506 



♦ KNOWLEDGE ♦ 



[August 2, 1886. 



Yet in any large gathering of persons variously trained 

 mentally, one or two will nearly always be found who are 

 quite unable to interpret the puzzle, and who appear to re- 

 gard the extra square in the long rectangle as the work of 

 the enemy of mankind. Probably some of those taken in 

 by the Bagdad bagman attributed then- loss to Ahriman in 

 veritable earnest. 



But simple as this puzzle is, it is very seldom set as it 

 should be ; insomuch that as usually set a keen eye will 

 readily detect the imperfect nature of some of the squares. 

 Of course we cannot get all the squares right by any con- 

 struction, but we can double the chance of deceiving the 

 eye by planning the trick properly. Instead of drawing a 

 square as in fig. 1 and dividing as there shown, as is usually 



c 



^* 



e ~~^ 



^ E 



Fig. 2. 



which really exists between fig. 1 and fig. 2 is equally dis- 

 tributed between the two arrangements, instead of all falling 

 on one (the arrangement of fig. 2) as usual. 



Of course, if the divT.sion has to be made in public, one 

 cannot apply this method. But it is far better to have the 

 pieces neatly cut beforehand, as the effect of the puzzle is 

 much enhanced by having the squares all neatly drawn. By 

 the wa)', the chance of deceiving even the keenest eye may 



Fig. 1. 



done, it is better to proceed as follows : — Draw a rectangle 

 as in fig. 2, and then pencil lightly a straight line from B to 

 h ; it will be found that this pencilled line passes above e 

 and below e (the nearest corners of small squares) cutting 

 fa and af in li and g respectively. Draw then a straight 

 line from b to a point midway between // and E and to 

 a point midway between e and g ; draw also from h a 

 straight line to these same points, and make cuts along 

 these fom- lines. You thus remove a long parallelogram 

 having b 6 as its longest diagonal. This, however, is only 

 half the long parallelogram really wanting when the pieces 

 of fig. 1 are put into the form of a rectangle having sides 

 with five and thirteen divisions. Thus, when you complete 

 the division by cutting along ea and ae, the discrepancy 



be yet further increased by very slightly curving the lines /« 

 KL, so as to bring their point of intersection somewhat nearer 

 than e to 6, and the like with the lines af and kl. 



Three puzzles interested us as leading to further analogies. 

 Oddly enough, they seemed related severally, as the .student 

 may find on examining them, to the three conic sections — 

 the ellipse, parabola, and hyperbola. We give them for 

 solution and examination in the next number of Knowledge, 

 noting that we cannot find space for the names of those 

 among our readers who may solve them, so that it would be 

 wasting postage to send solutions. 



1. A farmer has 19 trees, which he wishes to arrange in 

 9 rows, 5 in each. How should he plant them \ 



2. A man has a piece of oilcloth 4 yards long by 3 feet 

 broad, and he wishes to divide this into two portions which 

 shall fit a hall 3 yards long by 4 feet broad ; how .shall he 

 cut his oilcloth ? 



3. A man marks 6 straight lines on a field in such a way 

 as to enclose 10 spaces. How does he manage this^ 



MIND ACTING ON BODY. 



By Richard A. Proctor. 



|ASES, such as have been hitherto described, 

 throw far less light on the powers which 

 the mind possesses over the body than those 

 in which actual organic change results from 

 the mental act, continued long enough. The 

 following case, in which blindness (of one 

 eye) was certainly not dependent on defec- 

 tive nerve-force, is in this sense particularly 

 interesting. Mrs. S. had had severe rheumatic fever in 1839, 

 during the coiu-se of which the left eye was affected, in such 

 sort that both its internal and its external structure suffered 

 injury. In 1842, when Mrs. S. first consulted 3Ir. Braid, 

 this eye was free from pain, but was useless. More than 

 half the cornea was covered by an opaque film, any oly'ect 

 placed op])Osite the outer or left half of the ej'e (the tem- 

 poral half, doctors prefer to call it) being seen through a 

 dense haze ; and the objects placed towards the opposite side 

 were seen very imperfectly, owing to the injury which the 

 choroid and retina had sustained in the points on which the 

 images of such objects were reflected. The opacity was not 

 only an obstacle to distinct vision, but was also a source of 

 annoyance from its disfigurement, being obvious even at a 

 considerable distance. " Mrs. S. was a relation," Dr. Todd 

 mentions, "of Mr. Braid, and was in his house three months 

 before he operated upon her, during which time no change 

 took place. Violent pain in the arm and shoulder induced 

 her to submit to the hypnotic treatment, which proved suc- 

 cessful ; but what was more surprising, and quite unlooked 

 for by Mr. Braid, her sight was so much improved that she 

 was able to .see everything in the room, and to name different 

 flowers, and distinguish their colours, whilst the right eye 

 was shut, which she had not been able to do for more than 

 three and a half j-ears previously. The operation was con- 

 tinued daily, and in a very short time the cornea became so 

 transparent that it required close iiispection to observe any re- 

 mains of opacity. After the first operation there was con- 

 siderable smarting in the eye, which continued all night, 

 and in a less degree after future operations, which no doubt " 

 (be it remembered, it is not Mr. Braid, but Dr. Todd, who 

 expresses this opinion) " roused the absoibents, and effected 

 the removal of the opacity. Stimulating the optic nerve 

 to greater activity, however, must have been the chief cause 

 of the very rapid improvement which enabled her to see 

 objects after the second operation. Mr. Braid adds to the 



