31)1 



♦ KNOWLEDGE ♦ 



[JoNE 29, 1883 



(fildcd youth at prcnont ndorn thomselves (aB " A Woman "seems to 

 dvocato " muffling," I should have thought they would have met 

 with hor approval). 



With re^;!ii'd to the convenience of trousers, did it never occur to 

 " A Woman " that there niiglit be some especial reasons for discard- 

 ing them when indulging in particular exercises ? Thus, in bi- 

 cycling, running, and football a man does not put on knickerbockers 

 because trousers impede the free use of his legs, but because, in 

 the first case, they show his socks when riding ; in the secorul, be- 

 cause the long spikes of his shoes are apt to catch in the bottoms ; 

 and, in the third case, because football is a dirty kind of game, and 

 stockings are more easily washed. 



The greater number of my rowing acquaintances go on the river 

 in cricketing trnusers, and I am not aware of any inconvenience 

 attending their use. If not impertinent, I should venture to suggest 

 that the gentleman who found it so "jolly to dance without 

 trousers " had attracted attention by the symmetry of his calves, 

 and regretted that ho would bo unable to do so on future occasions. 



Similar reasons may be found for our discarding braces in athletic 

 sports. As a rule, the '* silks " require no suspension, and a belt, 

 if used at all, is mostly for show. A pair of ordinary braces going 

 over the jersey would look slightly out of place, and T find some 

 difficulty in conceiving how they would be kept on without the use 

 of a waistcoat. Unlike *' A Woman," I am unable " to imagine 

 many inconveniences attending their use." I can safely say, as far 

 as I am concerned, that I have not experienced any. On the con- 

 trary, my experience tends in the opposite direction, and both for 

 comfort, and from a hygienic point of view, I prefer them to the 

 use of the belt. 



There are two sides to the artistic view of the question ; on one 

 is Nature, on the other Art. I need go no further than to 

 remind your readers that the human frame, if in its unsullied 

 grandeur, is, of all the Creator's works, the most artistic. Conse- 

 quently, I contend that the dress which best adapts itself to the 

 form and rcciuirenients of that frame has the best right to be con- 

 sidered artistic. The mind of man has discovered for himself a 

 dress which, I hold, fulfils both of these requisites. It remains 

 to be seen whether the mind of woman is equal to the task of 

 devising a similar one for herself. G. Clavering Mesnakd. 



A FEW OBSERVATIONS ON HEAT. 



[856] — First Laic. — Heat and mechanical energy are mutually 

 convertible. A unit of heat = quantity of heat required to raise 

 one pound of water 1^ Fah. in temperature = energy required to 

 raise 772 pounds 1 foot in height. This is expressed — 

 E = JQ 

 where E = amount of energy in foot-pounds, 

 Q = quantity of heat in thermal units, 

 J = 772 foot-pounds = Joule's equivalent. 

 Second Law. — The energy converted from one of these forms to 

 the other during a given change in any substance, is proportional 

 to the absolute temperature. 



\_Ahsolute Temperature is measured according to a scale in which 

 equal divisions correspond to equal quantities of energy.] 

 This law is expressed — 



T,-T., 

 E = JQ,-^- 



where Ti and To are the initial and final temperatures. 

 These two laws are the result of experiments. They are also the 

 result of any theory founded on the collisions of molecules of gases, 

 or on the centrifugal energy of molecular vortices in solid bodies. 

 The absolute zero so found isTo=— 4G0F. This zero also corre- 

 sponds to that at which gaseous elasticity disappears. Thus, it is 

 found that air expands 0'366 of its volume between 32° and 212°, 

 hence — 



180° 

 T„ = 32°-T577.= -4G0°. 



The quantity of heat in a body when no change of state is 

 involved is the product of the specific heat into the absolute 

 temperature, or 



Q = iT. 

 Sensible or thermometric heat = kinetic energy. Latent heat = 

 potential energy = heat which disappears in molecular changes 



T(V,— V) dP 

 = ■ — , where V and Vj are the volumes of unit of mass 



in the first and second states, and i — the variation of pressure jier 

 dT 



degree of temperature. This formula is arrived at as a result of 

 the two laws. It gives 96fi thermal units for the latent heat of 

 steam at 212°, and 144 thermal units fur the latent heat of ice. 



It predicted the fact that the freezing-point was lowered by 

 ])ressure, from V for ice being greater than V, for water. 



For perfect gases, i.e., those without viscosity 

 P V _ Pq V„ . 



T " 'i'l, 

 without communication of heat, P V'"' = const. T. J. Dewab. 



MUSICAL QUESTION. 

 [857]— The reply to "Musical Question" (808), by G. Wolff, is 

 very apt to mislead such persons as W. Jones, who are in want of a 

 true one to the question proposed. Mr. Jones finds the chord of 

 C preferable to that of C shaqi. It is very evident that he has a 

 keener musical ear than Mr. Wolff, if we are to consider the latter 

 as one of the audience'.who, he says, would be ignorant of the fact 

 that a nocturne of Chopin, written in D flat, had been played in D 

 natural. It also shows that the tuner had, to a certain extent, 

 tuned the chord of C with the natural number of degrees between 

 the notes, whilst in so doing he must have sacrificed the correctness, 

 amongst others, of the chord of C sharp. Mr. Chatterton has given 

 the reason very generally accepted as correct ; and if it is correct, 

 it is quite natural that those chords, the correctness of which had 

 been sacrified to others by the tuner, would sound harsh and 

 incorrect. 



Taking the chord of C. Now the number of degrees from 3rd to 

 5th (E to G), should be 125, and from 5th to 8th (G to C), 107. 

 Then take the chord of D. From 3rd to 5th should be 125, but if 

 the piano were tuned correctly in the key of C, the number would 

 be "„"-h72 = 112. Thus, to make the chord of D more correct, F 

 sharp should be made 125 — 112 = 13 degrees nearer F than is usual 

 on the piano which is tuned on the equal temperament. Taking 

 the supposition that there are two pianos tuned so that C natural on 

 the one should be C sharp on the other, then, if the tuner had tlirown 

 the greatest amount of error in those keys which are the least 

 used, the chord of the key of C would become the most perfect on 

 both pianos, and therefore, although G and C sharp on the two 

 pianos were exactly the same note, yet the chord on that piano on 

 which it is played as the chord of key of C, would be much more 

 satisfying to the ear than that on which it was played as the chord 

 of C sharp. Most of your readers have doubtless heard the 

 song, " Some day." It seems to me in order to hear the full 

 effect of the song, one requires it to he played on a piano that has 

 been tuned naturally in that very key in which it is written. On 

 most pianos (tuned to equal temperament), many of the notes in 

 the most touching parts of the song seem to have a degree of 

 sharpness about them which clash very perceptibly with the natural 

 notes produced by the voice, owing to the many accidental notes 

 which were introduced into the song. The error in one accidental 

 note would pass almost unnoticed ; but when many such accidentals 

 are introduced, the amount of incorrectness reaches such a height 

 as to call one's attention to it. E. A. Martin. 



A DISCOUNT DODGE— FIGURE CONJURING. 



[858] — " T. J. K.," in letter 829, page 314, says I fell into an 

 error in my communication 812, relative to an easy way of cal- 

 culating discounts. In reply, I beg to say I fell into no error 

 whatever. I merely professed to give a method used by a late 

 friend of mine, and I stated that method correctly. As to the 

 absolute mathematical correctness of that method I gave no 

 opinion, and, consequently, am not fairly chargeable with having 

 fallen into any error. Even now I prefer my friend's method to 

 that of "T. J. K.," inasmuch as it seems to me to be equally usefnl 

 for all practical purposes, and easier to be manipulated correctly. 

 Calculating the discount on a large invoice to the 59.200th part of 

 a penny is cutting the thing rather too finely. I hope the wealthy 

 Scotch publisher mentioned in page 313 of Knowledge will not 

 get to see this correspondence, or he will be offering Mr. Proctor 

 2 59-200d. per line for a review instead of 2id. 



I found the other day, in a French conjuring book, a plan by 

 means of which a person may discover a figure thought of by 

 another party, without seeing the said figure at all. The trick, 

 however, would, I think, present a more mysterious appearance if 

 worked on four figures instead of upon one. As the details of this 

 experiment may probably be both novel and interesting to many of 

 the arithmetical readers of Knowi.euge, I will state them in full. 



The performer gives his friend pencil and paper, and asks him to 

 write down, privately, any four figures he may choose ; he must 

 then multiply these fonr figures by 2, then add 4, then multiply the 



