Oct. 12, 1883.] 



♦ KNOWLEDGE ♦ 



2:33 



I describe it in detail, and show how it e.^plains the sea-serpent of 

 the old Norsk traditions ; not the puny thing of a few hundred feet 

 long described by modern observers, but the veritable Kraken, three 

 orfour and more miles lonj;. I saw him myself, of such dimensions, 

 and have pictured him in the last edition (1S7G) of that work. 



W. ;Mattieu Williams. 

 [Mr. Williams's explanation seems to me scarce consistent with 

 the observed phenomena. A film of rarer air would have shown 

 the rest of the upper masts, sails, etc. So would a film of denser 

 air ; but in this latter case the sea horizon and surface would be 

 Been, and the reflected masts, &c., beloio the sea horizon would be 

 lost — as was, in point of fact, the case. Of course if the film were 

 limited in extent part of the upper rigging would be lost ; but the 

 parallelism of the observed sea limit with the true horizon would in 

 that case be only explicable as a most marvellous coincidence. — 

 R. P.] 



SIR WILLIAM HERSCHEL. 

 [95G] — I have only just seen letter 917 (p. 21'J), in a locality 

 between 200 and 300 miles from my own library. Under these cir- 

 cumstances I really cannot say, off hand, the name of the work in 

 which I found the statement as to the loss of an eye by Sir William 

 Herschel ; but, immediately on my retiirn home, I will hunt up the 

 reference and give it (as Colonel Herschel requests) in these 

 columns, for the benefit of all interested in the matter. 



A Fellow of the Royal Astronomical Society. 



SMALL WHEELS v. LARGE WHEELS. 



[957] — I have received so many letters from cyclists who have 

 read my articles in Knowledge stating that they agree with what I 

 have written on this subject, that I propos^ briefly replying to 

 " Sigma's " last letter, and then withdrawing from the further dis- 

 cussion of this question. 



With regard to the pace travelled by Mr. Marriott I had assured 

 myself before writing, by comparing notes with a tricycling 

 sporting expert, that the pace made by Mr. Marriott on the 40-inch 

 " Ilumber " was faster than he travelled on the ■12-inch " Humber" 

 on a more level road in far better condition. 



It was also faster, slightly, than Lowndes made over a better 

 course on a " Coventry ; '' but if it had been slower, surely " Sigma " 

 must see that would have had but little bearing on the matter. 



The i-)erforniance of the same man on the savie class of viachitie 

 first with large and then icith smaller wheels is the criterion. 



There is nothing in " Sigma's " suggestion that probably the 

 " Humber" alone among tricycles may run better for having small 

 wheels. 



Mr. Salmon, as he stated in his lucid letter in last week's Know- 

 ledge, has been led to adopt small wheels from his experiments 

 with a Coventry Rotary, Mr. Grace has done so after experimenting 

 with rcar-steerers of the "Meteor" type, while Mr. Howard and 

 myself have used front -steerers of the " Salvo" type, and we have 

 all arrived at the same conclusion. 



Small wheels are certainly at no disadvantage in hill-riding, as 

 compared with large wheels. 



"Sigma" gives us one experiment ho made with 44i-in. wheels. 

 1 have tried hill riding on fifty machines, and I can ride Godstone- 

 hill. the sfecpost incline I care to ride, on my 38-in. Humber, geared 

 to -lO-in., easier than on any other machine. 



I can easily produce a witness that I have quite recently done 

 this on the 38-in. machine if " Sigma" doubts my word. 



I do not in any way refer to this as a feat, but name it because I 

 have been compelled to dismount on this hill on every other machine 

 but my 3S-in., though that is geared to 46-in., while 1 have failed 

 to ride it with 48-in. wheel machines geared down as low as 30 in. 

 I have also failed to ride it on a -ll-in. "Humber" geared level, by 

 which I do not mean that I coidd not have struggled u]), but that I 

 preferred to dismount rather than run the risk of breaking a blood- 

 vessel. 



These systematic experiments prove to mo conclusively that 

 small wheels are at no disadvantage in hill-riding. 



Mr. Salmon is correct in supposing that my articles in Know- 

 ledge are not written for the gnidanco of racing men, or even hard 

 riders, but for those who are content to rido at a moderate speed, 

 with a pleasurable amount of exertion. 



If any novices should follow "Sigma's" advico and attempt to 

 rido over hills with machines geared up to 60 inches, they will 

 probably soon give up riding, voting it simple slavery. 1 write 

 ailrisedly, for I have reconciled several men to riding who were 

 about relinquishing it, by having their machines geared down to 

 •l-fi inches when I found they were trying to ride machines with 

 50-in. wheels geared level, and in every instance, I believe, they 

 wore stronger men than myself. 



1 have a friend — a strong man and a good oarsman. Some time 



since he got a machine from a dealer. After riding for a few weeks 

 he sold it. On inquiry I found it was a machine with 50-iu. 

 wheels geared up to 5G. I did ray best to persuade him to try 

 another machine geared down, but he had been sickened. He 

 replied that he was not afraid of work, but tricycling was some- 

 thing more than work, it was — and he said something with a very 

 big i) indeed. 



Contrary to " Sigma's " suggestion in a former letter, I do not 

 find that novices who are set to ride a machine which runs easily 

 at a moderate pace, quickly become disgusted with tricycling. 

 JouN Browning, 

 Chairman of the London Tricycle Club. 



P.S. — Mr. Shaw has written another long article in the Tricy- 

 clist, which I can dismiss in a postcript, as he has only one strong 

 point in it. He asks why I do not propose to ride on geared-up 

 castors? I might, with as much reason, have asked why he did not 

 propose to build machines with wheels 160 in. in diameter instead 

 of 60 in. ? But I did not reply to him in this way, because I pre- 

 ferred to meet all his theoretical suggestions by statements of facts, 

 or arguments based on experiments, without descending either to 

 ridicule or even exaggeration. 



DR. FRANKLIN'S MAGIC SQUARE OF SQUARES. 



200 2171233 249 8 25' 40 57 721 89104 121136153168185 



581 39 26 7 



198 219 



60[ 37 

 201I2I6 

 55! 42 



203 214 



53 44 21 12 245 



230251 6 

 28 5252 



231218 



233 248 



23' 10 



27 38 

 229J220 



24: 41 



I 



234215 



46 19 14 243 



239 242 



17i 16 



196 221 



63| 35 

 194'223 



228 253 

 30 3 

 226 255 



22 43 



227 222 

 3l| 34 



199186:167.154 135 122103 90 71 



59 70 91 102 

 I97'iss'l65'l56 



56i 73 

 202I183 



123134155 



I I 



133|l24[l01 

 120137 152 

 I38|ll9106 



52 77 84109 



206179174147 



50 79 82 Ul 

 208!l77 176145 



61; 68; 93100 

 195190163158 

 63 66 95 98 



6t 33 32 1 i56 225 224 193 192 161 160 129 128! 97 96:65 



lis 139 150 



114 143 146 

 144118112 



131126 99 

 127130159 



166187 



92| 69j 

 169184' 



87i 74 



17l'l82l 



iira'isn' 



175 178 

 Sll 80 



164189 



94' 6: 



162!l91 



[958] — The chief properties of Dr. Franklin's Square which 

 accomijanies this, are as follow : — 



1. The sum of the sixteen numbers in each column or row, 

 vertical or horizontal, is 2,056. 



2. Every half column, vertical or horizontal, makes 1,028, or just 

 one half of the sum 2,056. 



3. Anv half vertical row, added to anv half horizontal, makes 

 2,056. 



4. Half a diagonal ascending added to half a diagonal descending, 

 makes 2,056, taking these half diagonals from the ends of any side 

 of the square to the middle of it, and so reckoning them either 

 u)iward, or downward, or sideways. 



5. The same with all the parallels to the half diagonals, as many 

 as can bo drawn in the great square ; for any two of them being 

 directed upward and downwai-d, from the place where they begin to 

 that where they end, make the sum of 2,056; thus, for example, 

 from 64 up to 52, then 77 down to 65, or from 194 up to 204, and 

 from 181 down to 191 ; nine of those bent rows may be made from 

 each side. 



6. The four corner numbers in the great square added to the 

 four central ones make 1,028, the half of any column. 



7. If the great square be divided into four, the diagonals of the 

 little squares united make each 2,056. 



8. The same number arises from the diagonals of an eight-sided 

 square taken from any part of the great square. 



9. If a square liole,' equal iu breadth to four of the little squares 



