348 



♦ KNOWLEDGE ♦ 



Jn.NE 8, 1883. 



tion to Dulong and Pctlt'a law. Conscqiioiitly, may wo not infer 

 that thiTc is a temperature at which carbon i.s not an exception 'i 

 Hut, if onr equation bo universally applicable, M is a constant for 

 all substances and at all teniporatures ; so that when t° is also a 

 constant, hxl/X, i.e. Ii-clj vcjlunic x density. Honco, we may, jier- 

 liaps, conclude that the Bpecilic heal depends upon the mode of atomic 

 aggrcKatiou, a conclusion that is in uccordiinco with experiment ; 

 and, if so, wo have an easy mode of ascertaining the changes in this 

 mode, provided that we can fix the value of M approximately. 

 Water and iodine may bo nicutioned as simple instances ; in each 

 case, tho spocitic heat of the liquid is exactly twice that of the 

 vapoiu-. In the same way, too, we might explain tho divergence of 

 chlorine and bromine from tho law ; for there seems no reason why 

 they should bo treated in one way and carbon in another. 



To return to the formula with which wo started, hf = v. It may 

 be asked what are h and C respectively equivalent to in dynamics ? 

 It is difficult to answer tho question with any certainty ; but as v=- 

 space 



time ' "^""^ ^® temperature seems to correspond to space, we may 

 regard specific heat as inversely proportional to time ; a result that 

 accords with " Method by Cooling." It must not be forgotten that 

 I' has been taken to represent the velocity, not of progression, but 

 of vibration ; but, when care is taken not to confound the two, the 

 laws of dynamics appear to be ap])licab]e to problems connected 

 with either. For, from the motion of two balls impinging obliquely 

 on each other, we can deduce the laws of the refraction of heat and 

 light ; from the motion of a ball impinging obliquely upon a fixed, 

 smooth plane, we can deduce the laws of reflection, and so on. Of 

 course, in the case of a constant som-ce of heat, we have uniformly 

 accelerated motion to deal with, and different formula! must be 

 employed. By the aid of these it is not impossible that we shall be 

 able, theoretically, to estimate tho boiling points of different 

 liquids ; an hypothesis that I trust, before long, to be in a position 

 to verify. H^-on Colkman- Davidsox. 



HOW TO USE THE EYES. 



[843] — I have read the articles under this heading, by Mr. John 

 Browning, with special interest, and for personal reasons, similar 

 to your own, my eyes being extremely odd, instead of a pair. I 

 tliink that the experience of oculists will bear me out in the 

 assertion that perfect equality of focal length is not so 

 common, nor disparity so rare, as is generally supposed. 

 But although a trifling inequality of vision between the right 

 and left eyes is a very common defect, yet I believe that my 

 own case would be found to bo unsurpassed, if even equalled, in 

 the extreme disproportion that exists. At the present moment, the 

 focal length (for natural vision, without effort or straining) is 

 about 5 in. for my left eye, and 36 in. for my right" eye. 

 In my youth the focal length of my short-sighted eye 

 was about 3 in. The other eye always has been ex- 

 tremely long-sighted, and so remains. As an obvious conse- 

 quence, my vision is distinct but single. Dual vision, distinct 

 or indistinct, combined or double, is beyond my personal experience 

 or power of conception. In either case, of short or long sight, the 

 one image is enabled, by its own clearness and distinctness, en- 

 tirely to obliterate the other, which is dim and blurred; and, 

 although I can, by an effort, obtain double and indistinct vision of 

 an object at a distance of 10 or 12 inches, in practice I never do. 

 The stereoscope and binocular are of no use to me— have no raUon 

 d'etre in my eyes ; indeed, I dispute the truth of the scientific 

 explanation of the former ; inasmuch as, with either eye singly, I 

 can distinguish a plane from a convex or concave surface, or a solid. 

 Similarly, spectacles are, in my view, superfluous disfigurements. 

 No optician could make a pair to suit my vision, because the dimi- 

 nution for the one eye and the m»gnifying for the other would 

 present two well-defined images of immensely different dimensions, 

 which would not coincide and coalesce, whereby I should have dis- 

 tinct dual in lieu of as now Single Vision. 



[My own experience is closely akin to " Single Vision's "; but 

 the explanation of the stereoscope is right enough.— R. P.] 



WART CHARMING. 



[844]— ^ot to occupy your valuable space with unnecessary 

 prefatory matter on tho above subject, I would inerely wish to 

 mention, m corroboration of the cllicacy of the moans described in 

 your last in reference to tho removal of warts on tho hands that 

 one of my daughters was troubled for some years with these un- 

 sightly excrescences, until, happening to hear of a "charmer," in 

 tho person of a not very distant neighbour, she waived her in- 

 credulity for tho time and paid the operator a visit. The modus 

 operandi was precisely the same as that narrated by "Puzzled 



Sceptic," the warts were counted, and my daughter left. Before 

 tho end of a month every wart had disappeared. Very strange, 

 but very true I W. 



EASY MULTIPLIKG. 



[845] — I discovered tho rule for squaring numbers mentally some 

 years ago. It does not apply to particular cases only, but ia 

 general. The formula is as follows : — 



a-=(o + i)) (a— t) + fc= 

 To take the number given by yonr correspondent 

 35 = a 

 5 = b.-. 35'=(35-r5) (35-5) -i- 5- 

 35"= (40) (30) -(■25 

 35' = 1,200 + 25 

 1225 = 1225 

 Take 87. Here I will equal 3 — 



&7"=(87-t-3) (87-3) -H 3- 

 87-= (90) (81) + 9 = 7560 + 9 

 7509 = 7569 

 This rule I find extremely useful in practice. Most elaborately- 

 looking squares may be done mentally in a moment. It is also ol 

 great service in multiplying feet and inches of a square form. 

 Take the following — 7 ft. 6 in. by 7 ft. 6 in. — according to the 

 formula : — 



(7'6"y=j(7'6").6"jj(7'6")-0|.(0"/ 



The result when worked out being 56 ft. 3 in. Practically I add 

 and deduct 6" mentally, which gives 8 by 7 and add 3 inches, the 

 result as above of the square of 6 inches. 



Some curious mental juggling may be done in this way. Take, 

 for example, 75. This may be thrown into the form of 7'5, which 

 is 7 ft. 6, and this squared will give 56 ft. 3 in. The 3 in. is '25, 

 and substituting this for 3 in. will give a result 5625, omitting the 

 decimal point. Robebt Mooke. 



LETTERS RECEIVED AND SHORT ANSWERS. 



.i^ON. Vis inertias may be " a bodiless bogy," but it is quite im- 

 possible to accept conclusions based on the assumption that the 

 first law of motion is absurd, even though you have had the news 

 from one somewhat more fully acquainted with the laws and forces 

 of nature than tho great Newton himself. — W. B. Pray, believe 

 that no offence being meant, none is taken. L. M. H. P. Baery. 

 Regret that have at present no space conveniently available. — 

 C. E. Bell. No room for discussion of the gold question. Your 

 solution of chance problem not quite correct. — A. K. Hartixgton. 

 Thanks ; but no available time. — E. F. B. H. No space for descrip- 

 tion of the telescope you mention. — Amatevk. Consult text-bookon 

 microscope. — P. Chapman. No one who considers the mechanism 

 of the foot can doubt for a moment that the fashionable boots are 

 most injurious. — Student. The fears as to probable early exhaus- 

 tion of English coal rather exaggerated. — A Constant Subsceibee. 

 You seem to know all about the surface of tho sun. I congratulate 

 you. You are the only man living who does. How gratifying that 

 must be to you. — .^EoN (last letter). Newton conceived grarity as 

 acting by a series of impulses, but he did not imnjiiie that it so 

 acted. — E. Sellon would like some information about the natural 

 history of the parasite infesting the ivindpipes of chickens, and 

 producing the disease known as " gapes." 



®nv iWatftrmattfal Columiu 



GEOMETRICAL PROBLEMS. 



B\- Richard A. Proctor. 



Construction — (contin ued). 



SUPPOSE we had to solve such a problem as the following : — 

 From a given point mitside the acute angle conJained hv two 

 given .straight lines, to draw a straight line so that the part inter- 

 cepted between the two given straight lines may be eqiial to the part 

 between the given point and the nearest liyie. 



Here the natural process, in constructing the figure, would be to 

 draw the lines. AB and BC (Fig. 2), and taking P as the given 

 point, to draw 1' D E, so that P D and D E might be as nearly equal 

 as possible. The proper way, however, is to draw a straight 

 line, P E, bisect it in D, and through the points D E to draw tho 

 lines, A D E, C E B, meeting in B. 



