11^ 



KNOWLEDGE 



[Apkh, 1, 1800. 



variable stars. But I think that he has in this instance 

 mistaken Mr. Peek's meaning in supposing that the sharp 

 irregularities of the Rousdon curve are intended to repre- 

 sent the true variations of the star's light. Mr. Peek has 

 simply joined the points corresponding to the brightness 

 of the star at the dates of observation by straight lines — 

 without attempting by freehand drawing to round off any 

 of the angles. Such smoothing of curves must always be 

 a matter of guess-work, and it is probably more desirable 

 to let the diagram represent as exactly as possible the 

 means of the estimates of brightness made at each of the 

 various dates of observation. 



The great question of interest is whether it would be 

 possible to conceive of the irregularities shown as only due 

 to accidental errors of observation. It seemed to me that 

 Professor Pickeiing's observations of S. UrscF MtijoHs, as 

 well as those made at Rousdon, indicate that there are 

 greater irregularities in the estimates of the star's bright- 

 ness than can be accounted for by errors of observation in 

 comparing the brightness of the variable with other stars 

 in its neighbourhood, whose brightness would be equally 

 affected with that of the variable by changes from night to 

 night in the clearness of the atmosphere. The question 

 is, however, one on which further observations are much 

 needed. — A. C. Raxy.\ed.1 



DIVISIBILITY BY 37. 



1)ear Sir. — In your March issue Mr. T. y. Barrett has 

 mistaken how to apply the test. Let me show him. His 

 first number was 2027742.59. Take the sums of every 

 third figure 9 + 4 + 2 = 1.5; 5 + 7 + 6 = lH; 2 + 7 + 2 = 11. 

 Now take 11 from 18 = 7; and 11 from 15 = 4, and since 

 74=37 M, the given number also=37 iM. 



Again, take 973112691, his other number. 



Here the sums of every third figure are G, 17. IG, 

 respectively, and 10 from 17 = 1 (ten), and 10 from G= - 10. 

 Then since 10 — 10=0, the given number=37 M. 



The mathematical proof of the test is unsuited to your 

 columns, but I shall be happy to forward it to anyone 

 interested. I have constructed simple tests for divisibility 

 by any number. 



r"± r"~i + j-""-. . . +/-±1 or its factors. There are several 

 tests for the number 7, one of which is easier than the 

 above. My object in the February number w-as not to 

 give tests of divisibility, but to show the connection 

 between the periodicity and the divisibility. There are 

 other points I should like to have touched upon did your 

 space and the pressure of my business permit. — Yours 

 faithfully, Rout. W. D. Cheistie. 



Wavertree Park College, Liverpool, 

 leth March 1890. 



P.S.--I take this opportunity of correcting a clerical 

 ■■—• -in p. 73, lines 23 and 25 from bottom. Instead of 

 l)/2 andP (/j-1),2, read 9 [q-l)i2 and P (7-l)/2. 



error on 

 9(/ 



MAGNITUDE OF STARS. 

 ?'o the Editor of Knowledge, 

 Sir, — Referring once more to the diagi-am of the dis- 

 tances of the fixed stars in your February issue, I should 

 like to ask if it is possible to infer w-hat magnitude of star 

 our own sun would correspond to, if it were placed at the 

 distance of a Centauri, or Sirius. 



Thanking you for your answer to my former question, 



I remain, 

 Tvnron, Scotland, Yom-s trulv, 



12 March 1890. ' J. Shaw. 



[Various determinations of the light of the sun as com- 

 pared with the light of the full moon, and the light of the 

 moon as compared with that of stars, have been made. 

 Huyghens, in 1698, compared the light of the sun with 

 that of Sirius by allowing the light of the sun to shine 

 through a minute hole. According to his experiments, 

 the sun gives 756,000,000 times ' the light of Sirius. 

 Wollaston, in 1829, compared the image of the sun and of 

 a lamp refiected in a silvered bulb of glass with the light 

 of Sirius. According to these experiments, the sun gives 

 20,000,000,000 times the light of Sirius.* Steinheil, in 

 1836, from comparisons between the light of the sun and 

 moon, and that of Sirius, gave the ratio as 3,840,000,000. 

 In 1801, l)ond determined the relative light of the sun 

 and moon by comparing their reflections in a glass globe 

 with that of an artificial light. Combining his measures 

 with the comparisons of the moon and Sirius bv Herschel 

 and Seidel, he deduced the ratio 5,970,500,000 i In 1863, 

 Clark found that, if the sun was removed to 1,200,000 

 times its present distance, and Sirius to 20 times its pre- 

 sent distance, they would appear equally bright, and equal 

 to a sixth-magnitude star. This corresponds to a ratio of 

 3,600,000,000 between the Ught given by the sun and 

 Sirius. Prof. E. C. Pickering, in his remarkable paper on 

 Algol, published in the proceedings of the American 

 Academy for 1880, computes the brightness of the sun, 

 measured in star magnitudes fiom Huyglien's measures, 

 as 22-2 magnitudes brighter than Sirius ; from A\'ollaston's 

 measures, 25-75 magnitudes ; SteinheU's, 23-96 ; Bond's, 

 24-44 ; and Clark's, 23-89 ; from which Prof. Pickering 

 assumes (taking Sirius as of the -1-5 magnitude) that 

 the light of our sun, measured in stellar magnitudes, may 

 be considered as corresponding to about minus twenty-five 

 and a half magnitudes of the stellar scale. 



The scale of star magnitudes has been so arranged that 

 if any star were removed to ten times its present distance 

 (where it would give a hundredth part of its present light) 

 its brightness would be decreased five magnitudes. Conse- 

 quently, if the sun were removed to a himdred thousand 

 times its present distance (i.e. to a distance of about li 

 light j-ears), it w-ould, according to Prof. Pickering's 

 estimate, appear about one magnitude less bright than 

 Sirius, and at the distance of a Centauri it would not 

 differ greatly from a star of the first magnitude. — A. C. 

 Raxy.aed.] 



THE MEANING OF A MINUS PARALLAX. 



Sir, — Will you kindly explain how a minus parallax is 

 obtained, and what it means ? — Yours faithfullv, 



•J. F. Ki.v(;. 



[In the case of an absolute parallax, it must be taken 

 to mean that there is some systematic error "which vitiates 

 the observations. But in the case of a relative parallax 

 it may mean that the comparison star or stars are nearer 

 than the star whose shift in the heavens is measured. — 

 A. C. Raxy.\rd.] 



Til the J-'ilitiir of Knowledge. 



Dear Sir, — With regard to the list by Mr. Sadler 

 following your own most interesting article on stellar 

 parallax in the number of Knowxedge for February, 



* Pliil. Trans, csix. 28. 



t Mem. Amer. Acid, viii., N.S., p. 298. 



