316 



♦ KNOWLEDGE ♦ 



[May 25, 1883. 



it in this last manner defeats its principal objects, which are clean- 

 liness in walkinR and absence of drag and twisting round the 

 ankles. It sliould bo at least four inches longer than the light over- 

 skirt or drapery. I have worn it this way for the lost two years, 

 and it does not look remarkable in any way. 



A small sketch of three ligiires in the dress can bo obtained by 

 sending a stamped and directed envelope to the Secretary of the 

 K. D. S., asking for a circular of the Society's rules, Ac. Her 

 address is Miss K. JI. Carpenter, CO, Shaftesbury-road, Hammer- 

 smith, W. A Member of the K. D. S. 



[" A Lady " refrained from advising a change which seemed hope- 

 less to advocate, as nine ladies out of ten (herself included) would 

 bo unwilling to wear such a dress. But she states, from her own 

 experience, that wearing a dress such as she described secures all 

 the advantages of the divided skirt, and does not in any percep- 

 tible degree defeat its purpose. — K. P.] 



HEATING POWER OP STEAM. 

 [836] — Having met the paragraph at foot in " Lectures on Arts 

 connected with Organic Chemistry," by W. T. Brande (p. 213), at 

 the Royal Institution, 1S52 (Longmans), and being at a loss for 

 the reason of the apparent contradiction, I should be glad if yon 

 will kindly explain it. I may add that the statement occurs in the 

 lecture on Sugar Refining, in connection with remarks on working 

 the vacuum-pan ; but it is general in its application, and being 

 published by a man in Mr. Brande's position, evidently cannot 

 but be well considered. Bristol Boiler-Makeb. 



"In stating that high-pressure steam has not so great a heating- 

 power as steam under 10 lb. to the square inch, the remark must 

 be limited to the condition of heating a fluid by means of a steam- 

 warmed jacket or coil. If a fluid be heated by injecting steam 

 into and through it, then high-pressoi-e steam, weight for weight, 

 is the more powerful." 



LETTERS RECEIVED AND SHORT ANSWERS. 

 T. C. Really, does it matter how those particular names are 

 spelled. I thought all that nonsense had died out, except, of course, 

 among the majority, who ever have been, and ever "will be, behind 

 the age. — E. Hull names Medlicot and Blanford's " Manual of the 

 Geology of India" as a book giving valuable information about 

 Savalik Hills.- — A Spelling Refobmeu. Can scarcely give so much 

 space to the subject as your letter would require. It is a barren 

 subject, anyway ; for no good will ever come of showing how much 

 good ivould come from reform. — Phoncs. Same reason applies. — 

 H. W. B. B. We have wider ideas of the domain of science. In 

 what yon think remote from science may be discerned very 

 interesting evidence of the inherent savagery of man. — 

 Paepeop.\ri. Ah, well I we differ then. If you were as indifferent 

 to converting me as I am to converting you, you would hardly 

 have written your letter. What can it matter, anyway ? 

 — A. McD. Thanks for your genial letter. Such a letter is as 

 cheering as a glass of wine (pace Sir W. L. !) They are a " can- 

 tankerous lot," and the fable of the old man, his son, the ass, and 

 the other asses, doex often occur to me. — Thos. Littlf. Lectures 

 not published, possibly because not yet committed to paper. — E. C. 

 Webner. Mr. L.'s letter removes all doubt on that point ; he dis- 

 claims all knowledge about the matter. — Ignoramus. Hope soon 

 to make room for translation of original dream. — Magister. Glad 

 the "First Hook of Knowledge" pleased you as well as it did me. 

 Cannot, nnfortunately, speak of other books of the kind. — J. R. 

 (Edinburgh). The book is useful, though, as you say, cumbrous 

 and ill-written ; I do not think more was claimed for it in review 

 than it deserved. It is evidently the result of much hard work. 



(Bar iilatt)cmatiral Column. 



JROBLEM. — To (iiid a root otlier than unity of tlio equation 



(1) 



= 1. 



= 1 



.-. x'--l=(.r'^ + .r'^-t- ... +rr-i-l) (x-l)=0 

 Hence wo have by a due arrangement of terms 



l + x + ic>^ + x' + x'''+ . . . -h.i;"-ha:' = 



or l + x-^ — + x^ + l-+ . . . +!if + — ==0 



Let V = a; -r _ - -^ :c' +—+.,■' + — + .i" + _ 



(2) 



y + l--(I'-^.L-^a:S•^ -L- 



Hence, by multiplication [remembering that x'~ = Ij : — 



x* X- x^ X* x' 



1 . -. . 1 . -» . 1 . - . 1 . -. . 1 



1 



x' 



1 

 1 



+ _■4-x-^_= — 4 



-Hi'+r. + x* +- +x' +~ +3^ & . 



■i- X^ + - + X^ + - + X* + - + x' + ^ + x' + -+ i 



X* 0^ ac* x' r" 



4 -14 



Selecting the upper sign, we have 



1111 v'lT-l 



X + - + X-+ -,-^- X* + -i + x' + -^ = — :-, — 



X or X x^ 1 



,1 ,1 .1 ,1 -^/•ly-l 



And hence a;' + -i -H .t'' -)- — . -f- x' -1- "« -I- x' ■<- — 7 = 7, 



v/17-1 1 1 



Hence from (4) ;, — — : = x- -H -. -)- .t" -1- -j 



•v'17-f 1 



(3) 

 (•t) 

 (-) 



/ V"!' + J- \ 1 1 1 - 



\ I ) j/ X x' 



1 1 1,1 



+ -s-f-r" + -. + x^ + ri + ^ + Ti = - 1 



^/l7-l (^/l7-i)- le-Hjvn-iv 



10 



IG _ 



2(17- x/17) 



= = 4( v/l? - 1 ± ^"2 v/l7 - v/17 ) 



Selecting the upper sign, we have 



1 , 1 1/ _ _ , =.\ 



Letu = x'-h — + X* -^i- 

 x-i x^ 



Hence from (5) — ^ — u = x'^ + — -hx'-i-^ 



And bv multiplication as before we have 



(z4--.).= -i 



, ^/17 + l (v/17-Hl)- _ (v'17-i-l)--t-lG 

 " "^ 2 ""^ 16 ~ lt> 



2(17-hv/T7 ) 

 16 



•»=-(- v^l7 - 1 ± v'2 yi7 -^ v'i?) 

 Selecting the upper sign, we have 



»' + -7j + ■'' + — = j(- >/17 - 1 -H v/2 ■JY! + v''17) 



Let r = .i+l 



(C) 

 (7) 



(8) 

 (9) 



,by.(7) Q(v'17-l-l-v'i:v'l7-^/17)- rju 



=x- -h jL + x'-h 



=;(_,. 17- i+,/2v/ir;^>>-w 



