5 so 



NATURE 



[April 5, 1894 



of a force perpendicular to the line joining two elements. If 

 in any particular case the mutual force between two elements 

 ^/,/act along the line joining them, all the expressions of the form 

 (5) would vanish; but the point to which I particularly wish to 

 call attention to is that ^/le principle of angular tnoiyientum 

 cannot be deduced from Newton s laws, but a further hypothesis 

 is necessary. 



We have not yet considered Newton's first law, and if we 

 discard the hypothesis that the mutual action between two 

 elemeats consists of a force acting along the line joining them, 

 the next step is to inquire whether the first law will assist us. 

 We have already pointed out that all the molecular forces i may 

 be compounded into a wrench. Now Newton's first law asserts, 

 in effect, that when thi mass is at rest or is moving uniformly 

 in a straight line, this wrench is zero; but the first law is limited 

 to these two cases, and asserts nothing with regard to what 

 happens when the mass possesses acceleration, and it is easy to 

 see that when the mass is in either of the states contemplated 

 by Newton's first law, the molecular forces are not the same as 

 when it is in other states. For example, the molecular forces 

 exerted across any section of a pendulum rod, which is oscil- 

 lating, are not the same as when the rod is held at rest in any 

 of the positions which it assumes during its motion. Newton's 

 first law does not therefore help us. We have, however, proved 

 by Newton's second and third laws that the force constituent of 

 the wrench due to molecular forces is zero ; and if we assume 

 that the couple constituent is also zero, the sum of all such 

 terms as (5) will vanish, and (4) becomes 



2'«(xy - yx) = 2(;«:Y - jj-X) (6) 



which is the analytical expression for the principle of angular 

 momentum. 



The latter principle may therefore be deduced from Newton's 

 laws with the aid of one or other of the following additional 

 hypotheses, viz. : — 



{a) 7 he molecular action between tiuo elements consists of a force 

 acting along the line joining them. Or, 



{b) The resultant couple due to molecular action is zero, whether 

 the mass oj 7?tatter be at rest or in motion. 



We must lastly consider the principle of energy. 



Assuming that the bodily forces have a potential, we easily 

 deduce from (i) and (2) — 



^^2/«(i-^ + f + z^ + ^ = (/i. +/13 

 dt dt 



...)A 



+ (<?-i2 + Sn + ■■■)yi + •• + (A +/23 + -)^-2 + ■- • (7) 

 whence if T denote the kinetic energy, and F denote the right- 

 hand side of (7) the equation becomes 



(8) 



^ + ^=F 



dt dt 



The function F is an unknown quantity which it is impossible 

 to determine without making some special hypothesis respecting 

 the constitution of matter or the law of molecular force. We 

 shall presently show that F is zero when the matter is rigid. In 

 the case of a viscous liquid it can be shown by means of the 

 general equations (which depend upon the principles of linear 

 and angular momenta, combined with a certain hypothesis con- 

 cerning molecular action) that F is the dissipation function ; 

 whilst, in the case of an elastic solid it can similarly be shown 

 that — F represents the time variation of the potential energy 

 due to strain. That F is zero when the matter consists of a 

 rigid body can be proved as follows : — Let oij, cdo, coj be its 

 component angular velocities about the axes ; then 



■*•.' = A - (y-2 - Jl^'^3 + (=2 - -l)'^-2 



and the terms in F depending on the mutual action of Wj and 

 m^ become 



(/12 +/jl^^l -/2l(>'2 - yd<^Z +/2l(Z2 - Zi)cOo 



+ similar terms in "" and h. 

 This may be written — 



(/12 +/2i)-ix - <->i{f«i{y-2 - y-d -g-2i{x.2 - Jfi} - ... 



1 It seems hardly necessary to suppose that the mutual action between 

 two elements consists of a couple as well as a force ; for even in the case of 

 magnetized matter, we may regard each element as the limit of a pair of 

 positive and negative ones which are rigidly connecied together, and we 

 may deduce th^ theorem that the mutual acti.m between two magnetic 

 elements consists of a couple by considering the forces between each pair of 

 simple elements. 



NO. 1275, VOL. 49] 



By the third law /j, +/21 = °> ^"^ ^^^o by either of the sub- 

 sidiary hypotheses {a) or {b) all the expressions of the form 



'>'32!Ai(>'2 - y^ - i-2A^-2 - ^1)} 



vanish ; whence F = o, and (8) becomes 



T + V = const., 



which is the analytical form of the principle of the conservation 

 of mechanical energy. A. B. Basset. 



The Artificial Formation of the Diamond. 



With your kind permission I wish to make a few observa- 

 tion on Prof. Joly's interesting letter in your issue of March 22. 

 in which he c includes from a consideration of the curve repre- 

 senting the expansion of diamond by heat that "the diamond is 

 a form of carbon which has been subjected to high pressure 

 when crystallising," and in which he remarks that these theo- 

 retical considerations gave rise to experiments which he only laid 

 aside finally upon hearing of M. Moissan's success. He also 

 says: " M. Moissan has shown that the added condition of high 

 pressure has rendered a method previously unsuccessful now for 

 the first time successjul." (The italics are mine.) Prof Joly 

 here makes a claim for M. Moissan which I must say, injustice 

 to that gentleman, he has never made for himself. 



If Prof. Joly will kindly turn to my paper on the " Artificial 

 Formation of the Diamond," in the Proceedings of the Royal 

 Society, No. 204, 1880, he will find that pressure is not an 

 " added condition," and that M. Moissan has not " rendered a 

 method hitherto unsuccessful for the first time successful." 



Further, he will find that his theoretical deductions were 

 practically demonstrated by me fourteen years ago, and I then 

 described experiments showing that carbon, set free by metals 

 under great pressure, was denser and harder the higher the pres- 

 sure, and my experiments culminated in the preparation of 

 minute quantities of carbon identical in hardness, density, and 

 action on polarised light with natural diamond. 



M. Moissan has done no more, but he has devised a process 

 of great ingenuity which does not entail the danger and expense 

 of mine, and which can be repeated with much greater chance 

 of success. 



If Prof. Joly will turn to my paper, he will find that, like 

 Moissan, I obtained my diamond in conjunction with a fused 

 mass containing iron, and fused under extreme pressure. Again, 

 in the Proceedings of the Royal Society, of June 14, 1888, he 

 will find that the Hon. C. A. Parsons there describes experi- 

 ments which produced true diamond (thoroughly corroborated 

 since the publication of his paper), and he proved conclusively 

 that pressure is absolutely essential ; and as his method is one 

 which lends itself to the treatment of carbon in quantity at the 

 necessary temperature and at any pressure, it is of much greater 

 practical importance than Moissan's method. 



I have the highest admiration of Moissan's work, not only 

 with his electric lurnace, but in the several fields in which he 

 has distinguished himself; and as he has courteously admitted 

 that I was the first to define the conditions and actually prepare 

 artificial diamond, I feel constrained to point out that both 

 Parsons and I had fully enunciated the conditions which Prof. 

 Joly attributes to Moissan. 



I quite agree with Prof. Joly's concluding paragraph, and 

 my researches led me about a year ago to the construction of 

 an apparatus capable of producing pressures up to forty tons 

 on the square inch, in which I have good hopes of being able 

 to melt carbon in quantity and produce diamond by fusion 

 instead of solution. 



Carbon, at ordinary pressures, passes directly from the solid 

 to the gaseous state, and only under enormous pressure can it 

 be made to pass through the liquid state. 



It would be premature for me to say more at present, but I 

 hope you will kindly allow me to put these facts on record, as 

 they seem to have been forgotten even by those who are work- 

 ing in the field. J. B. HannAY. 



Cove Castle, Loch Long, N.B., March 26. 



I WAS in hopes that the limited claim for priority which 

 I made for M. Moissan would have secured me from controversy 

 as to the claims of previous workers. Although well acquainted 

 with the paper to which Mr. Hannay refers me, I had never 

 derived from it the idea that Mr. Hannay attributed his results 

 to the crystallisation of carbon out of a metal. 



