2l6 



NATURE 



\_7uly 3, 1879 



mined not by the motion of one rope alone, but by that of 

 several, and suppose/ further, that all this machinery is 

 silent and utterly unknown to the men at the ropes, who 

 can only see as far as the holes in the floor above them. 



Supposing all this, what is the scientific duty of the 

 men below. They have full command of the ropes, but 

 of nothing else. They can give each rope any position 

 and any velocity, and they can estimate its momentum 

 by stopping all the ropes at once, and feeling what sort of 

 tug each rope gives. If they take the trouble to ascertain 

 how much work they have to do in order to drag the 

 ropes down to a given set of positions, and to express this 

 in terms of these positions, they have found the potential 

 energy of the system in terms of the known co-ordinates. 

 If they then find the tug on any one rope arising from a 

 velocity equal to unity communicated to itself or to any 

 other rope, they can express the kinetic energy in terms 

 of the co-ordinates and velocities. 



These data are sufficient to determine the motion of 

 every one of the ropes when it and all the others are acted 

 on by any given forces. This is all that the men at the 

 ropes can ever know. If the machinery above has more 

 degrees of freedom than there are ropes, the co-ordinates 

 which express these degrees of freedom must be ignored. 

 There is no help for it. 



Of course, if there are co-ordinates for which there are 

 no ropes, but which enter into the expression for the 

 energy, then, if the motion of these co-ordinates is 

 periodic, there will be "adynamic vibrations" communi- 

 cated to the ropes, and by these the men below will know 

 that there is something peculiar going on above them. 

 But if they pull the ropes in proper time, they can either 

 quiet these adynamic vibrations or strengthen them, so 

 that in this case these co-ordinates cannot be ignored. 



There are other cases, however, in which the conditions 

 for the ignoration of co-ordinates strictly apply. For 

 instance, if an opaque and apparently rigid body contains 

 in a cavity within it an accurately balanced body, mounted 

 on frictionless pivots, and previously set in rapid rotation, 

 the co-ordinate which expresses the angular position of 

 this body is one which we are compelled to ignore, because 

 we have no means of ascertaining it. An unscientific 

 person on receiving this body into his hands would imme- 

 diately conclude that it was bewitched. A disciple of the 

 northern wizards would prefer to say that the body was 

 subject to gyrostatic domination. 



Of the sections on cycloidal motions of systems, we 

 can only here say that the investigation of the constitution 

 of molecules by means of their vibrations, as indicated by 

 spectroscopic observations, will be greatly assisted by a 

 thorough study of this part of the volume. 



We have not space to say anything of what to many 

 readers must be one of the most interesting parts of the 

 book— -that on continuous calculating machines, in which 

 pure rolling friction is taken from the class of unavoid- 

 able evils, and raised to the rank of one of the most 

 powerful aids to science. Rolling and sliding have been 

 more than once combined in the hope of obtaining accu- 

 rate measurements, but the combination is fatal to accu- 

 racy, and these new machines, one at least of which has 

 been actually constructed and used, are the first in which 

 pure rolling friction has had fair play given it as a method 

 of mechanically accurate integration. 



A method is also given of combining a number of disk, 

 globe, and cylinder integrators, so as to form a machine 

 the motions of two pieces of which are related to each 

 other by a differential equation of any given form. 

 These machines all work in a purely statical manner, 

 that is, in such a way that the kinetic energy of the system 

 is not an essential element in the practical theory of 

 the machine (as in the case of pendulums, &c.), but has 

 to be taken into account only in order to estimate the 

 magnitude of the tangential forces at the points of 

 contact which might, if great enough, produce slipping 

 between the surfaces. Thus, by means of a machine, 

 which will go as slowly as may be necessary to keep 

 pace with our powers of thought, motions may be calcu- 

 lated, the phases of which in nature pass before us too 

 rapidly to be followed by us. 



In the original preface some indications were given of 

 what we were to expect in the remaining three volumes of 

 the w^ork. We hope that the reason why this part of the 

 preface is omitted in the new edition is that the work will 

 now go on so steadily that it will be unnecessary to 

 preface performance by promise. 



J. Clerk Maxwell 



ARTIFICIAL MANURES 

 On Artificial Manures, their Chemical Selection, and 

 Scientific Application to Agriculture. A Series of 

 Lectures given at the Experimental Farm at Vincennes, 

 during 1867 and 1874-5. By M. Georges Ville. Trans- 

 lated and Edited by W. Crookes, F.R.S. (London : 

 Longmans and Co., 1879.) 



THOSE who take up this volume with the hope of finding 

 the chemistry of artificial manures fully treated will 

 be much disappointed. Not only are many of the com. 

 monest manures scarcely mentioned, but some of the 

 most" important and practical aspects of the subject are 

 never noticed. The behaviour of manures after they 

 come in contact with the soil is surely of the greatest im- 

 portance. Chemical investigations have long ago proved 

 that some of the ingredients of manure — as phosphoric 

 acid and potash — are firmly held in combination by the 

 soil, while others — as nitric acid, chlorine, and soda — are 

 feebly retained, and readily pass away in the drainage 

 water after rain. It has also been abundantly proved 

 that though ammonia is firmly retained by a fertile soil, 

 it rapidly undergoes conversion into nitric acid, 'which is 

 easily washed out. The practical conclusion from these 

 facts is plain. Diffusible manures must be applied only 

 when the crop can m.ake immediate use of them. Now, 

 though M. Ville speaks voluminously concerning the ap- 

 plication of phosphates, nitrates, and ammonium salts, no 

 reference to the facts just indicated is to be found in his 

 book, beyond the mere statement that clay is capable of 

 temporarily retaining potash and ammonia. 



The lectures of M. Ville are chiefly occupied by the 

 consideration of the present state of agriculture in France, 

 and by the recommendation of a system of artificial 

 manuring of which he regards himself as the inventor. 

 The condition of French agriculture is clearly, as a whole, 

 very low ; the existence of the peasant and small farmer 

 is only maintained by the exercise of much thriftiness 

 and self-denial. To improve this condition M. AHlle very 



