Ja-v. 



1882.] 



• KNOWLEDGE 



273 



IXTELLIGENXE IN ANIMALS. 



[227] — Reading to an old sportsnion Tour article on this subject 

 in No. 6, and the correspondence which followed, he related to me 

 how he used to acconi|>any a, friend possessing a pointer (bitch), 

 who, when her master missed tliree consecutive shots, woaUl slink 

 home, heedles.s of any calls to remain in the field. The friend alluded 

 to was a first-rate shot, and rai-ely missed his mark, except after an 

 evening's extra glass. 



In thus administering a rebuke to her master, the animal, I think, 

 exhibited a rare amount of humour. It could not be s;iid that the 

 dog herself was unmindful of her own duties, for on one occasion, 

 when her master went home to lonch, returning after two hours' 

 absence, she was found at the same spot where left, pointing to a 

 hare lying at the bottom of a hedge. This, of course, was due to 

 ptKxl training, but her conduct in the former instance must have 

 been the result of reasoning. A. Gaubert. 



ELECTRICAL IMAGES. 



[228] — Having baen lately reading Jlaxwell's " Elementary 

 Treatise on Electricity," I have been able to follow the reasoning 

 and do all the mathematics except one part on page 85 relating to 

 electrical images. The diflSculty is to obtain his results without a 

 clumsy and laborious process of multiplying. He says: "If we 

 now write — 



. a'* 

 1 qaa = a + + etc. 



, C^-i)' 



' I —ah a-b- . 



qab = . — — —etc, 



c c(<r»-a»-fc=) 



i,hb = b + 



c'-c 



etc. 



. the whole charge on the sphere a will be 

 Ka = qaa Pa + qab Pb, 

 and that of the sphere b will be 

 Eb — qab Pa + qbb Pb." 

 That is all clear enough. But he goes on to say : "From these 

 results we may calculate the potentials of the two spheres when 

 their charges are given, and iJE we neglect terms involving 'b, we 

 find— 



Po = i Ea 



Eb 



Pb = 



Ea 



(\ - ^^1_\ Eh." 

 \b c'{c'-a'J 



The second result, I cannot for the life of me make out, though 

 1 have tried lots of times. On page 186, Fig. 48, it seems to me that 

 the direction of the current in the branch C 0, should be from C to 

 0, and not, as in the figure, from to C, the battery being placed 

 , at E. It occurs in the large treatise as in the elementary one. 

 Surely the Editor should have seen that such an important matter 

 as Wheatstone's Bridge should have bet'U correctly represented. 

 He is not reputed to be over mercif al towards the blunders of other 

 minor planets. A Student. 



MORTALITY FROM CANCER. 



[229]— In an article on the "Duration of Life" (Knowledge, 



No. XL, p. 228), Mr. AUinson states that diseases of more ad- 



■ need life, "such as cancer," are increasing in fatality. Is it a 



t that cancer is increasing, or is there only an increase in the 



: ;inbcr of recorded cases, due to a readier diagnosis on the part of 



medical men ? In the Registrar-General's Report for 1879, the 



total average mortality from cancer is stated at 0'5 per 1,000 of 



T"'i'ulation. If this is correct, my neighbourhood contrasts badly 



•v;th the country in general. In the south-western suburb of Lon- 



II, in which I live, there have been in my own small circle of 



iuaintance within the past year five cases of cancer in elderly 



rsons, in four instances abdominal. Can Mr. Allinson point to 



y trustworthy statistics in support of his statement, which my 



Iierience latterly goes far to confirm ? It seems to me a question 



' 1' great interest whether the occurrence of this most frightful 



fease is influenced by locality. H. A. Everest. 



RICHTER'S DREAM. 



'' [230] — Richter's Ijeantiful " Dream of the Universe," or " Traum 

 tier das All," is in the book called " Der Komet," vol. 28, p. 129, of 

 the 34 vol. Berlin edition. Loosely translated by De Quincey, 

 vol. 14, p. 134. J. KlKKMAN, M.A. 



ARRANGED SQUARES. 

 [231] — In the Villa Albani, near Rome, opposite the foot of the 

 staircase, as you descend, is a stone tablet let into the wall. On it 

 is engraved the subjoined arrangement of the square of 9, with the 

 quaint Latin inscription, which I have copied and annexed to the 

 square figure : — 



" Qxittdratus 

 ilaximus. 



Lector si doctus 

 admirator ; si ig- 

 norus scito quad- 

 ratus hie mathe- 

 matice constructus 

 ah uno usque ad 

 octoginta unum 

 3321 unitates in- 

 cludit qntelibct ip- 

 sius columns; tarn 

 in linea planilqnam 

 in recti et trans- 

 versali unitatis 369 

 qua) ductaj per 

 noreni easdem 3321 

 unitates rcstituunt 

 et appellatur maxi- 

 mus quia maximam 

 possidet extensionem. Vale.— Caietanus Gilardonus Eomanus 

 philotechnos inventor a.d. mdcclxvi." 



The inscription is in capital letters, and without punctuation. 

 I am unable to discover any principle of construction in the arrange- 

 ment of figures, and, therefore, do not see how it admits of 

 unlimited extension. Can you suggest what the principle of 

 construction is ? 



As regards the squares of even numbers, I have before me the 

 square of 4, 6, and 8, but can discover no principles whatever in 

 them. The square of 4— absurdly called " the game of 34," every 

 body knows. The square of 6 stands thus : — 



3 X 37 



= 111 



1 30 19 18 12 31 



32 26 23 20 8 2 



33 9 16 22 28 3 

 4 10 15 21 27 34 



35 29 14 17 11 5 



G 7 24 13 25 36 

 The square of 8 stands thus -. — 



= 4 X 05 

 = 260 



1 16 48 33 25 24 56 57 



63 55 42 34 20 IS 15 7 



62 54 19 27 35 43 14 



5 13 20 28 36 44 53 61 



4 12 21 29 37 45 52 00 



59 51 22 30 38 4« 11 3 



58 50 47 39 31 23 10 2 



8 9 41 10 32 17 49 64 



I believe these squares may be arranged by plac"'.fr 

 S = 2 X 17 the diagonal numbers in what I may call their 

 = 34 natural squares in the first Instance, and working up 



to them ; but I have only 

 succeeded with the square 

 of 4, as shown by the 

 large and small figures in 

 the annexed square. 



