Dec. 30, 1881.] 



KNOWLEDGE 



187 



nty cells in the sqnare directly opposite to them, as seen in 

 _■ 2 — which will then be a magic sqnare, whose root is 7 — and 

 1" snm of the nnmbers in each vertical and horizontal band, and 

 -o of those on the two diagonals is 175. 



POIGNABC' 



lor a square whose root is 7. 



In the sqnare, Fig. 1, place 



in the top horizontal row the 



lirst eoven numbers of the 



progression 1 to 7 in any order 



whatever, as 3, 7, 5, 1, 6. 4, 



-. Then choose a number 



Wiich is prime to the root 7, 



I which, when diminished 



unity, does not measure it, 



iv ;t. Begin the second row 



null the third figure of the 



tirst. The third row with the 



ihird figure of the second, Ac, 



and fill up tlie sqnare. 



Method. 



Fig.l. 



In the top row of Fig. 2, 



I uce the multiples of the root 



beginning with a cipher, 



. 0, 7, 14, 21, 28, 35, 42, in 



y order at pleasure ; and fill 

 1' the square on the same 

 principle as in Fig. 1, taking 

 care not to assume the same 

 number for varying the order 

 of the figures. As 3 was 

 taken for Fig. 1, we may take 

 4, or 5, or 6, for Fig. 2, say 4. 

 Then the square will be filled 

 np as in the margin. Now 

 add the corresponding numbers 

 in each cell of Figs. 1 and 2, 

 and place the sum in Fig. 3, 

 which will be a magic square. 



It is easily seen that by this 

 method the position of the 

 numbers in the finished square 

 may be varied greatly, and I 

 leave it to the readers of 

 Knowledge to say how many 

 ways there are of varying the 

 square of 7. 



J. A. Miles. 



Fig. 3. 



INTELLIGENCE IN ANIMALS. 



[158]. — Referring to Mr. Henslow (p. 46, No. 3), is not his 

 Icaeoning somewhat curious ? He tells us that had the dog not 

 been tanght to ring the bell, his reasoning would have been abstract. 

 As the fox was not taught to do what he did, why was not his 

 reasoning abstract ? 



Another story is still more apropos. In this case the fox cut the 

 line connecting the trigger with the bait, then went up deliberately 

 (aa seen ty his track on the snow) and ate the latter. In this case 

 the fox cdnld not scrape a trench, so as to get safely at the bait, as 

 there were only a few inches of snow on the ice where the bait lay. 



In neither of these cases had the foxes been tanght to do what 

 they did, yet each in his own way used reasoning powers which 

 enabled him to accomplish his object in the only way by which it 

 oonld be safely attained by an individual fox (or man), ignorant of 

 the mechanism of firearms. Was this abstract reasoning ? 



Mr. Henslow is rather hard upon brutes and boys. Every day 

 we find what are supposed to be educated, reasonable, aad, I pre- 

 sume, reasoning men and women, doing as silly things as the most 

 Btapid " boy or brute " conld be guilty of." 



Ask twenty persons what they would do if, whilst exposed to 

 great cold, they found their faces freezing ? Probably, nineteen of 

 the twenty would reply, " mb with snow." This would be proper 

 treatment if a person frozen was brought into a warm house, but 

 is not right whilst he is exposed to the low temperature that is 

 freezing him. 



This snow application was improved upon by Major Bumaby. 

 when, on his ride to Khiva, ho thought his hands were freezing. 

 He added brandy to the snow before rubbing it in, and thus made a 

 sort of freezing mixture, as anyone can easily provo by trj-ing it on 

 some cold day, and exposing the part rubbed to the air. The brave 

 lady who ascended Mont Blanc in >vinter adopted the same plan. 

 and thought it successful. J. Rae. 



[In a paragraph, which we have omitted, Mr. Rao appears to 

 have misunderstood Mr. Hcnslow's remark about " pulling the 

 string out of the line of tire." Mr. Henslow meant the fox being 

 out of the line of fire while pulling, not the fox pulling the string 

 away from the Une of fire. — Ed.] 



[159] — In favour of the lower animals possessing reasoning 

 powers, I submit the following ; — 



While living in Dublin, a few years ago, we had two female cats — 

 one a " tabby," the other a " tortoiseshell." The tabby, my especial 

 pet, was of rather fierce disposition, but an excellent mouser, and 

 was in the habit of bringing her prey, generally alive, to show me 

 before devouring it. The tortoiseshell — a feline beauty— passed the 

 greater part of the day on the rug before the fire. One day,. 

 "Tabby" brought no less than three mice, consecutively, into our 

 sitting-room. The first two she ate; but the third, after playing 

 with it for some time, she hid under a mat at the door, evidently 

 meaning to reserve it till a hungrier moment. As soon as she left 

 the room, the tortoiseshell, who had been sitting, as was her wont, 

 with half-closed eyes before the fire, went to the mat, poked out the 

 mouse, and gobbled it. This theft amused me so much that I 

 resolved to watch the consequences. Tabby did not come in again 

 till evening, when she proceeded instantly to fetch out lier mouse. 

 She searched well under the mat, but not finding her bonne bouche, 

 began growling ominously. At length her eyes fell upon the guilty 

 tortoiseshell, upon whom she rushed, and beat and scratched her 

 until in pity we rescued the culprit. Another time both cats were 

 with kitten. The tortoiseshell disappeared for a few days, and 

 returned looking very lean and miserable. Tabby, who had mean- 

 while brought forth her j-oung, received her more amicably than 

 usual, and after some rubbing of noses and purring, the tortoiseshell 

 took charge of the kittens, and suckled them. This was not the 

 only time she was seen doing duty as wet-nurse, whilst the other 

 was rambling somewhere round. A. F. R. 



A BEARS MEMORY OF LANGUAGE. 

 [160]— The strategic shifts of Colonel Perkins' (Purtons' ?) dog. 

 Bully, at Bangalore, reminds me of another story connected with 

 Bangalore. The late Rev. William Campbell, who was formerly a 

 missionary there, on visiting Dublin, to advocate the claims of the 

 London Missionary Society, went with some friends to see the 

 Zoological Gardens in that city. While walking through the gardens, 

 their attention was drawn to a particular den by the excitement of 

 a small crowd before it. On approaching the place, they found it 

 was the den of the Indian bear. Bruin was in a bad humour, and 

 sat resolutely on his haunches, with his back to his visitors. Some 

 tried to coax him with buns, others to startle him with shouts, and 

 a few tried to stir him up with walking-sticks and umbrellas. All 

 their efforts were in vain. At last it occurred to Mr. Campbell to 

 address the bear in the language he was accustomed to in his youth, 

 so he shouted " Cuddapah ! Cuddapah ! " (Get up ! Get up !) To 

 the surprise and amusement of the spectators. Bruin immediately 

 turned round with a delighted grin. — Yours, &c. Cuddapah. 



AN ILLUSION.- DURATION OF FLASH OF LIGHTNING.— 

 RAINBOW. 



riGl] — Wheatstone calls attention to the following illusion 

 first mentioned by Professor Necker, of Geneva. The rhomboid 

 AX is dravrn so that the solid angle A 

 should be seen the nearest to the spectator, 

 and the solid angle X the farthest from him. 

 But in looking at the rhomboid, it will 

 occasionally so change that the solid angle 

 X will appear the nearest, and the solid 

 angle A the farthest away. Necker attri- 

 buted the alteration of appearance not to a 

 mental operation, but to an involuntary 

 change in the adjustment of the eye for 

 obtaining distinct vision. Wheatstone, on the other hand, supposed 

 the effect to depend entirely " on our mental contemplation of the 

 figure intended to be represented, or of its converse." 



I think Mr. Molloy (letter 116, p. 121) will find no account of any 

 experiments of Wheatstone's on the duration of a flash of light- 

 ning in the collected volume of his papers issued by the Physical 



