March 31, 1882.] 



♦ KNOWLEDGE ♦ 



483 



^otes on art anli ^ticncf. 



Dolloxd's Sipereal Watch. — Almost everj- amateur astronomer 

 requires to know approximately, if not exactly, the sidereal time. 

 He can calculate it, of course, from ordinary time, for any given 

 instant, but the difference between sidereal and ordinary time is 

 Always chan^'ing, so that the calculation made at one time will not 

 avail at another. On the other hand, not every astronomer can 

 afford an instrument so costly as a sidereal chronometer. Mr. 

 Dollond, the well-known optician, has devised a neat, simple, and 

 very useful sidereal watch — such an instrument as every amateur 

 astronomer should carry in liis pocket. 



Pbofessor Pasteur's I'REVE.NTm: Ixoculatioxs of Charbox. — 

 The Prussian Minister of Agriculture, the Deittsche Med. H'ocA. 

 (Feb. 11) states, has appointed an influential scientific committee 

 to superintend and report upon a series of inoculations to be per- 

 formed by one of Pasteur's assistants. This gentleman then pro- 

 ceeds to Russia for the same purpose, and on his return to Saxon 

 Prussia, where the experiments are to bo made, will perform a 

 second series of inoculations. Besides some celebrated veterinary 

 professors. Professor Virchow is expected to take part in the 

 inqniry; but regret has been expressed that Professor Koch, the 

 able critic of Pasteur, has not been nominated. 



Plawts IX BF.nROOMs. — Plants are unhealthy in bedrooms for this 

 reason, that during the night they give out carbonic bi-oxidc, which, 

 as is well kno^vn, is injurious to life. Plants, like animals, are 

 constantly breathing — taking in oxygen, and giving out carbonic 

 dioxide. During the day-time they feed as well as breathe, one of 

 their chief articles of diet being the very same poisonous gas which 

 they are constantly expiring. This carbonic di-oxide, under the 

 influence of sunlight, and by means of the colouring matter 

 (chlorophyl) is separated, the carbon being assimilated, and the 

 oxygen evolved. In the daytime there is more oxygen given off 

 than carbonic di-oxide, so that plants may be said to be healthy in 

 the Ught, but unhealthy in the dark. I may add that the quantity 

 of either gas given off in a room from a few plants is so small as to 

 be hardly worth noticing. — F. D. H. 



(Bnv iHatftfinati'ral Column. 



MOGUL'S PROBLEM. 



THE problem being " Given any rectangle, divide it by the fewest 

 possible straight cuts, so that the parts can be put together to 

 form a square," my solution is as follows : — 



;B'\fc 



On the line a 6 of the rectangle aicd take a e equal to a d, and 

 make ef perpendicular to a i ; bisect ab at 9, and, with the radius 



a y and centre g, describe a circle cutting <;/ at /, join a/ and bf, 

 and niake//i and hi equal to o/; draw hk audi I parallel to af. 



By cutting the rectangle at such parts of the lines a /, kli, li, and 

 fb as pass through it, you will obtain pieces which will form the 

 desireif square, vide Fig. L, in wliich rectangle, n 6 is six times ad. 

 The principle, however, will bo the same, whatever may be the pro- 

 portion between the sides ; but in cases where the proportion does 

 not exceed two to one only two cuts will be necessary ; not exceeding 

 five to one, three cuts ; not exceeding ten to one, four cuts ; not 

 exceeding seventeen to one, five cuts ; and so on. 



It will be observed that my method of finding the side of a square 

 whose contents are equal to that of a given rectangle, is different 

 to that given by Euclid, II., 14. Calling the sides of the rectangle 

 X and 1/ respectively, Euclid's method is equivalent to the mathe- 

 matical proposition that — 



-2- J -L-2-J 



whereas my method is equivalent to the proposition — 



It may puzzle some of your readers to discover how my method 

 involves this last equation. — Mogul. 



[Correct solutions by R. Home (two, both very neat), P. E. M., 

 H. W. Partial solutions by H. J., N., E. Whitby, and others. 

 Solutions by G. H. Bonner, and H. Jones incorrect. — Ed] 



PROBABILITIES. 



The true method in dealing with problems of the kind considered 

 in our last, is to reduce them to the general law first established by 

 determining — (1) How many possible events there are ; (2) Whether 

 those arc all equally likely ; and (3) how many are favoui-able. 



Our question is : What is the chance of throwing one Ace at least 

 in two trials with a single die ? Now, when such a die is tlirown 

 twice, the following are the possible throws : — 



1, 6 2, 6 3, 6 4, 6 5, 6 6, 6 



The table being formed by combining first throw 1, with any one of 

 the second throws 1, 2, 3, . . . 6 ; first throw 2 with any of the 

 same set of 6 ; and so on. The total number is 3G, or 6 times 6. 

 Any pair in the .first column, or in the top line, gives at least one 

 Ace— that is, there are 11 favourable pairs out of 36 possible pairs. 

 Also, it is obvious that any pair of the 36 is as likely to be thrown 

 as any other. Hence, by what was shown in paper I., the chance of 



throwing Ace at least once in two casts of a single die is ^' The 



25 



chance of failing is z^-.' It will be noticed that the number of un- 

 3b 



favourable cases is 5 times 5, the total number of cases being 6 

 times 6. It is clear that a table containing all the unfavourable 

 cases would be formed in precisely the same way as the above 

 table ; and that, in fact, such a table is actually included in the 

 above table, omitting the upper line and the left-hand column. 



Now the way in which the above result is obtained would be in- 

 convenient in practice. Suppose, for instance, that instead of a die 



