CAUSTIC. 



i 4U8TIC. 



referral to convexity, and the elevmtion to concavity, by the same lort 

 of language as would be used if the flrat of each couple were the rent 

 fauta of die second. Thi* U a language of convenience, but i* apt to 

 be misinterpreted. 



Question* aa to whether hypothetical caiuee are true or not, do not 

 now occupy tha attention of philoiophen to the extent which was 

 formerly the caae. When the motion* observed to exist in any system 

 are sufficiently known, the pressure* or other admissible species of 

 action which would be sufficient to produce these motions are at once 

 substituted as hypothetical causes. Thus, though the connexion 

 between magnetism and electricity renders it on object of curiosity to 

 trace them to some common hypothesis, few, we imagine, would 

 attempt to find the ratue of magnetism in the sense of the rmt raiua. 

 It is otherwise when an hypothetical cause is found not to be sufficient 

 to produce all observed effects. For example, the undalatory theory 

 of light has prevailed over the rmun'uH theory, not because we have 

 less reason to suppose that light U an emanation of particles from the 

 sun and stars than existed a hundred years ago ; but because it is 

 found that many lately discovered facts are not such as would be true 

 if light were an emanation, but arc such as would be true if it con- 

 sisted in undulations excited in an elastic medium. And though 

 this cannot but favour the supposition tliat the undulations are the 

 rera cauta, yet that remains only a probability ; the certainty is that 

 the phenomena of reflexion, polarisation, Ac., AS hitherto observed, are 

 all such as would necessarily follow, if the theory of undulations were 

 true. 



It must appear at first that this application of the word cause 

 makes the ultimate end of natural philosophy much lees imposing, if 

 not less important, than the more common idea ; which consists in 

 supposing that the reasons (rarer caustr) of phenomena are discovered. 

 But whether this be so or not, it is the only rational and demonstrable 

 method of using the word. And it must be observed that all similar 

 phenomena are thus, as it were, bound up together, and made to 

 belong to one system. If then we refuse to say, with many popular 

 works on physics, that "Newton was the first who found out why 

 water runs down-hill," we conceive that we are not altogether without 

 a substitute when we say, that Newton was the first who connected 

 the motion of water down-hill with all the motions in the solar system 

 in such a manner that any new information as to any one of them can 

 be extended to all. 



But the great use of hypothetical causes lies in this, that they tell 

 us, a* long as they hut, what to look for. The cause being assumed, 

 the application of mathematics points out the time or circumstances 

 under which to look for new phenomena, or to look at old ones in a 

 new light. Thus several phenomena with regard to light, which 

 might have remained long unobserved, have been predicted by com- 

 putation from the undulatory theory, and subsequently verified. And 

 in the planetary system, several motions too small to be easily 

 detected, except by a person who previously knows in what manner 

 and at what time to watch for them, have been added by theory a!n< 

 to the list, and verified by observation ; and it is by such means that 

 Neptune and some of the asteroids have lately been discovered. 



The language of causation is sometimes misapplied in thix way; 

 the proof that a thing u, is called the reason why it is. Thus we 

 remember seeing in the notes to Simaon's edition of Euclid an aaser- 

 hat geometry gives the reason ichy two sides of a triangle are 

 greater than the third, whereas we never could detect anything more 

 than the proof that they are so. Another misuse of the word has 

 been pointed out by Dr. Reid. " In natural philosophy," he says, 

 " when an event is produced according to a known law of nature, the 

 law of nature is called the cautc of that event. But a law of nature 

 U not the efficient cause of any event ; it U only the rule according 

 to which the efficient cause acts." Hence, it is not right to say that 

 the cawe of the acceleration of force in gravitation is that Indies move 

 towards each other with a velocity which varies inversely as the square 

 of the distance. 



CAUSTIC. A term used in Pharmacy, chiefly to denote nitrate of 

 silver (lunar cauttic) and hydrate of potash. In chemistry it is applied 

 as a prefix to the name* of the alkalies and alkaline earths : thus we have 

 caustic potash, soda, or ammonia, and caustic baryta, strontia, lime or 

 magimri* ; by which U understood, in the case of the alkalies, their 

 compounds with water, and in the case of the alkaline earths, either 

 the pure instances themselves, or their compounds with water. 



CAUSTIC (iii Optics). When a number of rays proceeding from a 

 point are reflected or refracted at or through any number of media, 

 they will not, in moat canon, be all thrown to the same point again, but 

 will be dispersed in such a manner a* to touch some curve or surface 

 depending for it* form and position upon the position of the lumi- 

 nous point, and the form and position of the reflecting or refracting 

 surface. This curve is called the eatulie of the surface. We will 

 give a case of the most simple kind. A reflecting curve A B c of a 

 semicircular form receive* rays coming from a point on B o produced i 

 but at no great a distance, that they may b considered as parallels. | 

 The rmy. I, II, HI, Ac., strike the semicircle at (1), (2), (8), Ac., and 

 are then reflected in the direction* (1)1, (2)2. (3)3, Ac. The curve 

 A M c, having a cusp at M, Is constructed in *uch a manner that any I 

 ray whatsoever moving parallel to z B, shall, after reflection at the j 

 circle, touch or graze this curve, which is therefore called the cautlic 



by rtftctim from parallel rayt of the semicircle A M c. And the space 

 A M z will not be illuminated by any of the rrfartrtl rays coming from 



any point on A B, but only by those which come from a part of B c, 

 which, after touching c M, their branch of the caustic, proceed and cut 

 through A M. The consequence is, that the space A u c B will be much 

 more highly illuminated than the exterior space ; an effect which may 

 be rendered visible by placing a ring, with a bright interior surface, or 

 a piece of steel spring highly polished, upon a table, in the sun-light. 

 It will then become evident, by a part of the table within the ring, of 



the form A u c B, becoming brighter than the rest, that the greater 

 portion of the reflected light strikes the table within such a curve. 

 Caustic curves are often well shown at the bottom of cylindrical vessels 

 of china or earthenware, when favourably situated with respect to the 

 sun or the light of a candle. In such cases the depth of the vessels 

 causes the rays to fall too obliquely on their cylindrical surfaces, but 

 by inserting a circular piece of- card or white, paper about an inch 

 beneath their upper edge, or by filling them to that height with milk, 

 the caustic curves can be finely exhibited. Caustics by refraction can 

 be produced by exposing a glass globe full of water, such as the belly 

 of a round decanter, to the rays of the sun, or the light of a candle. 

 and receiving the refracted lighten a sheet of paper held nearly parallel 

 to the axis of the sphere, or in such a way that ite plane may pass 

 nearly through the luminous body. Under such circumstances th.-re 

 will be seen on the paper a luminous figure bounded by two bright 

 caustics forming a sharp cusp or angle at the focus of refracted rays. 

 These curves are evidently produced by the intersection of the rays, 

 which being incident on the sphere at different distances from the axis, 

 are refracted to foci at different points of the axis, and thus crowi one 

 another. 



The point which it is of most importance to notice in relation to 

 caustics is the following : It is usual to suppose, for the sake of <n 

 venience, that all reflected or refracted rays converge to a )>>int. 

 This is practically true ; or rather we may say that such a number of 

 rays are collected by mirrors and lenses so near to a point, that the 

 effect of a complete convergence is produced. If we look at the 

 diagram, we see that all the rays which enter between I and III are 

 far from being nearly reflected to a point, but are scattered along 

 the caustic from 1 to 8. But an equal number of rayx entering 

 between V and VI is collected between 6 and 6 on the caustic, very 

 near to M. The consequence is, a sufficient convergence of rays near M 

 to give a bright image of the luminous point whence the rays came, 

 in the formation of which it in evident that only the parts of the 

 mirror near B will be efficient. No curve except a parabola would, in 

 the circumstance* of the diagram, make every ray converge accurately 

 to one point. 



A complete theory of caustics would include that of telescopes and 

 microscope* of every kind ; but would be of no practical ue, except so 

 far as relates to the cuips and the part of the curve near them. These 

 curve* were first considered by Tchirnhausen, who gave them their 

 name, and afterwards by John Bernoulli. They are much treated of in 

 t|j<- ]'(' r l"nnlili works on optics, in a geometrical manner. The 

 algebraical question, in iU most general form, ha* been investigated by 



