140 



NATURE 



[December 8, 189; 



Given t, e, and v, we can calculate the right-hand side. But 

 we seek, however, the maximum value of 



y-ev\.a.n F-i/log tan (45°+ i/2F) = sin F - »/ log tan (45°+ 1/2F) 

 by determining e as function of v. It is 



9^-=fcosF--''-]^ = -^^^^^^=^. 

 Thus y increases so long as ^ < — -, and decreases continu- 



ally for e > , . The maximum for r lakes place when <?- =- . 



and is _ 



, /I + v^i - j-N 



Vi - . - Hog(^ — -- - j. 



ct[Y\ (IJZJ.Y' " 



\<\cj \i + u) • 7 /i + Vi - ^\ 



VI - »' - " logl ^ "t; 1 



V 

 and with — = 30 and / = 60 days, 



M > 278oof L-l-^ \ 



Thus we have 



(8) 



- C'*-:^;- 1 



For the above example :-" = o'9 results ;it> 2800 as considerably 



larger masses than formerly. 



I have now further to prove that a very close proximity of the 

 two bodies can have only taken place for a very short space of 

 lime. To do this we use the following relations. 



We find above for the parabola : 



H ^ ; X = sin |z/(l - 2/3 sin- l/2z^). 



^k-x 



It follows, therefore, that 



Thus we have 



2^/2 



06 V/ 



(9) 



For the hyperbola we have 



2/C'V 



and, according to formula (5) 



(V- - V 2,3/2 



Therefore, 



^/Cn: "v'2 



For eccentricities which are not very nearly equal to I, we 

 had 



''>^'^\v Vv^' - Vo^ . / > i-o5 VV^ - \^'i . (10) 



and it is certainly 



j3/i 

 2 



For Vo = o. 



(10) is naturally changed into (9). For the hyperbola, how- 

 ever, it is possible to suggest a second relationship. 



Since 



a _ V2 _ v^2 



(5) can also be written 



^'V = (^fVo^vx. 



and because P/jl -- «Vo", it follows that 



y?.Vo.X = V.;., 



where 



^ - cos F 



' cos F ' ^tan F - log tan (45° + 1/2 K)' 

 NO. 1206, VOL. 47] 



An easy calculation yields now 



. [(i + f-)cosF 



oK ^sinF - cos F log tan (45° + 1/2F) 



+ d sin F log lan( 45° + I /2 F)]. 



It is quite evident that the quantities in brackets always remain 

 positive, for it is 



log tan (45°+i/2F) = 2taniF-f |tan3 1/2 F+ ... > 2 tan 1/2 F, 



(e - i)'cosF. 



From 



and in consequence of it the quantity in brackets 



Thus, 5^, is negative, and _y decreases as F increases 

 or 



this it follows that y>i, and the relation r^V^, is the result. 

 If we apply this formula to Nova Aurigse, we obtain for 



^0 = 0-5 s/v^-Y/= 108 miles, V^ = 60 



In the vicinity of perihelion the velocity has been under every 

 condition greater than 120 miles, and we shall therefore obtain 

 values of r that are considerably too small, by supposing 

 r>i X 85 miles. One day before or after perihelion it is there- 

 fore certain that r>y;^ million miles. 



It will therefore hardly be possible to assume that any notice- 

 able influence of the supposed two bodies can have lasted longer 

 than a few hours. 



Since the above article was written Nova Aurigse has by its 

 reappearance attracted considerable attention, and especially by 

 the observation as made by Prof. Barnard. With regard to this 

 reappearance one must necessarily s;e an evident confirmation 

 of the critical part of my article. Nor has my hypothesis been 

 contradicted in any way, for it is evident in itself that the 

 supposed formations of the nebulous or dusty matter are more 

 copious in certain parts of space, and one may have different 

 ideas of the distribution of density of these formations. 



To the observation made by Prof. Barnard {Asir. Nach., 

 31 14) I wish to add the following remarks. I had formed an 

 idea of the whole process which caused the outburst of the Nova, 

 which idea is as perfectly represented in Prof. Barnard's drawing, 

 kindly communicated to me by Prof. Kreutz, as I could expect. 

 During the appearance of the Nova in the winter nothing similar 

 was seen so far as I know. It does not follow from this, 

 therefore, that it did not exist, and it would also have been 

 possible to have expected information from the photographs as 

 has often occurred before. I applied on this account to Dr. 

 Wolf, in Heidelberg, and asked him whether he had photo- 

 graphs of the region of the Nova at that time, and whether, 

 perhaps, any nebulous object was to be seen on them ; but, un- 

 fortunately, Dr. Wolf did not possess such photographs. It 

 remains doubtful, I am sorry to say, wljetherso delicate an object 

 would have been visible on the plates. W. J. LocKYER. 



HINTS FOR COLLECTORS OF MOLLUSKS> 

 A FTER the collector has brought home the spoils of his 

 ^*' excursion there is still a good deal to be done before the 

 wet and dirty shells, covered with parasitic growths or in- 

 habited either by the original mollusk or some hermit crab, will 

 be ready to be placed in the cabinet. Some of them, if living, 

 may find a temporary place in an aquarium for the study of their 

 habits, but, for the most part, the collector will wish to prepare 

 his specimens either for anatomical use in the future or as dry 

 specimens for his cabinet. The preparation of mollusks for 

 anatomical purposes has been described in a special chapter of 

 these instructions. For ordinary rough work nothing is better 

 than clean 90 per cent, alcohol diluted with a proper proportion 

 of water. If the specimens are large they should be first put into a 

 jar kept for that special purpose, in which the alcohol is com- 

 paratively weak, having, say, 50 per cent, of water added to it. 

 After the immersion of specimens in this jar for several days the 

 fluids will have been extracted by the alcohol, and a specimen 

 can then be removed, washed clean of mucus and dirt, which will 

 almost always be found about the aperture of a spiral shell, and 



■ Reprinted from " Instructions for Collecting Mollusks, and ether Useful 

 Hints for the Conchologist," by William H. Dall ; issued by the Smithsonian 

 Institution as Part G oi Bulletin of the U. S. ^ational Museum, No. 39. 



