July 20, 1883.] 



* KNOWLEDGE ♦ 



45 



piece ami a threepenny bit — well, I should have required rigid proof. 

 Even as to the image midway between the size of the bronze coins, 

 1 don't quite see where the demonstration [Qy., explanation R. P.] 

 <-omes in, or how it can be obtained. 



Now, as regards Single Vision No. 2 and yourself, I am some- 

 what uncertain as to the precise fault found with me ; and it would 

 seem ns if some definitions of terms were needed, for which I am, 

 perhaps, responsible. I must therefore define that by " distinct 

 dual vision," I did not mean distinct vision by both eyes in unison ; 

 but two distinct images, one with each eye ; and further, that by 

 *' single vision " I mean one image, with one eye, exactly as if the 

 other were closed or non-existent. With this explanation I dis- 

 tinctly re-affirm my proposition, adding that it is based on my own 

 personal sensations and experience — inasmuch as, under certain 

 conditions, and in a medium position, where the images formed in 

 my two eyes are equally blurred and indistinct, I do, as a matter of 

 fact, see two different images — of course, of equal size. 



In conclusion, sir, permit me to remark that, as I have had a 

 mathematical education, been assistant in an astronomical observa- 

 tory, and aided theoretically and practically in calculating the 

 radius of curvature for lenses, and grinding and polishing to corre- 

 spond (in making object glasses for refracting telescopes), " Single 

 Vision No. 2 " has made a bad shot in assuming that optics are 

 unfamiliar to Sixgle Vision. 



[The difference between my own eyes is very nearly as great as 

 between "Single Vision" 's, my left eye being very shortsighted 

 indeed 1(1 can see distinctly with it at a distance of two inches) 

 while my left eye sees distant objects with perfect distinctness. 

 Vet I see an object clearly and singly when the shortsightedness of 

 the left eye is corrected by a suitable convex glass. Has " Single 

 Vision No. 2 " altogether missed ? " Single Vision " seems to 

 imagine the disproportion in size between the two images, when the 

 .sight of his sliorter eye is corrected, is as 7 to 1 linear. If he will 

 consider the matter, he will find, without having occasion to cal- 

 culate curvatures or to grind or polish lenses, that no such difference 

 exists ; and that such difference as does exist, does not depend on 

 the shortness or length of the sight of either eye — that is, it does 

 not depend on the distances for distinct vision. — E. P.] 



WARTS. 



[876] — If you will allow me, I will add my experience — though 

 fifty-five years ago — to what you have already inserted as to wart- 

 charming. I enclose my card, for only private use, and I think the 

 paper on which this is written may give a healthy colour to my 

 veracity. My warts were counted exactly as described by " Puzzled 

 Sceptic." Two or three were so small that, not being quite sure 

 whether they were warts or not, they were not counted. The 

 person said to be able to charm them away was a woman in the 

 village in Yorkshire close to where I was born, and who had been 

 my wet-nurse. At the time in question I might be about twelve 

 years old. Having tried caustic, silk, and other Iiousehold remedies 

 unsuccessfully, I let her try. Whether, at that age, I had any 

 belief in success I do not remember, but I am sure I did not trouble 

 myself much about it. She said they would all be gone in three or 

 four months. As a matter of fact, I have to state that by the end 

 of that time the sole and only warts remaining were those which 

 had not been counted, and had afterwards developed themselves. I 

 Jiave the mark of a very large one, which had two or three heads, upon 

 one of my finger joints still. Being of an inquiring mind, I several 

 times asked " Jane Watson " what she had done. For some time she 

 lefused to toll me. At last, being pressed by her "foster-son," 

 she first extracted a promise from me (which I fear I have 

 not kept) that I would not divulge her secret. Upon this she con- 

 fided to me that she had taken a piece of worsted, and made as 

 many knots in it as the wai-ts that were counted. That she had 

 liuried it under a gooseberry bush in her garden, and, whilst doing 

 so, that she uttered the following incantation, viz. : — 

 " Pray, Lord, as this rots and decays away, 

 To take Master Robert's warts away." 



And now, having stated bare facts, I say no more. I know no 

 more ; but so it was. R. W. J. 



Royallnstitution, June G. 



[It seems likely that the charmer as well as the cliarmed should 

 bave full faith, in order that the right sort of mental influence 

 may be produced. The effective action of the mind seems exerted 

 while the counting is going on. — R. P.] 



AN ENIGMA. 



[877] — A very curious method of calculation for discovering any 

 person's ago having come under my observation, I think it suffi- 

 ciently ingenious to be worthy of notice in your important pajier. 



The system is as follows : — The person whose age you want to dis- 

 cover is requested to write down, privately, the day of the month 

 he was bom and the month of the year, then you ask him to mul- 

 tiply by two, add 5, multiply by 50, add the nge, and subtract 365. 

 You then ask him for the total, to which you add 115, and the 

 result will show the day of the month, the month of the year, and 

 the age. 



The following is an example worked out. Supposing the person's 

 age is 20, and he was born on the 5th of Januarv — 

 5,1 

 2 



5,370 

 365 



5,005 

 Then add— 115 



5th day, 1st month, iO j-ears of age. 



Can any of your readers explain this, to me, strange arithmetical 

 enigma ? C. Hollis Challex. 



[liCt us consider what you do with the numbers in question, and 

 we shall probably find an interpretation of the puzzle. Let ii be 

 the number for the day, N for the month, A the age in years. 

 Note next that multiplying by 2, adding 5, and then multiplying 

 by 50, is the same as multiplying by 100 and adding 250 ; while 

 subtracting 365, and then adding 115, is the same as subtracting 

 250 ; so that these four operations together are equivalent to 

 multiplying by lOU, or adding two cyphers to the number first 

 taken, which is 10m + N. As the only other operation is adding the 

 age, it is not very wonderful that we get the three numbers we 

 wanted, — provided always that N is not greater than 10, nor A 

 than 100. Thus, if you take 3, 7, and 15, multiply 37 by 100, and 

 add 15, you naturally get 3,715. — R.P.] 



GINGER-BEER PLANT. 



[878] — Perhaps some readers of K.nowledge could help me by 

 explaining the following facts : — 



A member of our family, while out visiting lately, brought home 

 what her friends called a "ginger-beer" plant. The plant (as we 

 will call it) consists of numerous small bottle parts (separate) 

 about the size of a pea, and somewhat resembling tapioca when it 

 has been soaked. The mode of making the "ginger-beer" is to 

 put a certain quantity of ginger (whole) into a good-sized bottle 

 containing some of the " plant" and filled with water, and then to 

 sweeten with a little sugar a short time before taking the " ginger- 

 beer " out of the bottle. 



During the maki-nri of the " ginger-beer," the plant shows strong 

 effervescing powers (sometimes sending large pieces of ginger to 

 the surface of the water). 



The "plant" has to be separated every three weeks, by which 

 time it will have doubled itself; and if not separated would burst 

 the bottle, if tho " ginger-beer " was not removed very frequently. 

 The "ginger-beer" can be strained off about twice a day; and, 

 although 1 have not tasted it myself, I am told it much resembles 

 tho bottled ginger-beer, but does not have the " gasey " taste which 

 characterises the latter. T. H. Pebry. 



INTELLKiENCE IX AX AXT. 



[879] — I witnessed, tho other afternoon, a very remarkable case 

 of intelligence in an ant. I was sitting on some grass by the side 

 of a small path, just in front of mo being a short stone step, when 

 mj- attention was drawn to two separate streams of ants, one going 

 from me up the path, tho other returning, carrying back with them 

 their food. Among these little scavengers returning was one with 

 a load much too heavy for him, so when the step was reached, over 

 which all the ants had to pass, this busy worker dropped its burden, 

 and then went over himself and got possession of it again. I 

 expected he would proceed with the others, but instead of this 

 he had a very laborious climb back again with the food, and then 

 again dropped it over the step. The same thing was repeated three 

 times, but at tho third attempt I cut tho piece of matter in two, 



