329 



TRANSLATION. 



TRANSPARENCY. 



330 



blow be struck, with the same force and direction, at the point c. 

 This point c will then describe a certain parabola c M H ; say that in 



three seconds it is at H. Next turn to the bar which moves on a 

 fixed pivot, and let/jr be its position in three seconds. Draw FO, a 

 position of the bar parallel to fg, H being its centre of gravity, and F o 

 will be the real position of the bar at the end of the given time, three 

 seconds ; and similarly for any other given time. 



Thus much of translation, mechanically considered : we now speak of 

 the wider use which the word has, or might have, in geometry ; at any 

 rate we have the thing to consider, and perhaps tramference might be 

 preferable to translation, as applied to the motion of a figure from one 

 part of space to another. The conception of the possibility of figures 

 differing only in position, and composed of perfectly equal and similar 

 ports of space, similarly bounded, is one which is demanded of the 

 beginner in geometry. Euclid requires this when he speaks of equal 

 figures ; and his test of equality, namely, the possibility of creating a 

 perfect coincidence, requires the notion of one figure being transferred 

 in any requisite manner, whether by what is called in mechanics trans- 

 lation, or by rotation, or both. It must be a sort of copy, or facsimile, 

 of one part of space which is thus moved into and made to occupy 

 another : for it is impossible to imagine ipace removed, or any part of 

 space made to change place. And this copy, or whatever it may be, 

 mut have rigidity, that it may not change form by the way : it must 

 be rigid in our thoughts, at least. We are thus required to imagine 

 space endowed with some of the essential qualities of matter, before 

 we can prove the fourth proposition of Euclid's first book : there must 

 be the consistence of matter without its impenetrability, but whether 

 it require force and time to change place, or not, is of no consequence. 

 Even a plane figure must be a sort of rigid consistence with two sides 

 to it, for it is necessary to imagine it turned round, so as to present a 

 different face to the spectator. In the fifth proposition of the first 

 book, the very first step is the application of the fourth proposition to 

 prove the equality of two triangles. Now the fourth proposition 

 requires one triangle to be placed upon the other, which cannot be 

 done in the figure of the fifth, unless one of the triangles be turned 

 round, so as to show the other front to the spectator. If Euclid meant, 

 by giving the triangle two handles, to make it easier to turn, he has 

 been unfortunate, for the proposition has acquired the name of the 

 OM'J bridge, probably as being that which stops a dull reader. The 

 following proof is as correct as that of Euclid, and it is not much 

 to ay that those who do not understand it will not understand the 

 one he gave. 



Let A B c be an isosceles triangle, having A B = A c. Let it be turned 

 round (for illustration, the dotted lines show the tracks of the three 

 points, and two intermediate positions are shown) into the position 

 D p. Then in the two triangles A B c, D E F, we have A B = D B, for D E 

 is AC( = AB by hypothesis) removed. Also AC = DF, for a similar 

 reason. And the angle B A c = the angle E D F, the second being only 

 the removal of the first. Hence we have AB = DE, AC=DF, and 

 /i B A c = XEDF, and now by the fourth proposition it follows that 

 /IABC = ^DEF. But ^DEF is only another position of /^ACB; 

 whence A B c = /_ A c B, which was to be shown. If preferred, the 

 triangle ABC might be turned round upon itself, and the reasoning 

 of the fourth proposition applied at once. 



It is not to be supposed that Euclid did not see the preceding : but 

 he in a writer who very rarely goes out of the most obvious path 



without some cogent reason connected with his system. The proof 

 given above would not serve to demonstrate the equality of the ex- 

 ternal angles without the previous introduction of the properties of 

 adjacent angles ; and it happens that the knowledge of the equality of 

 the external angles is immediately wanted. 



TRANSLATION. [VKRSION.] 



TRANSMUTATION OF METALS. [ALCHEMT ] 



TRANSOM. [MULLION.] 



TRANSPARENCY is that quality of certain substances or media 

 by which rays of light are allowed to pass freely through them. It is 

 doubtful whether any substance exists which is perfectly transparent ; 

 for even water and air stop more or less of the light passing through 

 them when the length of its path is very great. It is, however, exceed- 

 ingly difficult in such cases to say whether the observed stoppage be 

 due to the pure substance, or to foreign bodies present in proportions 

 otherwise perhaps inappreciable. On the other hand we have reason 

 to believe that all bodies possess the property of transparency in a 

 certain degree. Thus many metals have been obtained by mechanical 

 or chemical means in such a state of thinness as to transmit a certain 

 amount of light ; for example, gold, which in the state of gold-leaf 

 transmits a greenish light. 



There are two distinct obstacles to transparency, one a defect of 

 homogeneity, whereby a portion of the light in its onward progress is 

 continually reflected in another direction, at the surface of separation 

 of adjacent portions of the body having different refractive powers ; 

 the other the power which a very great number of substances possess 

 of absorbing light. [ABSORPTION OF LIGHT.] A good example of 

 the former is afforded by snow, which in sufficient thickness prevents 

 the transmission of light, but simply in consequence of its reflecting 

 the light backwards at the various surfaces of the icy crystals ; and 

 accordingly snow is brilliantly white by reflection, whereas the single 

 reflection from a sheet of water or ice is comparatively feeble. Other 

 examples are afforded by a mixture of water and oil, or water and 

 bisulphide of carbon, shaken up together ; or better still, an alcoholic 

 solution of bisulphide of carbon precipitated by the addition of water. 

 In these cases mixtures are obtained which, from the multiplied 

 reflections, have a milky appearance, and in sufficient thickness stop 

 transmitted light, though the mixed fluids (bisulphide of carbon and 

 watery alcohol in the last example) are separately transparent. The 

 transparency of white paper is greatly increased by oiling the paper, 

 the reason of which is that the quantity of light reflected at the com- 

 mon surface of the fibres and oil, which do not very greatly differ in 

 refractive power, is very much less than that reflected at the common 

 surface of the fibres and air. The mineral hydrophane derives its name 

 from becoming more transparent after being placed in water, which is 

 in consequence of its imbibing water in the pores with which it is 

 filled. 



Examples of the second obstacle to transparency are sufficiently 

 familiar, as may be gathered from the article on ABSORPTION. Thus 

 the common blue glass cuts off a large quantity of the light incident 

 upon it, and when in tolerable thickness may for most purposes be 

 regarded as opaque. Most commonly both obstacles to transparency 

 exist together, as in the case of wood, cork, brick, dyed cloths, &c. 



That homogeneity should be one requisite for transparency, follows 

 from the existence of reflection at the common surface of media of 

 unequal refractive power ; and therefore in considering the cause of 

 transparency it will be sufficient to confine our attention to homo- 

 geneous media. In such media transparency is to be contrasted with 

 the power of absorbing light ; the former in the absence of the latter. 

 The speculations at one time entertained respecting the cause of 

 absorption on the supposition that light consists in particles darted 

 forth by the luminous body can now only be matter of history ; we 

 shall confine ourselves to a consideration of the probable cause of 

 absorption, on the supposition that light consists in the tremors of an 

 elastic medium. 



In the case of gaseous media especially, the rate of absorption of 

 light passing through them changes, in many instances, in a very 

 remarkable manner with the refrangibility of the light. Hence the 

 spectrum of white light subjected to prismatic absorption on the part 

 of such media, presents fluctuations of intensity, simulating more or 

 less completely effects due to interference. Accordingly attempts have 

 been made to refer absorption to ordinary interference. But such 

 explanations labour under one fatal defect ; they suppose the annihila- 

 tion of vis rii-a. The effect of ordinary interference is not to 

 destroy light, but merely to alter the distribution of illumination. 

 Thus, when the light of a rather distant candle is reflected from a thin 

 plate of mica bent into a cylindrical form, and the linear image of the 

 flame is analysed by a prism, it is true that dark bands are seen which 

 remind one of the bands produced by the absorption of light by the 

 vapour of iodine, and were applied by the Baron von Wrede to the 

 explanation of the latter phenomenon, and of absorption in general. 

 (Poggendorff's 'Annalen,' vol. xxxiii. (1834), p. 853, aud Taylor's 

 ' Scientific Memoirs,' vol. i., p. 477.) But there is this difference 

 between the two cases, that in the experiment with mica, the light 

 which is defective in the reflected beam is found in excess in the 

 transmitted beam, which would yield a spectrum having bands com- 

 plementary to those of the former ; whereas in the case of absorption 

 the missing light actually disappears as inch. It is not however 



