Jan. 



1S85] 



♦ KNOWLEDGE ♦ 



]1 



^f. It is not only possible, l>iit easy. For instance, I 

 si all leave it to you as an exercise to estaUlish the two 

 following cases: — 



(1) P LP' (Fig. -t) is a cloud cuttins); the axis A A' of 

 the ellipse A P A' in L; MPQ, XPQ are ordinates 

 (perjx to A A') to the auxiliary circle Q A Q' ; Q Q' will 

 evidently pass through L. Show that, 



EUip'ical sequent P A P'= Circular sequent Q A Q . 



AO 



Fiff. 4. 



The proof consists in showing that any straight line 

 being drawn as rj pi perp. to A A', the part p e lyirg on the 

 elli|'tical area bears to the part q>l on the circular area, the 

 constant ratio 6 U to A C. 



Fig. 5. 



(2) Prove the like as to the sequents Py/ P', Q q Q', in 

 Fig. 5 (in which Q' p' Is, q p I, and Q P M are perp. to 

 A A'). 



[The proof is similar to that of case 1, — note that P P' 

 and Q Q', produced, meet on A A' produced.] 



(3) Prove that the parabolic segment P a P' (Fig. G) is 

 equal to two-thirds the parallelo- 

 gram TliP', when lal' is the 

 tangent parallel to P P', and there- 

 fore a M, parallel to the axis, is 

 the diameter of the chords parallel 

 to P P'. 



[The proof consists in showing 

 that ]j )/ 1, tangei.t at p, is bisected 

 in y, and hence that the elementary 

 area p m, parallel to P M, ia twice 

 the elementary area p n {p n d 

 being parallel to a M)]. 



(To he continued.) 



Fig 



TRICYCLING IN 1884. 



By John Browninc. 



ChdiruKin of the London T/'iVyr/c Clnh. 



\V1I.\T W i; G.UN BY USING THE TRICVCLK AS A MODE 

 OF LOCOMOTION. 



IN the very thoughtful article published by Dr. UicharJ- 

 son, in Lonymaiis Magazine, he claims for the tricycle 

 that, " it has doubled his power of locomotion." Before 

 the successful application of two speed gearings, as applied 

 to these machines bj' Burdess, Bowns, Hirst, and the St. 

 George's Foundry Co., i should have agreed entirely with 

 this claim. 



My own walking powers Ijeing considerably reduced in 

 the Idbt twenty five year.", 1 cannot walk, without over- 

 taxing my-elf, more than thirty miles in a i!ay, at the rat© 

 of about three miles in an hour. 



At the beginning of this year, I should have said that I 

 could not ride a tricycle more than sixty miles in a day, at 

 the rate of six miles an hour. 



For, while last year I found about eight or nine houis" 

 riding at the rate of about seven miles an hour as much 

 as I could conveniently accomplish, this year I have ridden 

 for nine hours at the rate of upwards of nine miles an, 

 hour, and I only left ofl' then because it was dark and I 

 could not get a companion to ride with me any further or 

 I would have ridden three hours more at the same rate of 

 speed. 



But even eighty tAO miles in nine hours may f'aiily le 

 said to be three times my power of locomotion unaided by 

 a tricycle. 



Again, as regards speed, I could at one time walk for 

 hours at the rate of five miles an hour ; then, the tricycle 

 would barely have enabled me to double my pace. Now 

 that I cannot walk more than three miles an hour for any 

 length of time, and yet can well ride at the rate of nine- 

 miles an hour on my tricycle without dilliculty, my pace i* 

 clearly trebled. 



From this I deduce the conclusion that the weaker a, 

 man is, the greater advantage he will gain by riding a 

 tricycle. 



After about nine months' experience on specially 

 light machines, with wheels not lai'ger than 40 in. in 

 diameter, geared up to from 48 to .^G in. for speed, and dowrt 

 to from li8 to 32 in. for power, I can honestly affirm thut 

 the tricycle lias trebled »ii/ power of locrmioliii')). 



Many persons have a])plied to me during the last three- 

 years to advise them resjjecting the adoption of a tricycle, 

 stating that they were weak men, and they feared tliey were 

 not Capable of the exertion of riding one. I have had the 

 pleasure of seeing or hearing from many <if these gentle- 

 men during the present year, and in no single instance 

 have I yet heard of one of thtni relinquishing tricycling on 

 the score of weakness-, while several have expressed their 

 great delight at finding they could ride so far and so 

 easily. 



As regards the power of locomotion when rncumberecl 

 by luggage or carrying of weights in any fcjrm, the 

 gain in using a tricycle is much greater. In Starley iSj 

 Sutton's " Coventry Chair" an untrained man acting as a 

 driver carried another man weighing twelve .stone, or one 

 hundredweight and a half, from Coventry to Biruiinghani 

 and back, a distance of thirty-five miles, at the rate of 

 eight miles an hour. What time would it take him to 

 transport such a weight to such a distance without the aid 

 of a tricycle ? 



And now that two-.speed gearings have done so much for 

 us, much requires more. 



