Curious Paradoxes. 483 PARADOX IV. PARADOX VI. ANSWER. There is a certain place of the earth, There are three remarkable places where a fire being made, neither flame on the globe that differ both in longinor smoke would ascend, but move cir tude and latitude, and yet all lye under cularly about the fire ; moreover, if in one and the same meridian. that place one should fix a sinooth or plain table, without any ledges what ANSWER. foever, and pour thereon a large quantity of water, not one drop thereof would run over the said table, but By the globe, may be meant the arti. would raise itself up in an heap. ficial globe, and by the Meridian may be meant the Brazen Meridian, belong. ing to it, which may be five degrees thick; then suppose three places, A, B, C, A to be Dublin, in latitude fiftyThis place must also be the center of three degrees and an half, and longishe earth, for the reasons mentioned in tude twenty degrees; B, to be Lifhon, the lait. in latitude thirty-eight degrees and an half, longitude eighteen degrees; C, to PARADOX V. be the Isle of Paxaros, in latitude eight degrees, and longitude two hundred de. There is a certain place on the globe, grees, all which, though they differ both of a considerable southern latitude, that in longitude and latitude, yet may they hath both the greatest and least degree all lie under one and the same Brazen of longitude. Meridiar. Or without equivocation, suppose one place under the pole, a second on this fide, and a third on the other un der the same meridian circie, so may This may either mean the South Poles, which bath not only the lealt they all differ both in longitude and latitude ; but greatest, and all intermediate de.. for the pole contains all de. grees of longitude, all which meet in grees of longitude. the poles. Or all places that lie under the first meridian, have both the least and greatest degree of longitude, as at noon is the greatest and leatt number There are three remarkable places of hours ; because then and there we begin and end our reckoning. on the continent of Europe, that lie under three different meridians, and, Thus Trinidada is in latitude fouth 20 degrees, and under the first meri- yet all agree both in longitude and la titude. dian, with them who reckon from St. Michael's, or Triftam da Cunba, is in thirty-six degrees fifty-four minutes ANSWER. fouch latitude, and the same longitude with Teneriff; all which, according to Divers geographers begin their first the old way of reckoning longitude, are meridian at divers places; thus Ptolo, mot only in the beginning of the first my at Cape Verde (formerly one of the degree, but also in the end of the three fortunate islandas) Mercator at St. Min hundred and sixtieth degree of longi. chael's in the Azores; Bleau at Tenetude. riff, one of the Canary illes, &c. Now if ANSWER. PARADOX VII. 484 Recreations. if you take (under the fame latitude) places under different meridians, and three places (suppose ten degrees from one parallel of latitude, as Pico, St. Nieach of these firit meridians! they agree cholas, and Lisbon, and begin the lonall in latitude, allo in longitude, from gitude åt every one of them; fo will these three respective places, and yet they all be first meridians, and agree lie under three different meridians, in in having no longitude, and being in respect of the globe, or which is much the same parallel will agree also in lati. to the same purpose, chuse any three tude. SELECT ARITHMETICAL RECREATIONS. RECREATION 11. RECREATION I. in one Hand, and an odd Number in the A perf:n having fixed on a Number, in his DESIRE the person to maltiply the Bid him quadruple the number number in his right hand by three, thought on, or multiply it by 4, and, and the number in his left by two. having done this, delire him to add 6, Bid him add the two products toge 8, 10, or any number, at pleasure, to ther, and tell you if the sum be odd the product: then let him take the or even, half of this sum, and tell you how If it be even, the even number is in much it is; from which, if you take the right hand; but if it be odd, the away half the number you desired him even number is in the left hand. at first to add to it, there will remain the double of the number thought on. : No. in right hand. No. in left hand. 18 7 3 Suppose the number thought on is The quadruple of it is 14 28 14 14 4 taken from this leaves Therefore 5 was the number thought 68 fum of the products. EXAMPLE i. EXAMPLE. 2 20 on. EXAMPLE II. Another Method of discovering á Number thought on. No. in right hand, No, in left hand. 7 18 After the person has fixed on a 3 number, bid him double it, and add 4 to that fum ; then let him multiply 36 the whole by 5, and to that product add 12; defire him also to multiply this sum by 10, and after having de duced 320 from the product, to tell 57 sum of the pro- you the remainder, from which, if ducts. you cut off the two last figures, the num 21 36 21 EXAMPLE IO20 700amples. RECREATION III. Curious Recreations. 485 number that remains will be the one at the first fep, or halving, either 4 or thought on. 8, was the number thought on; if there was a necessity to add i both at the first and second steps, either 2 or 10 were the numbers thought on, &c. Let the number thought on be And which of the two numbers is 7 Then the double of this is 14 the true one, may always be known And 4 18 from the last step of the operation ; for This multiplied by şis if I must be added before the last half 90 And 12 added to it is 102 can be taken, the number is in the seAnd this multiplied by 19 is cond column, or otherwise in the first, From which deducting as will appear from the following ex 320 There remains Which by ftriking off the two cy. Suppose the number chosen to be phers gives 7, the number thought on. To which if we ada 9 The sum is 10 Then the triple of that number is 30 1. The half of which is 15 To te!) the Number a person has fixed upon, The triple of 15 is 45 without asking him any Questions, *2. And the half of that is 23 The triple of 23 is 69 The person having chosen any r.um 3. The half of that is 35 ber in his mind, from 1 to 15, bid And the half of that is Io* him add i to it, and triple the amount Then From which it appears that it was 1. If it be an even number, let him necessary to add i both at the second take the half of it, and triple that half; and third steps, or halvings, and there but if it be an odd number, he must. fore by the table the number thought add to it, and then halve it, and tri. on is either 1 or 9, ple that half. And as the lart number was obliged 2. In like manner let him take the to be augmented by i before the half half of this number, if it be even, or could be taken, it follows also, by the the half of the next greater, if it be above rule, that the number múft be odd, and triple that half. in the second column; and consequent3. Again, bid him take the half of ly it is 9. this last number, if even, or of the next greater, if odd; and the half of that Again, suppose the number thought on half in the same way; and by observ. 6 ing at what steps he is obliged to add i To which if we add in the halving, the following table will The sum is 7 shew the number thought on: Then the triple of that number is *1. The half of which is The triple of it is *2. And the half of that is 3 II SI *3. The half of that is 26 8 3 And the half of that is 13 3 9 From which it appears, that it was 15 7 neceffary to add i at all the keps, or Thus, if he is obliged to add i only halvings, 1, 2, 3, therefore, by the ta ble, to be 21 2 ооооо 1 2 1 2 6 14 2 1 486 V. IV. The Blind Abbess and her Nuns. ble, the number thought on is either 6 dent, that in this case also, there will or 14. still be nine in a row, as before, And as the last number required no augmentation before its half could be taken, it follows also, by the above rule, that the number must be in the Any Number being named to add a figure to first colump ; and consequently it is 6. it which thall make it divisible by 9. Add the figures together in your mind, which compose the number named ; and the figure which must be A curious Recreation, usually called the added to this sum, in order to make it Blind Abbels and her Nuns. diviñible by 9, is the one required. Suppose, for example, the number A BLIND abbess visiting her nuns, tvho were 24 in number, and equally of its figures is 23 ; and that 4 being named was 8654; you find that the sum distributed in 8 cells, built at the four added to this sum, will make it 27; corners of a square, and in the middle which is a number exactly divisible by of each-fide, finds an equal number in 9. every row, containing three cells. At You therefore desire the person who a fecond visit, he finds the same num. named the number 86.54, to add 4 ber of perfons in each row as before, it, and the result, which is 0658, will though the company was increased by be divisible by 9, as was required. the accession of four men. This recreation may be diversified, ing a third time, me ftill finds the same by your specifying, before the fum is number of persons in cach row, though named, the particular place where the the four men were then gone, and had each of them carried away a nun with figure fhall be inserted, to make the · number divisible by 9; for it is exthem. actly the same thing, whether the figure be put at the end of the number, Fig. 1. Fig. 2. or between any two of its digits. to And com Fig. 3. Provide a small bag, divided into Let the nuns be first placed as in two parts; into one of which put sefig. 1. 3 in each cell; then when the veral tickets, numbered 6, 9, 15, 36, four men have got into the cells, there 63, 120, 213, 309, &c, and in the must be a man placed in each cor other part put as many different tickner, and two nuns removed from ets marked with the number 3 only. thence to each of the middle cells, as Draw a handful of tickets from the in fig. 2; in which case there will evi. first part, and, after ihewing them to dently be ftill nine in each row; and the company, put them into the bag when the four men are gone, with the again ; and having opened it a second four nuns with them, each corner cell time, desire any one to take out as mamust contain four nuns, and every ny tickets as he thinks proper. other cell 1, as in fig. 3. it being evi. When he has done this, open pri varely Extraordinary Circumstancë. 487 vately the other part of the bag, and fum, must evidently. be divisible by An ingerious mind may also diver- then pronounce, that the ' fify this recreation by marking the ticket shall contain the number by tickets in one part of the bag with which the amount of the other num. any numbers which are divilidle by hers is divifible ; for as each of these 9 only; the properties of both 9 and numbers are some multiple of 3 their 3 being the lamë. ACCOUNT OF A BODY, WHICH HAD BEEN FOUND ENTIRELY CONVERTED INTO HAIR, À CONSIDERABLE TIME AFTER IT WAS BURIED. ABOUT forty-three years ago, a are of opinion; that hair, ivool, fears woman was interred at Nuremberg, thers, nails, horns, teeth, &c. are noe in a wooden coflin, painted black, ac- thing but vegetables. If it be fo, we cording to the cuftoni of the country. need not be surprized to see them grow The earth wherein her body was de on the bodies of animals, even after pofited was dry and yellow, as it is their death, as has been frequently ob. for the most part in the environs of served. Petrus Boreilus, Hift. and that city. of three bodies buried Obs. Med. Cent. I. Obf. 16, pretends: in the lame grave, this woman's was that these productions may be transe laid deepest in the ground; and there planted as vegetables, and may grow being an occasion to make room for a in a different place from that where fourth body, the grave was dug up they firit germinated. He also relates, anew; but, to the great surprize of the in some of his oblervations on that fubi digger, when he had removed the two ject, among others, that of a tocth uppermost collins, he perceived a con drawn out, and transplanted, which siderable quantity of hair that had may appear pretty singular. made its way out through the sits and Though the external surface of bo. creviccs of ihe cofin. The lid being dies is the usual place for the growth taken off, there appeared a perfect te of hair, it has, fiotwithstanding, been sembiance of a human figure, the eyes, sometimes found on the tongue, in the nofe, mouth, cars, and all other parts, interior of the heart, and on its surface, being very distinct ; but from the in the breasts, and inies; and in crown of the head to the foles of the other glandular and mullar parts. feet, it was covered with very long, but there is no internal part where it thicli, and frizzled hair, is oftener found than in the cvarium of The grave digger, after examining females. This has been observed in it for some time, happenet to touch three different fubjects by Dr. Tyson, the upper part of the head, but was as we find it related in the Philofophical more surprized than before, on seeing Collections of Mr. Hook, who also the intire body thrink, and nothing at tells us, on the testimony of Mr. Arlast remain in his hand but a bundle nold, that a man nanged at Tyżurn of rough hair, which insensibly alsuin- for a theft was found, in a very short ed a brotvnith red colour. time after he was taken atvay from the The learned Honoratus Fabri, Lib, gallows, covered over in a very extra3, de Plantis, and several othcr authors, ordinary manner with hair: VOL. 1, з с LIVES |