know it all ; that when, in another hundred 

 years of this specialisation, we have science divided into 

 a thousand little hermit-cells, each tenanted by an intel- 

 lectual recluse, we shall have completed our system of 

 scientific culture. No one can be so blind to the true 

 purposes of learning as to accept this condition of things 

 as the ideal of scientific labour. It maybe the order of 

 conquest, the shape in which the battle against the un- 

 known has to be fought ; but beyond it must lie some 

 broader disposition of scientific life, — some order in which 

 the treasures of science, won by grim struggle in the wil- 

 derness of things unknown, may yield their profit to man. 



The questions may fairly be asked, whether we have 

 not already won enough knowledge from nature for us to 

 return, in part, to the older and broader ideal of learning ; 

 whether we may not profitably turn away a part of the 

 talent and genius which go to the work of discovery to 

 the wider task of comprehension ; whether we may not 

 again set the life of a Humboldt along with the life of a 

 Pasteur, as equally fit goals for the student of nature. 



Until we set about the system of general culture in 

 science, it will be nearly impossible to have any proper 

 use of its resources in education. A sound theory of 

 general culture in science must be preceded by a careful 

 discussion of the mind-widening power of its several lines 

 of thought. This determination cannot be made by men 

 versed only in their own specialties ; it must be made by 

 many efforts to determine by comparison what part of 

 the sciences have the most important power of mind- 

 developing. At present there are few men whose opinion 

 on such a subject is worth anything, and the number 

 constantly grows less. 



The greatest difficulty partly expresses itself in, and 

 partly rises from, the multiplication of societies which 

 include specialists as members, and specialties as the 

 subjects of their discussions. We no longer have much 

 life in the old academies, where men of diverse learning 

 once sought to give and receive the most varied teaching. 

 The geologists herd apart from the zoologists : and in 

 zoology the entomologists have a kingdom to themselves ; 

 so have the ornithologists, the ichthyologists, and other 

 students. " That is not my department," is an excuse for 

 almost entire ignorance of any but one narrow field. If 

 naturalists would recognise this " pigeon-holing," not only 

 of their work, but of their interests, as an evil, we might 

 hope to see a betterment. Until they come to see how 

 much is denied them in this shutting-out of the broad 

 view of nature, there is no hope of any change. Special 

 societies will multiply ; men of this sort of learning will 

 understand their problems less and less well ; until all 

 science will be " caviare to the general," even when the 

 general includes nearly all others beyond the dozen experts 

 in the particular line of research. 



The best remedy for this narrowing of the scientific 

 motive would be for each man of science deliberately to 

 devote himself, not to one, but to two ideals, i.e. thorough 

 individual work in some one field, and sound comprehen- 

 sion of the work of his fellows in the wide domain of 

 learning — not all learning, of course, for life and labour 

 have limits, but of selected fields. In such a system there 

 will be one society-life meant for the promotion of special 

 research, and another meant for the broader and equally 

 commendable work of general comprehension. 



It is in a certain way unfortunate that investigation is 

 to a great extent passing out of the hands of teachers. 

 This, too, is a part of the subdivision work ; but it is in 

 its general effects the most unhappy part of it. As long 

 as the investigator is a teacher, he is sure to be kept on a 

 wider field than when he becomes a solitary special 

 worker in one department. 



The efforts now being made for the endowment of re- 

 search will, if successful, lead to a still further tendency 

 to limit the fields of scientific labour. A better project 

 would be to keep that connection between inquiry and 

 exposition from which science has had so much profit in 

 bygone times. 



TWO GREEK GEOMETERS 



DR. ALLMAN in his article " On Greek Geometry 

 from Thales to Euclid," in the current volume of 

 Hermathena (vol. v. No. 10), discusses in Chapter IV. the 

 discoveries of Archytas of Tarentum, and in Chapter V. 

 those of the Greek geometer Eudoxus of Cnidus. 



Archytas was a contemporary of Plato (42S-347 B.C.), 

 probably senior to him, and saved his life when Plato was 

 in danger of being put to death by the younger Dionysius. 

 These particulars and others of interest are skilfully 

 arrayed by the author ; one only of these we recall, viz. 

 Horace's reference to the death of Archytas by shipwreck 

 in an ode (Book I. 28), in which he recognises his 

 eminence as an arithmetician, geometer, and astro- 

 nomer. Unfortunately no undoubted works of his 

 have come down to us ; the authenticity of some that 

 have been attributed to him is here discussed, but 

 these do not treat of geometry. In former chapters 

 his contributions to the doctrine of proportion and his 

 demonstrations of theorems as well as solutions of 

 problems have been noticed. Here the question of his 

 identity with the Architas of Boethius' Ars Geometries is 

 discussed, and a strong case made out for the same. The 

 connection of Archytas with the Delian Problem (already 

 touched upon in Hermathena, vol. iv.) next comes under 

 consideration, and the passage in Eutocius is translated 

 at length and accompanied by a figure. An enumeration 

 of the theorems which occur in this passage is made, 



