NOTES, 



ASTRONOMY. 



By A. C. D. Crommelin, D.Sc, R.A. 



ENCKE'S COMET. — Dr. O. Backlnnd has recently 

 published some further researches on this comet. The 

 observations of each return since 1891 have been compared 

 with theory. The dates of perihelion (all expressed in Berlin 

 mean thne") are:— 1S95. February 4-785; 1898, May 26-898; 

 1901, September 15-501; 1905, January 11-916; 1908, April 

 30-946; 1911, August 19-0656. The mean daily motions at 

 these returns is 1070" plus the following: — 3"-934, 4"- 157, 

 3" -625, 5" -084, 5" -848, 5" -668. The other predicted elements 

 for 1911 are:— Node, 334° 29' 32"; Omega. 184' 39 '29" ; i, 12° 

 34' 32"; e, 0-845723. The most interesting feature of this 

 comet is the acceleration of its mean motion. Dr. BacUlund 

 finds evidence that this suddenly changed its amount in 1858, 

 1868, 1895 (beginning), and perhaps 1904 (end). Several of 

 these dates are near sunspot nia.ximum, and it is suggested that 

 the cause is to be sought in some solar disturbance. 



The comet was extremely faint at its last return, in 1908, 

 and was only obtained (by photography) at the Cape Observa- 

 tory. It is not thought that this means any permanent loss of 

 light, as it had often before been very faint when in a similar 

 position with regard to the Earth. It is brightest at winter 

 returns, of which the next will occur at the end of 1914; at 

 these times it is quite a conspicvious telescopic object, and is 

 sometimes visible to the naked eye. Before its periodicity 

 was known it was independently discovered at three consecu- 

 tive winter returns — those of 1786, 1795, 1805 — which shows 

 that it nuist have been a fairly conspicuous object. The 

 following is an ephemeris for the present year, for Berlin 

 noon : — 



R.A. N.Dec. R.A. Dec. 



July 



Aug 



Aug. 6... S 12 3 23° 55' 



„ 24. ..10 44 31 5° 46'N. 



„ 2S...11 16 6 1° 2'N. 



Sept. 1...11 46 24 3 28' S. 



,. 5. ..12 15 45 7 ' 41' 



„ 9. ..12 44 22 11° 32' 



„ 13. ..13 12 17 14= 59' 



.. 17. ..13 39 27 18° 2' 



,, 21. ..14 5 44 20' 38' S. 



If seen at all in luuope it will be in July. It will then be 

 about one hundred and fifty million miles from the Earth. 



HALLHVS COMET.— This is still being diligently 

 followed at the Yerkes Observatory. Popular Astroiioiiiy 

 for May contains a reproduction of a photograph taken by 

 Mr. F. Slocum with the two foot reflector, with one hour's 

 exposure. The comet appears quite distinctly as a short 

 trail. It was then one hundred and ten million miles further 

 from the sun than on September 11th, 1909, and yet \ery 

 much brighter, showing that the physical brightening at 

 perihelion persists for a long time. It will be followed at 

 least up to conjunction with the sun, and possibly recovered in 

 the autumn after that. Professor Barnard writes that he got 

 good measures on April 16th, 23rd and 25th; an observation 

 on May 2nd was doubtful owing to moonlight. The comet 

 was of magnitude 15 in .\pril, but is rapidlv getting fainter; its 

 diameter is about 10". On April 23rd at 14" 45"' 48" 

 Greenwich mean time, its right ascension was 9" 53™ 27°- 28, 

 South declination 7° 48' 23" -9. This was more than a year 

 after perihelion passage. 



A query that appeared in " Knowledge" for April, page 

 135, asks how the distance of this comet from the sun and its 



speed can be calculated at any time. There are probably a 

 sufficient number interested in this problem to justify its 

 discussion here. I deal with it only on the assumption of 

 elliptical motion, as the discussion of perturbations would 

 need too much space, t denotes the interval in days since the 

 perihelion passage of 1910, April 19-68. u is an auxiliary 

 angle known as the "eccentric anomaly." We must find it by 

 trial from the equation 



?X0--012967 = H°-55°-4216 sin n 



For example put ^ = 731 days, which brings us to 1912, April 

 19-68. The left hand side =9°-478. Trying in succession 

 40°, 50\ 57° for ;(, the right hand side becomes 4' -37, 7°-54, 

 10"- 52. Interpolating and making a few more trials we 

 obtain the correct value of ;(, viz.. 54° -721. 



Next we find r, the distance from the Sun, bv the equation 

 r = 17-945 (1 - 0-96729 cos u). 

 Substituting 54'-721 for u, this becomes 7-9197, the unit being 

 the Earth's distance from the Sun. To bring to miles we 

 muhiply by 92,820,000. 



The velocity expressed in units of the Earth's mean velocity is 



V- 



- -055726. 



To reduce it to [uiles per second we multiply by 18-47. 

 In the present case we get 18-47 \ -252534 - -055726 

 log. 18-47 = 1-2665 

 log.- 196808 = 9-29404 

 half this = 9 - 64702 

 log. miles per second = 0-9135 



Miles per second = 8-194. 



M.^SSES OF STARS. — Professor Lowell has an article in 

 Piypnlnr Astronomy for May, on the masses of binary stars. 

 Grouping the results according to parallax, he finds the 

 resulting mass steadily increases with the distance. This is 

 discussed, and shown to indicate the unreliability of the 

 smaller parallaxes, r'-f of a second being determined as the 

 smallest that can be trusted. The following are the final 

 figures : 



Limits of p:u-allax. 



Above 0" - 4 



0"-2 to0"-4 



0-1 toO-2 



0-067 to 0-1 



0-033 to 0-067 



0-017 to 0-033 



0-007 to 0-017 



This shows that for the best determined parallaxes the mass 

 of each component is very near that of the Sun. We have 

 good reason for thinking that there are stars (such as Aldebaran 

 and Arcturus) whose mass vastly exceeds the Sun's, but these 

 are probably exceptional. Professor Lowell altogether dis- 

 cusses twenty-six pairs, and his result tends to the conclusion 

 that the masses of the stars vary much less widely than their 

 lustre. 



BOTANY. 



By Professor F. Cavers, D.Sc, F.L.S. 



FORMALDEHYDE AS FOOD FOR GREEN PLANTS. 

 — It has long been known that the first product in the making 

 of organic food by green plants, from the carbon dioxide and 

 water absorbed by their leaves and roots respectively, is 

 formaldehyde (CHjO), the starting-point for the formation 

 of carbohydrates and of higher compounds. Various experi- 

 menters have endea\oured to show that plants can utilise 

 formaldehyde as food material when presented to them, in 



Mass of binarv (Sun = l). 

 1-93 

 1-77 

 1-33 

 1-43 

 1-95 

 3-46 

 33-43 



229 



