INTERFERENCE. 



INTERFERENCE. 



m 



By taking the first nine multiple! of any one of thwo logarithms, a 

 table of tfvrn place* might be formed, which should be correct in 

 errry figure. The following, for instance, is the table for 1 per cent, 

 per quarter, or 4 per cent per annum, payable quarterly : 



For instance, suppose it required to find out in how many years 

 money will increase tenfold at 4 per cent, payable quarterly : or to 

 solve the equation (I'Ol)'" = 10. 



Log. 10 = 1-0000000 



8642748 . . 200 



1357252 

 1296412 . . 30 



0060840 

 0048214 . . 



0017626 



r. The amount of 11. in 232 quarters, or 58 years, will lie a 

 little more than 101. 



We now describe the tables which follow : 



Table I. gives the present value of II. to be received at the end of 

 the several years marked. Thus, in the column of 4 per cent, oppo- 

 site to 15 years, we find -55526, which is the sum that will in fifteen 

 years, at 4 per cent, amount to II. The present value of 1001. simi- 

 larly circumstanced, is 55'526/. or 557. 10. 6}d. 



Table II. gives the present value of an annuity of II. Thus opposite 

 to 20 years in the column of 5 per cent, is 12-46221, meaning that II., 

 to be paid at the end of every year from this time for 20 years, is now 

 worth 12'46221/.,if money will make 5 per cent. 



Table III. shows the annuity which It. will buy for any number of 

 years. Thus in the column of 4 per cent., opposite to 7 years, we find 

 16661. If then loo/., now lent, were to be repaid by instalments in 

 seven years, the first instalment a year hence, so as to allow compound 

 interest at 4 per cent., then each instalment should be 16-661/. 



Table IV. gives the amount of II. improved at compound interest 

 during a number of years. Thus opposite to 1 1 years in the column 

 of 3 per cent, is found 1-38423, meaning that It in 11 years, at 3 per 

 cent, amounts to 1-38423, and 100/. to 138-423/. 



Table V. gives the amount of an annuity of I/., as it will be the 

 moment after the hist payment has been made , if the preceding pay- 

 ments have been allowed to accumulate. Thus in the column of 3J 

 per cent , under 27 years, we find 4375906, so that the proceeds of an 

 annuity of 10<V. for 27 years, allowed to accumulate at 3j per cent., 

 will at the last payment have realised 4375-906/. 



The following equations show easy means of verifying any one of 

 these tables by another. Let I, II, HI, iv. v, represent the results of 

 the five tables for some one number of years, and rate of in 

 Then 



ixrv = l i+rxn = l 



ii x in = 1 iv r x v = 1 



Inlerrri, as payable upon a debt not discharged on the day it 

 becomes due, is unknown to the Common Law, payment of such 

 interest being still rather the exception than the rule. Some debts it 

 is true carry interest by the custom of merchants or traders, being 

 those constituted by bills, and since the statute of Anne, by pro- 

 missory notes. But unless there is an express agreement to such effect 

 between the parties, debts do not carry interest at all. This uncom- 

 mercial rule of law led to the statute 3 & 4 Will. IV.,c. 42, which 

 enables a jury, if they think fit, upon all debts or sums certain, to 

 allow interest to the creditor, at a rate not exceeding the current rate 

 of interest, from the time when such debt* or sums were payable, if 

 payable by virtue of a written instrument at a certain time ; or if 

 payable otherwise, then from the time of a demand of payment in 

 writing, no as such demand give notice that interest will be claimed 

 from the date of such demand. This statute also empowers juries to 

 give damages, in the nature of interest, in respect of the detention or 

 appropriation of goods. By 1 & 2 Viet, c. 110, judgment-debts carry 

 interest at the rate of 4 per cent, per nnnnm from the time of entering 

 up the judgment. Legacies: are payable at the end of one year after a 

 tortator's death, and from the end <>f that year cany interest at the 

 rat* of 4 per cent, per annum ; unless the testator has made special 

 provisions in his will ait to tin- time of payment and the rate of interest. 

 See farther, ASM'ITY, BOTTOMHY, USURY. 



ISTKRKKHEN'CK is a term used to express the mutual influence of 

 two utreams of light, or series of pulsations of sound, or, generally, two 



series of vibrations of any kind. The term is most commonly em- 

 ployed with reference to light. 



We owe to Dr. Young the discovery of the grand principle of the 

 interference of light, and the explanation thereby, in the moat simple 

 and satisfactory manner, of various phenomena of which no rational 

 account had previously been given. 



The principle itself, when considered merely as embodying the 

 phenomena which belong to it, may be thus stated. When two streams 

 of light from the same source, after traversing paths very slightly 

 differing from each other in length, mix together, crossing at a small 

 angle, they partially or completely neutralise each other's effect, or else 

 strengthen each other, according to the difference of path. Wlu-n the 

 two interfering streams are of equal intensity the neutralisation is 

 complete, and we have realised the apparent paradox of two lights 

 producing darkness. The law which determines whether the illumina- 

 tion due to this joint action of the two streams is a maximum or 

 minimum is this : When the difference of the two paths (both being 

 supposed to be in air) is zero, or an even multiple of a certain funda- 

 mental constant, the illumination is a maximum, when an odd mul- 

 tiple it is a minimum. This fundamental constant depends only on the 

 refrangibility of the light, and decreases in magnitude from the red to 

 the violet end of the spectrum. \Vhen the incident light is white, the 

 light of each particular degree of refraugibility of which it is composed 

 presents the phenomena of interference independently of the light of 

 other refrangibiiities; and the precise circumstances of the interference 

 being determined by the value of the fundamental constant belonging 

 to the particular kind of light, a value which, as we have seen, changes 

 from one colour to another, a maximum of illumination as regards one 

 part (if the spectrum may coincide with a minimum of illumination as 

 regards another. Thus, alternations of colour are observed, and not 

 merely alternations of intensity, and by the time the difference of path 

 amounts to that belonging to the 7th or 8th maximum for mean rays, 

 the colours are so mixed, that the result is sensibly white light of 

 uniform intensity ; though, if the interfering light is subjected to 

 prismatic analysis, the interference may be traced up to a difference of 

 path amounting to many thousand tunes the value of the fundamental 

 constant. 



The idea we attach to the fundamental constant depends on the 

 notion we form of the nature of light. The theory of undul.it ions 

 alone affords a simple and clear explanation of the phenomena of 

 interference, and is competent to meet the demands of the science 

 of optics in its present state. According to this theory, the two 

 streams consist of two perfectly similar scries of undulations propagated 

 in the " ether," of which in this theory the existence must be assumed. 

 According to the general dynamical principle of the coexistence of 

 small motions, the disturbance which one series will produce in the 

 ether will be sensibly the same, whether that portion of ether be or be 

 not agitated by the other series. If the lengths of path be equal, the 

 front of the same wave belonging to each series will arrive at the same 

 moment at the same point of the ether, and the displacement of the 

 particle will be the sum of those due to the series taken separately. 

 The same will still be the case if one series be in advance of the other 

 by one, two, or any exact number of wave's lengths. If, however, one 

 series be in advance of the other by just half a wave's length, or any 

 odd multiple of half a wave's length, the displacements simultaneously 

 produced in the ether by the two series respectively will always be 

 in opposite directions, and the actual displacement will be only the 

 difference of the two displacements, or zero in case the two are equal, 

 that is, in case the two streams are of equal intensity. In this way 

 the phenomena of interference admit of the simplest explanation ; in 

 short, the fact of interference, as well as its laws, might have been 

 predicted from the fundamental principles of the muhilatory theory. 

 The fundamental constant above mentioned evidently represents half 

 the length of a wave of light. 



If a portion of the path of either stream lie in glass, or other refract- 

 ing medium, since according to the undulatory theory the velocity of 

 propagation is sinner in such a medium than in air, in the ratio of the 

 refractive index to unity, it follows that the interference must take 

 place as if the stream had described a longer path in air in the above 

 ratio. This agrees with observation. 



The laws of interference were applied by Dr. Young to the explana- 

 tion of the colours of thin plates, and to various phenomena of 

 diffraction [DIFFHACTION], and come into incessant use in the expla- 

 nation of the phenomena of light. It will be sufficient here to 

 mention a fundamental experiment of Fresnel's, which is easily 

 repeated. Its fundamental character depends upon the circumstance, 

 that in this cane the interfering streams neither graze the edge of 

 diffracting bodies, nor are reflected from thin plates, but simply from 

 two ordinary mirrors. 



Take two pieces of plate glass, 3 or 4 inches each way, having each a 

 clean edge (that is, pretty free from chipping), and varnish the backs 

 so as to stop the reflection from the second surface. On a block of 

 wood place balls of kneaded wax, and on the balls place the pieces of 

 glass, with their clean edges in contact, so that each piece rests on 

 three balls. By pressing on the balls adjust the mirrors so that their 

 planes make a blunt angle, pointing inwards, of say 1 794. Great care 

 must be taken that neither piece juts out above the other, as the 

 experiment will fail if the mathematical line of intersection of the 



