138 



NA TURE 



[December 8, 1892 



from it and will adopt very quickly that velocity which the 

 adjacent parts of the cloud possess. 



It is interesting to compare this process with a similar one, 

 which takes place in a well-known way in the appear- 

 ance of shooting stars or fireballs. In this case a com- 

 pact body enters with a certain velocity into a formation 

 of very thin matter (the upper stia'a of the atmosphere), is 

 heated and partly vapouri^ed, and a luminous tail, which is 

 clearly visible for a long lime after the sudden appearance of 

 the meteor, marks the path which the latter has taken. The 

 detached particles have quickly lost their relative velocities 

 against the air, for they apparently do not partake of the move- 

 ment of the meteor. 



If we consider spectroscopically the star on its commence- 

 ment to become bright by resistance, two superposed spectra 

 will openly reveal themselves, one in general continuous and 

 provided with absorption bands in consequence of the heaping 

 up of the glowing gases, and the other in the main consisting 

 of bright Imes. Both spectra, according to the relative motion 

 in the line of sight, will appear pressed up against one 

 another. Thus altogether an appearance is found very similar 

 to that observed in Nova Aurigae, and they will agree entirely 

 if one assumes that also those parts of the cloud nearest the 

 body have sustained physical perturbations by a direct frictional 

 warming of the detached particles, &c. This assumption 

 seems to me to contain by no means a difficulty considering our 

 lack of knowledge with respect to the properties of this 

 cloud matter. Whether this is at all necessary I am unable to 

 say on the ground of the publications at hand. 



The investigation is important to decide whether, on the 

 lines laid out, we can obtain a plausible explanation of the 

 great relative velocities shown by the two spectra. When the 

 body approaches the cloud the latter will evidently lengthen 

 i'self in the direction of the former. This lengthening will 

 grow with the mutual approach, just as the relative velocity of 

 the single parts of the cloud will grow towards the body. 

 Without certain suppositions on the structure of cloud matter 

 it is difficult to conceive of the processes of movement which 

 take place, so we must content ourselves with contemplating 

 the one or the other case, which admits of a closer invest- 

 igation. 



If, for instance, we suppose that the single particles of the 

 cloud follow for the main part the effect of the body, they will 

 describe conic-sections — that is, hyperbolas round ttie centre of 

 the latter as forces. Their greatest relative velocity decreases 

 quickly with the distance of the body, so that the surroundings 

 of the latter will be filled with particles moving with very 

 different velocities. One can easily see that no very extra- 

 ordinary assumptions are necessary to suppose very great velo- 

 cities for these particles that pass near the surface of the body, 

 velocities amounting to those stated in the case of Nova Aurigas, 

 even if they are at the outset very small. It follows from the 

 above that the spectral-lines of the particles which are moving 

 from the body with such different velocities must be very much 

 enlarged, and that to explain the different brightenings of the 

 single parts of the lines as probably intensity u)axima does not 

 laise the least difficulty, but is a necessary accompanying phe- 

 nomenon. This point seems to me to be important, for it can- 

 not be deduced from the hypothesis of two compact masses 

 passing close by one another, and must here lead to the rather 

 improbable assumption of several moving bodies. 



As long as the body remains in this, so to speak, atmospheric 

 formation, the appearances above mentioned must always be 

 called forth anew, whence it follows that the peculiarities of the 

 >pectrum conditioned by the whole st^te of things, not consider- 

 ing smaller perturbations, must on the whole remain constant 

 lor some time, a point which in the above hypothesis is at first 

 not by any means clear. In a similar manner it will not be as- 

 tonishing if the star during that time changes its brightness less 

 strongly, while after its exit from the cloud this brightness will 

 decrease rather rapidly. This too agrees with the light-curve in | 

 the case of the Nova. P'inally, even the periodical fluctuations 

 of the magnitude can be explained quite naturally. We call to 

 mind here the well-known fact confirmed lately by the photo- 

 graphs of Max Wolf, that similar occurrences appear in shooting 

 stars, which may, indeed, be explained with difficulty. 



We must, however, in any case assume that the star entered 

 the cosmical cloud in question about the beginning of December 

 and left it not long belore the beginning of March. Now the 

 question is urged upon us How was it possible that for such a long 



time the great relative velocity could remain constant though 

 such a resistance must have taken place that could develope 

 the heat necessary for the glowing of the body ? We are here 

 going to decide this question by comparing the resi-ling power 

 of the star t j ihat ol a meteor in the upper strata of our at- 

 inospbere. 



Let us assume, quite generally, that the motion of the star in 

 a straight line is given by the equation 



'\ -- - lv„ )0 



at 



( I ) where v is the velocity, n a positive number > I and A. a con- 

 stant, which is directly proportional to the surface of the globular 

 body and the density of the medium and inversely proportional 

 to the mass of the body. We compare equation (l) with the 

 equation for the motion of a meteor 

 dv' 



~df' = - ^' ^'" 

 in which the time t' is referred to another unit selected for the 

 purpose. If we suppose 7/ = jxv ; t\= vt ; \ = A vij."~'^. The 

 latter equation beco.nes identical with (i), that is the movement 

 of the star corresponds point to point with the motion of the 

 meteor, if the latter equations are satisfied. Representing now 

 1/1, O, r, 5, m\ O', r', 5', as masses, surfaces, radii, and densities 

 of the star and meteor, and U and D' the density of the cosmical 

 clouds and the upper strata of the atmosphere in question, we 

 have : — 



\ _ ^Om^ . I I50;«' 



a' ^ U'Wm ' " M"~^ ■ D'O'w. 



or al'so 



/ U'/ r5L)'- 



If we put r — k times the sun's radiu-; ( = 700 million metres) 



and r = r metres, and further corresponding to the observations 



of the new star & = 30 (unit of velocity of Earth in its orbit) and 



t = 100 days and v' ^2 which corresponds to a relatively 



quickly-moving meteor and finally n — 2, we have : — 



15 D5' r' 



k L»'5 700 millions 



and/' = o=. 185^;/=;-^,'^- 



liOVJ 



Thus the movement of the star takes place proportionally in 100 

 days, just as that of the meteor in o'i85 seconds if we suppose 



f—i. As we are free to assume ■— , small, we can obtain a 



very small fraction of a second, and since within a hundredth 

 part of a second the movement in the highest regions of our at- 

 mosphere shows no longer a perceptible decrease of velocity, 

 such a decrease will not enter in the case of the star. We have 

 evidently to deal here with the same appearance which points 

 out that small heavy objects possess a far greater resistance to 

 air than large ones, and that with large meteors (fireballs) the 

 air resistance, as it has been proved, influences the elements of 

 the orbit far less than is the case with small meteors. 



We have still to show that in spite of the small decrease of 

 movement, enough energy of movement is changed into heat in 

 order to bring the star inio a surface-glowing condition, and such 

 a condition has by all means taken place in the Nova. We 

 must therefore calculate the quantities of heat Q and Q' which 

 is radiated in one second of time, and from a unit of surface on 

 both bodies. If we call P and P' the losses in acting power 

 during the times t and t\ z/^ and z\l the velocities belore the 

 entrance into the resisting media, we have : — 



"- 0/ ^ uv 



and P = m {v^{' - v"); P = ni' {v^^- - v"-) 

 and taking into consideration the above equations : 



Q ^D (vY^^ 



Q D'U'7 

 with the above numbers ~,= 15; n will be =2 



NO. 1206, VOL. 47] 



D 



3375- r- 



so that we can assume that the density of the cosmic medium, 

 compared to these already very thin air strata, in which evidently 



