NA TURE 



[November 4, 1897 



LETTERS TO THE EDITOR 

 [ The Editor does not hold himself responsible for opinions ex- 

 pressed by his correspondents. Neither can he tmdertake 

 to return., or to con e'^p'^nd with the zvriters of, rejected 

 manuscripts intended for this nr any other part of NATURE. 

 I-/o notice is taken of anonyinoiis conimun'caiions.'\ 



A Bee's Movements in a Room. 



The following was communicated to me by a friend of 

 mine, Mr. E. W. Winstank)', of Trinity College, Cambridge, 

 and, as it may have some value respecting the relations of in- 

 sects to flowers, I think it worth putting on record. The observ- 

 ations were written down on the day after the occurrence, when 

 he related to me the facts, and I reproduce them here in his 

 own words : — 



" Sitting reading in my room (15 Jesus Lane) by the open win- 

 dow, about noon, October 21 — a sunny day — I became conscious 

 of a buzzing sound, and, on looking up, found it due to the entrance 

 of a bee. Noticing that certain objects seemed to arrest the in- 

 sect's attention, I paid special heed to its movements. It first 

 went across to the pictures on the opposite wall, following them 

 round the room, and hovering a short time close to each of the 

 coloured ones, then passing out of the door, which was wide 

 open ; returning, after a few seconds, it flew straight to the gas- 

 shades, which, two in number, are situated one on each side of 

 the mantelpiece ; it lingered over the top of one, and then passed 

 on to the other, and repeated this movement. It now took a 

 second tour of the pictures, and after stopping a moment or two 

 near one of the brass knobs of the curtain-pole, came again to 

 the gas-shades and made a closer investigation of thtm, both by 

 hovering over the top and by entering at the bottom around the 

 gas-burners. It then visited in succession four ornaments on the 

 mantel-mirror, drew near once more to the large central coloured 

 picture, made a second exit by the door, coming back almost 

 immediately, and, after dwelling near the two small coloured 

 pictures for the third time, flew straight out of the window. 



" It never actually alighted anywhere, remainfng near the 

 objects by the rapid quiver of its wings. The whole visit the 

 bee paid me occupied probably five minutes or less. Although 

 I did not examine it closely, I considered it to be a hive and not 

 a humble bee." 



The special features to notice in the above are the systematic 

 way the bee flew about, and the nature of the objects which 

 attracted its attention. 



Any one on surveying the room would admit, I think, that the 

 gas-shades and the pictures are the most brightly coloured 

 things in it. 



The gas-shades are semi-opaque, lily-shaped, and tinted from 

 yellow to bright pink upwards ; in fact, they resemble very large 

 gamopetalous flowers (corollas). 



The pictures in the room numbered seven, consisting of a 

 large frame enclosing five photochrome views, of two small 

 photochromes, and four photogravures. My friend says it was 

 distinctly the coloured ones that attracted the bee, giving the 

 other ones a mere glance, as it were. The photochromes are 

 vividly coloured, blue predominating. 



The remaining objects visited, the ornaments, are not striking 

 or large, but have flowers painted on them on a white ground, 

 mostly resembling blue forget-me-nots. My friend was some- 

 \vhat astonished at the bee regarding these, as he was not aware, 

 till he looked, that the vases were decorated thus. He is not a 

 botanical student, and has no bias towards any theory of the 

 flower ; it was the methodical way the bee went about the room 

 that arrested his attention. It is mainly owing to this fact that 

 I thought it worth while to make his observations known. 

 Recently some observers have put forward reasons for con- 

 sidering that the colour of the flower exerts little, attraction 

 towards insects, and that it is chiefly the odour. The above 

 piece of information favours decidedly colour attraction. There 

 was no perception of odour, or any flowers or plants present in 

 the room at the time. 



To my mind it seems rational to assume that colour and 

 odour may play somewhat equal attractions, the scent serving 

 to bring bees from a distance, and the colour helping to guide 

 them directly to the honey. A bee becoming accustomed to 

 associate nectar with conspicuously coloured objects, might thus 

 learn to visit flowers wholly from colour-sensation, and, not 

 having sufficient discriminating power, visit other brightly- 

 coloured things as well. J. Parkin. 



Trinity College, Cambridge, October 23. 



NO. 1462. VOL. 57] 



A Test for Divisibility. 



May I venture to supply a long-felt want amongst arith- 

 meticians, viz. a general test of divisibility ? 



Let N be any integral number, and 5 any divisor, then 

 N = a + lod + 10-c + &c. 



=z a + d{S<j + r) + c (S,/ + rf -f- &c. 



= 5Q -f a -f (5r 4- <:r2 -t- &c. 



= 8Q + a -f 3 (5^1 -I- ^ ) + f (i,j + ;. ) + ^c. 



= 8Q + 8Q1 + Ni 



= 5(Q + Qi)+Nj. 



Here Nj is the least general .substitute for N, and is of the 

 form 



a -V br^^ cr.^ + dr^ -f &c. 

 where the number of values of r,, r<^ &c. cannot exceed 5 - i. 

 but may be much fewer, and constitute a recurring series found 

 from 



-— , where « = i, 2, 3, 4 <S:c. 

 



Let 5 =: 2, 5, then Nj = a 



= 4, = a -V 2b 



= 8, ■= a + 2.b + a,c 



= 16, = a h 10^ + A,c -V ^d 



= 3. 9. = « + /^ + c -f &c. 



= 7. = a + ■x,b + 2c + 6d + 4e + Sf \ 



+ ^+ 3^i + 2i + 6y + 4>^ -h &c. I 

 = 37. = a + lob + 26c 1 



+ d + loe -f 26/ -t- &c. / 

 = 11, - a + 10b + c -i- lod + &c. 



and so on. 



The practical importance of this general test must primarily 

 depend on the brevity of the recurring period, of r„, but in 

 special cases this objection may be removed. 

 Thus when 5= 11, if Nj -^ 5 = 11^ we have 



Ni = (a + f + &c.) + io{b + d + &c.) 

 = S X loS] = 11(7. 



But S - (/ =^ 10 (q - Si) 

 where (S - q) -^ 10 = q - S = q^ suppose ; 

 also Sj = (i i^ - S) -^ ID ; 



S - Sj 



i/S_-^ 



V 



10 ; 



11^,. 



That is, the difference of the sums of the alternate series of 

 digits is divisible by 1 1 if N or Nj be so divisible. This result 

 may be applied thus : Let ^3, b.^, c.^ &c. denote triple periods, 

 and 5 = looi, then 



Nj = ^3 + lo^b^ + C3 + 10V3 + &c. 



= («3 + ^3 + &c.) + 10^ (^3 + d^ + &c.) 

 = S + lO^Si which may be changed to 

 S - Si. 



Thus S - Si is a test for divisibility by 7, 11, 13, 77, 91, 143, 



lOOI. 



Again, if a^, b^, c^ &c. denote quadruple periods and 

 S = 10,001, then 



Ni = a4 -f 10% + ^4 4- &c. = S - Si 



and is a test for 8 = 73, 137, loooi. 



Again, if a^, bg, Cg &c. denote sextuple periods and 

 S = 1,000,001, then 



Nj = ^6 -t- io^3g + ^6 + &c. = S - Si and is a test for S = loi ; 

 9901. 



As examples take 



(i) N = 807,929,122 ; 8 = 7, II, 13, 143, 77, 91 ; 

 S - S] = 122 + 807 - 929 = o. 

 . • . the proposed number is divisible by 8. 



(2) N = 67, 3558, 3491 ; S = 73, 137. 

 S - Si = 3491 + 67 - 3558 = o. 



(3) N = 360, 4536, 7388 ; S = 73. 



S - Si = 7748 - 4536 = 3212 = 73 X 44- 



(4) N = 390, 9569 ; 8 := 137. 

 S - Si = 9179= 137 X 67. 



(5) N = 585622, 677027 ; 8 = loi. 

 S - S, = 91405 = 905 X loi. 



(6) N = 954221, 304387 ; 5 = loi. 

 S - Si = 649834 = 6434 X loi. 



