I 



March 30, 1893] 



NATURE 



509 



January 3, 1893, not having opened the box for some days, I 

 made an examination. The egg was in its former position, so 

 far as I could tell, but the shell was split on one side and the 

 young Peripatus had escaped. This young Peripatus was 

 found lying dead on the glass floor of the hatching box, 25 mm. 

 distant from the shell. It must have crawled off the rotten 

 wood and along the glass to the position in which it was found. 

 It was only about 5 mm. in length, so that, even assuming that it 

 moved in a perfectly straight line, it must have crawled lor a dis- 

 tance five times its own length. To the naked eye the young 

 animal appeared of a pale greenish colour. It could not have been 

 dead for very many days, but decomposition had already set in, 

 and the animal was stuck to the glass on which it lay. It was 

 impossible to remove it without considerable injury, but I 

 ultimately succeeded in mounting it in Canada balsam, and it 

 is impossible, even in its present condition, to doubt that it 

 really is a young Peripatus, for the characteristic jaws and claws 

 are well shown. I also mounted the ruptured eggshell, and 

 found that the characteristic sculpturing on the outside was still 

 clearly visible. 



This egg, then, hatched out after being laid for about seven- 

 teen months (from about July 1891 to about the end of Decem- 

 ber 1892). I cannot believe that under natural conditions the 

 embryos take so long to develop. At any rate it now appears 

 certain that the larger Victorian Peripatus lays eggs which may 

 hatch after a lapse of a year and five months. 



Arthur Dendy. 



The University of Melbourne, February. 



A Simple Rule for finding the Day of the Week corre- 

 sponding to any given Day of the Month and Year. 

 A RULE was lately mentioned to me by a friend for finding, 

 almost by inspection, the day of the week for any given year 

 and day of any month in that year, during the present century. 

 The basis of the rule is so obvious, when once the rule is stated, 

 as to require no demonstration, but it struck me as so ingenious 

 as to be worth while communicating it to you in case you 

 deemed it worthy of insertion. I also append a very easy 

 method of extending the rule to any date subsequent to the 

 introduction of the Julian intercalation either in the past or 

 future, except indeed for the eighteenth century, in which the 

 introduciinn of the new style requires a special treatment. 



The nineteenth century rule above alluded to is this. Each 

 of the 12 months has its special numerical constant, thus: — 



Jan. Feb. Mar. Ap. May June July Aug. Sept. Oct. Nov. Dec. 

 366250231361 



Write down four columns thus 



A I B I C I D 



Under A enter day of month, under B constant for that 

 month, under C year of century, under D greatest multiple of 4 

 in the year of century. 



Add together the numbers under these heads, divide by 7, 

 and the remainder is day of week ; except that in Leap Year 

 I must be subtracted for any day before February 29. 



Example.— June 18, 18 15 (Battle of Waterloo) : — 

 A B C D Sum. Remr. 



18 o 15 3 36 36 



February i, 1892 : — 

 A B C D Sum. Remr 



I 6 92 23 122 ^^^ 



Subtract i for Leap Year before February 29. . /«j-.— 3 — i = 2 or Monday 

 December 25, 1892 : — 

 A B C D Sum. Remr. 



141 



7 



To extend the rule to any future century, we have only to 

 alter the monthly constants, adding 5 to each for each added 

 century after the present, and i for each century, an exact 

 multiple of 4, in the interval. 



Thus for the thirty-first century. Number of added centuries 

 is 12, and there are 3 centuries, sijcceeding multiples of 4 

 (twenty-first, twenty- flffth, and twenty-ninth). Therefore add 

 5 X 12 -f 3 =63, or omitting multiples of 7, add o. 



NO. 1222, VOL. 47] 



Hence, constants for thirty-first century are the same for the 

 present century. 



New Year's Day, 3001, 



A R C D Sum. Remr. 



I 3 I o 5 5 Thursday. 



For centuries anterior to the eighteenth we must first of all 

 find by special method what the monthly constant." would have 

 been throughout the eighteenth century without the change of 

 style, and then subtract 6 .for each century short of the 

 eighteenth. 



It may easily be seen that the constants throughout the 

 eighteenth century would have been without change of style. 



Jan. Feb. Mar. Ap. May June July Aug. Sept. Oct. Nov. Dec 

 25513614025O 



For the eleventh century subtract 7 x 6 or 42, i.e. since 

 this is multiple of 7 subtract o, and we get the same repeated. 



For the seventeenth subtract 6, and remember that when the 

 result is negative we must replace it by the defect of the corre- 

 sponding positive number from 7, and we get 



36624025 12 5 I 

 Example.— Bsiltle of Hastings, Oct. 14, 1066. 

 A B C D Sum. Remr. 



14 2 66 16 98 -o Saturday. 



Execution of Charles I., Jan. 30, 1649, 



A BCD Sum. Remr. 



30 3 49 12 = 94 94 3 Tuesday. 



H. W. W. 



" Roche's Lintiit." 



With reference to Prof. G. H. Darwin's notes (Nature, 

 March 16, p. 460) on the investigations of M. Roche as to the 

 smallest distance from its primary at which a satellite can exist, 

 does not the distance given — viz. 2*44 times the radius of the 

 primary — refer to the case of the satellite having the same 

 density as its primary? In Note 3 Prof. Darwin warns the 

 reader that Roche's limit depends, to some extent, on the 

 density of the planet. Suppose the density of the planet to 

 remain the same while that of the satellite is taken at double. 

 In this case the tidal or differential influence of the planet on 

 the two halves of the satellite will have doubled, while the 

 gravitational attraction of the two halves of the satellite on 

 each other will have become fourfold ; and generally, the power 

 of the planet to pull the satellite asunder will be inversely as 

 the density of the satellite, and directly as the density of the 

 planet. 



An alteration of the size of the satellite does not much aft'ect 

 the question, because both forces are thereby equally altered, so 

 long as the satellite is very small in comparison with its distance 

 from the planet. 



.Seeing that the tidal or differential influence of a planet on 

 its satellite is inversely as the cube of their distance apart, per- 

 haps it would be correct— as far as gravitational influence alone 

 is concerned — to state the limit at which a satellite can exist as 



25 



92 



23 141 



Sunday. 



3 Sunday 



I Sunday. 



being equal to 244 R x (-^V 



where 



R = the radius of the planet, 

 D = the density of the planet, 

 (/ = the density of the satellite. 



As an interesting case of the same problem from a different 

 point of view, suppose two very small equal spheres in contact, 

 and a third much larger sphere placed in line with their 

 centres, all three having the same density; then, when 

 the distance of the point of contact of the small spheres 

 from the centre of the large one is 2*52 times the radius 

 of the large one, the attraction of the two small spheres for each 

 other just balances the differential influence of the large one 

 tending to draw them asunder. The effects of variation in density 

 and size being the same in this case as in the former. 



It would probably be interesting to many of your readers to 

 have Prof. Darwin's views as to whether it is a reasonable sup- 

 position that a small satellite, such as Jupiter's fifth, is likely to 

 have the same density as Jupiter ; and whether the meteorites 

 forming Saturn's ring are lilcely to be of so small density as 



