54 



NA TURE 



[Mav 1 6, 1 90 1 



of the observctl portion of the inner corona, the bolomelric 

 effect of its visual radiation may be supposed to be equal to that 

 of the latter ; but the observations above recorded show that 

 the total radiations from the moon being 55 + 30, or eighty-five 

 bolomctric divisions, are seventeen times as great as the radia- 

 tions from the inner corona, and hence it may be supposed that 

 the corona lacks that large amount of infra-red radiation which 

 is proper to the moon's spectrum. 



The moon's spectrum, however, is that of a heated solid body, 

 and all heated solid bodies, and heated gaseous bodies as well, 

 send to the bolometer large amounts of infra-red radiation. So 

 far, then, we might conclude that the inner corona has not the 

 radiations of a hot solid or gaseous body, but, owing to the lack 

 of a contemporary measure of the sky radiation just outside the 

 corona, and of a full knowledge of the influences that the 

 atmospheric radiations would have on our ability to discriminate 

 this, the above conclusions seemed to me only probable, and 

 worth verification at the forthcoming eclipse. 



Smithsonian Institution, .April 29. S. P. I.anci.ey. 



The Persistence of the Spectrum of Carbon 

 Monoxide. 



The letter of Dr. Carl v. Wesendnnk (p. 29), which giVes an 

 .iccount of the spectrum of carbon monoxide appearing in a 

 vacuum tube containing silicon tetrafluoride, affords an instance 

 of the extreme difliculty of obtaining vacuum tubes charged with 

 (lerfeclly pure substances. The case he cites of silicon fluoride 

 being prepared from " pure" sulphuric acid, glass and fluorspar, 

 without any but glass joints to connect the different parts of the 

 apparatus, is one in which neither the perfect freedom of the 

 sulphuric acid, nor of the glass itself, from carbon compounds 

 can be relied upon. In experiments on the absorption spectrum 

 of ozone made by me in 1 88 1, it was found that strong sulphuric 

 acid free from all the usual impurities was not absolutely clear, 

 but by being kept in an atmosphere containing a large propor- 

 tion of ozone it became perfectly brilliant and absolutely colour- 

 less when seen in volumes of half a gallon to two gallons at a 

 time. It appeared from further experiments that the impurities 

 were either carbon or some form of organic matter probably 

 coming from dust or dirt. As to the purity of the glass used for 

 vacuum tubes, it may be remarked that dust and condensed 

 vapour from carbonaceous matter, such as the products of com- 

 bustion from lamp oil or coal, adheres to its surface with much 

 tenacity. It is probable that the fluor spar contained organic 

 matter, for the rea.son that this substance is associated with lime- 

 stone of a bituminous character in England and that it has been 

 asserted thai its colour is due to organic substances. By the 

 action of sulphuric acid a gaseous carbon compound might 

 easily be evolved which would contaminate the silicon fluoride 

 even if there were no carbonates present. Next we have to 

 consider the traces of air which may remain in the tube, and 

 must not regard these as being absolutely free from hydrocarbons. 

 M. Armand Gautier has shown that there are combustible gases 

 in the atmosphere, one of which is a hydrocarbon, the other 

 hydrogen, and there is also some carbon monoxide. The diffi- 

 culty of removing these by ordinary chemical treatment is so 

 great that special operations and reagents were provided for 

 their removal. 



In vacuum tubes it is know'n that carbon monoxide shows its 

 spectrum brilliantly when -the pressure is extremely low, and 

 that subsequently it disappears. The very interesting research of 

 I'rof. Smilhells on " The Spectra of Carbon Compounds," in the 

 April number of the /'/(//. J/ny., illustrates this. Furthermore, it 

 shows distinctly that the same spectrum is obtainable from both 

 carbon monoxide and carbon dioxide (/«(. «V. pp. 489 and 490). 

 We know, too, from the experiments of Regnaultand of Bunsen 

 on the analysis of atmospheric air, th.at carbon dioxide is absorbed 

 by glass. In view of the facts quoted by Prof. Smithells, the 

 carbon monoxide spectrum is, in his opinion, really due to carbon 

 dioxide, but this latter may easily be decomposed into carbon 

 monoxide and o.xygen under the influence of the spark discharge. 



The Swan spectrum, attributed variously to a hydrocarbon 

 and to the element carbon by previous investigators, is, accord- 

 ing to Smithells, to be attributed to carbon monoxide. It 

 appears also in Dr. v. Wesendonk's letter that when the glass 

 lubes in which the electrodes were fused had become heated, 

 the carbon monoxide spectrum was faintly visible. This would 

 be quite in accordance with the probability that carbon dioxide 

 vtas evolved from the glass. 



NO. 1646, VOL. 64] 



A tube containing silicon hydride also showed the {carbon 

 monoxide and the Swan spectrum, as well as hydrogen and 

 mercury lines, but no silicon lines were observable. Con- 

 sidering all the facts of the case, it is not conceivable that the 

 spectra in question arise in any way from the decomposition or 

 dissociation of the silicon in the compound, either in the state 

 of vapour as fluoride, of gas as hydride, or in the solid state as 

 glass. W. N. Hartley. 



April 25. 



The Use of "Axis-vectors." 



The effort to popularise the elements of vector algebra is 

 commendable. The power and the direct insight conferred by 

 the use of vector quantities should be sought consistently in the 

 study of physics ; and it is true that the introduction of these 

 methods has been needlessly postponed. But it lies in the very 

 nature of such benefits that they are not to be secured except 

 upon tenable grounds and as the result of a continuous argument. 

 If a particular cjuantity is to be classed with vectors, that cannot 

 be done upon a basis which is reducible to the bare statement: 

 " This magnitude may be represented by a straight line of given 

 direction and length ; therefore it is a vector." Witness, for 

 example, moment of inertia, which is not properly a vector, 

 although its magnitude can be associated with a rotation-axis. 

 Vector (juantities must be subject to the process of " geometrical 

 addition " : there is a total obtainable as the vector sum of con- 

 stituent parts. This is equivalent to saying that there is a greatest 

 value <^> (resultant) for one direction, and that the law of 

 orthogonal projection applies. Thus the value <,), for any other 

 direction must satisfy the equation 



<J, = Q cos (Q„ Q). 

 This projective property must be proved somehow in each case. 



The conception of a vector is usually established as an 

 elementary matter with the aid of instances like velocity and 

 force. Velocity is so closely connected with linear displacement 

 that the operations of geometrical addition and projection can be 

 almost intuitively recognised as valid for both quantities. The 

 graphical representation of forces, and the application to them 

 of the "parallelogram construction," can be approached from 

 the experimental side, furnishing a timely reminder that this 

 procedure (as regards physical quantity) is ultimately justified by 

 appeal to ]"ihcnomena. The inclusion of " axis-vectors " {e.g. 

 angular velocity and .acceleration ; moments of force and of 

 momentum) in the class is a second step, of no less importance 

 than the first. The proofs put forward to cover this extension 

 of the thought aflbrd fruitful material to the student of applied 

 logic, through their variations of scope and emphasis. The 

 analysis of some demonstrations now current prompts the remarks 

 which follow. 



First, linear vectors, like velocity, force, magnetic field, have 

 what may be termed objective direction. But direction is 

 assignable to axis-vectors by usage only, in the line ot a (possible 

 or actual) rotation-axis. Further, the sense in this line is arbi- 

 trary, being determined, for example, by the " rule of the right- 

 handed screw. " This double convention underlying the graphical 

 representation of axis-vectors must be insisted upon. 



Secondly, the theorem known .as the " parallelogram of 

 angular velocities " is really intended to prove that the linear 

 velocities of all points in a rigid body satisfy the conditions of 

 rotation in certain cases. The characteristic of rotation is a 

 relation to the axis as regards the direction and the magnitude 

 of all velocities, usually expressed as ?' = rai, r/ being perpendi- 

 cular to both ;• and the rotation-axis. The proof of the theorem 

 is only implicitly complete, if we content ourselves with showing 

 that simultaneous .angular velocities about intersecting axes 

 produce zero linear velocity on a particular line. And the 

 corollary covering the most important point is often not even 

 mentioned. Similar considerations apply to angular acceleration. 



Thirdly, the direct graphical representation of force-moment 

 is connected with areas and not with lines. These areas are in 

 general parallelograms, with adjacent sides representing the 

 force afid the distance of its point of application from a chosen 

 point on the rotation-axis. The fundamental case is that in 

 which the parallelogram is perpendicular to the axis, and its 

 area shows the moment for a line through one vertex. For an 

 oblique .axis through the same vertex, the moment is obtained 

 by projecting that area upon a plane perpendicular to the new 

 axis. This follows easily from the definition of force-moment. 



