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THE UNIVERSITY OF ILLINOIS LIBRARY THE DETERMINATION OF DIELECTRIC CONSTANTS BY A RESONANCE METHOD EARLE HORACE WARNER A. B. University of Denver, 1912 4 THESIS Submitted in Partial Fulfillment of the Requirements for the Degree of MASTER OF ARTS IN PHYSICS IN THE GRADUATE SCHOOL OF THE UNIVERSITY OF ILLINOIS Jh, 1914 Digitized by the Internet Archive in 2013 http://archive.org/details/determinationofdOOwarn UNIVERSITY OF ILLINOIS THE GRADUATE SCHOOL May 30 i9(j 4 1 HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY SUPERVISION BY SARLE HORACE WARNER ENTITLED THE DETERMINATION OF DIELECTRIC CONSTANTS BY A RESONANCE METHOD BE ACCEPTED AS FULFILLING THIS PART OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS In Charge of Major Work Head of Department Recommendation concurred in: Committee on Final Examination 284662 UKJC TABLE OF CONTENTS PART I HISTORICAL Page 1 Introduction L II Essentials of a Good Method S III J. J. Thomson's Method 5 IV C . B . Thwing's Method 5 V P. Drude's Second Method g VI E. S. Ferry's Method 9 VII C. Nevin's Method 12 VIII H. Rohmann's Method 14 PART II EXPERIMENTAL I General Description of the Method J 7 II Description of the Apparatus 1.9 III Calibration of the Condensers 22 IV Platinizing the Cone Condenser 24 V Determination of the Frequency 25 VI Discussion of the Method and the Accuracy 25 VII Statement of Results 23 VIII Summary 28 — — — — ™— — — — — — — PART I HISTORICAL I INTRODUCTION The subject of dielectric constants has been a live interesting topic ever since 1748 when Benjamin Franklin-* proved, by bis dissect- able L-eyden jar experiment, that the energy of a charged condenser resided in the medium between the conducting surfaces. The next ques- tion asked was, would the nature of the medium change the amount of the energy stored up? Faraday proved that it did. For a term, to show the quantitative measure of this dependence upon the medium, he used "the specific inductive capacity" and defined it as the ratio of the capacity of a condenser with the given substance as the dielectric to the capacity of the same condenser with air as the dielectric. This name has become antiquated and now the term "dielectric constant" is generally used in its place. Faraday^ explained the laws of electrostatics by assuming the existance of "lines of force" throughout the medium surrounding charged bodies. He considered these lines as starting from positive- ly charged bodies and ending on negatively charged bodies. He con- trasted them to elastic strings, for he thought of them as always tending to shorten and therefore tending to bring the opposite charges at their ends nearer together. They were different from elastic 3trings in that they repelled each other. To explain the presence of these lines he considered the dielectric as being composed of small conducting particles imbedded in the nonconducting medium. When a condenser was charged be pictured these conducting particles as all ieing turned in one direction, that is polarized (as in Swing's theo- ry of magnetism. ) Upon the discharge of the condenser the particles J Benjamin Franklin, Letters on Electricity. | ....icbael ^radav_ t _ V'x^erimBntal h e searches. ,ol. i f ,-'eo. 1 ■ . 2 would resume their original position. This theory was improved and strengthened by mathematical in- vestigation by Mosotti and the result is now known as the Clausius- Mosotti theory. 4 Faraday's theory was further improved by Maxwell and later by J. J. Thomson 5 . Supposing the "lines of force" had definite volume the name "tubes" was substituted for "lines". It was supposed that each tube started from a unit positive charge and ended on a unit negative charge. By mathematical deductions Maxwell derived a rela- tion between the dielectric constant, k, and the index of refraction, n, of a substance, namely k = n 2 (1) According to Maxwell's and Thomson's derivation (I) should hold for any frequency. k and n should however be measured for waves of the same frequency. Many dielectric constant values have been obtained with constant or slowly alternating electric forces. These values show wide discrepancies from this so-called Maxwell's Law. To best check this law dielectric constants should be measured with very short electric waves, that is, with very high frequency electro-motive forces . The theory which now receives the greatest approval is the electronic theory of H. A.. T .orentz. Dielectrics are characterized by the fact that the electrons, which accompany every molecule, are pre- vented from leaving the molecules by the forces which act upon them. 3 Glausius "Mech. W&rme theorie", Vol. 2, p. 94, (1 374). 4 J. C. Maxwell, Electricity and Magnetism, Vol. 2, p. J 75, etc 5 Sir J. J. Thomson, "Recent Researches in Electricity and Magnetism. " 3 When a piece of a nonconductor is acted upon by no external charges the electrons arrange themselves with respect to the molecules so that there will be no external ©lectro-static forces. When the nonconduct- or is brought between charged plates each electron will be displaced a small amount toward the positive plate, leaving the remaining por- tion of the molecule positively charged. Prom this theory it can be proven mathematically that k = n 2 only when k is determined with constant or slowly alternating electric forces and where n is the index of refraction for infinitely long waves . It is the purpose of this investigation to develop a method by which dielectric constants can be measured using high frequency alternations . II ESSENTIALS OF A GOOD METHOD A good method for determining dielectric constants will combine accuracy with ease and rapidity; it will not require large amounts of the material to be measured; it will not require that the dimensions of the material be known; the labour of computation must be a minimum; it must be possible to determine approximately the frequency of the alternations; and the arrangement should be such that it would be possible to study the dielectric under different conditions of temper- ature and pressure. Ill J.J. THOMSON'S METHOD 6 J. J. Thomson was one of the first to measure dielectric con- stants with rapidly alternating forces. His apparatus is shown dia- graamiatioally in Figure I. 6 J. J. Thomson, Proc, Roy . S0Cj) 48> p- S9g( ,, Jp , _ 4 b Pig. I AB and CD were the plates of a condenser, each "being 30 cm. in diame- ter. They were connected to an induction coil and also to the spark gap FH. L and M were small plates placed very close to the condenser plates. From these two plates long thin parallel wires LU and MT ex- tended for 20 meters. When the induction coil was started sparks oc- curred at FH and the system oscillated with its own frequency given by the formula T = 27TVLG O ) where L and C are the inductance and capacity of the oscillating sys- tem, and where the resistance is negligible. The impulses which were in the condenser sent electric waves down the two wires. These waves would be reflected and advancing waves would interfere causing points of maximum and minimum potential along the wire. The substance whose dielectric constant was to be measured (glass) was placed between the condenser plates and the induction coil started. The wave length of the oscillating system was determined as follows:- two equally long wires were connected to a spark micrometer P. The free ends were ther connected to T and U. The contact at U was moved out to some point a where the sparks in the micrometer were a minimum - showing that T and a were at the same potential. Then the contact at T was moved out to b where the sparking in the micrometer was again a minimum, 5 showing that a and b were at the same potential. Then b and T were at the same potential and since T is a point of maximum potential bT was a wave length. Knowing the wave length K. and substituting for T its value K, where v is the velocity of propagation of electromagnetic v 7/aves, into ('I) we have = k - T = — = 2ttvLC y (2) v X N ' From this equation , the capacity of the condenser with glass as the dielectric could be computed. Everything was then known except L, the was inductance of the circuit and this computed from a formula. C divid- ed by C , the capacity of the condenser with air as the dielectric, gives the dielectric constant k, i.e. k = !k (3) C a was computed from the formula where A is the area of one of the plates and d the distance between them. Allowance was made for the condenser having some of its capa- city due to other conductors in the field. Thomson computed his fre- quency to be about twenty-five million (25,000,000). It can be seen that the measured wave length was squared in order to solve (2) for C . Any per cent error in jywas therefore doubled in the result. To obtain bT, the wave length, two minimum sparking points in the spark micrometer were observed. Experience shows it to be very difficult to use a spark micrometer with accuracy. IV C. 3. SEWING'S METHOD 7 Thwing was the first to determine dielectric constants by a 7 Zeit. Phy. Chem. 14, p. 286, (1894) or Phys. Rev., 2, p. 35, (1394-95). resonance method. He states that the idea was suggested to him by Professor Hertz under whom he was working. The apparatus with which he worked is shown in Pig. 2. The circuit P, the primary, consisted simply in a rectangle of small wire, about 60 cm. square in which there was a spark gap anc -• •- F H + r"-i LftJ Pic;. II a variable air condenser C . The P induction coil I was connected to the primary as is shown. V/hen the coil was in operation sparks jumped across FH and the primary oscillated with a period deter- mined by the inductance, capacity and resistance of the circuit. In order that the secondary S, which was of the same dimensions as the primary and placed about 1.5 cm. distant, be in tune with the primary, the following equation must be true. T = 27TVLC, (5) where T is the period of both the primary and secondary, L and C a are the inductance and capacity of the secondary in Henries and Farads respectively. This assumes the resistance negligible. Evidently the maximum current will be produced in the secondary when it is in tune with the primary. In order that the two circuits be in tune the pri- mary capacity G p was varied until the current in the secondary was a maximum. This maximum current was determined by the dynamometer in- vented by Hertz. Its construction is shown in Fig. ^.TC The side ab was a thin German-silver wire divided in the middle and the two halves soldered to a small metal rod cd. cd was fastened 7 by thin steel wires, below to a stationary support e, and above to a torsion head T which was turned until the side ab was taunt and then it was set by the set screw S. When- ever a current was sent through ab it became heated and therefore expanded and the expansion turned cd around it vertical axis. A mirror was fastened rigidly to cd and the maximum current in the secondary was determined by observing a maximum deflection produced by means of a lamp and scale. Suppose the capacity in the secondary were C a , C a being the capacity of some condenser with air as the dielectric. When the coil was in operation the capacity in the primary was varied until a maximum de- flection was observed. Then the period in both primary and secondary would be T = 27rVLC a (6) Then this condenser was taken out of the secondary anri a variable parallel plate condenser was substituted and the distance between the plates -was changed until the deflection was again a maximum. Suppose this capacity were Cj . Its value in C.G.S. units was computed from irchhoff's formula, namely where R ia the radius of the plates and a the distance between them. Then T = SttVLCj (8) By comparing (6) and (S) it can be seen that In a similar way the capacity of the condenser with the unknown sub- stance as the dielectric was found to he some value, say Og. Then by definition of the dielectric constant, k would be C 2 k = t jo It is shown that when a spark jumps between two metal balls the resulting oscillatory current is by no means constant. Thwing says the alternate heating and cooling of the wire produces small oscil- lations in the mirror, which while blurring the image to such an ex- tent as to exclude the use of a reading telescope, are not sufficient to prevent accurate readings with a lamp and scale." If his dyna- mometer had been more sensitive this would not have been the case, so for refined measurements a modification is necessary. V PAUL DRUDE'S METHOD 8 P. Drude did an enormous amount of wcrk on dielectric constants and one of his many similar methods is a resonance method. This is bis so-called second method. Fig. Ill The high frequency current from a Tesla coil T, causes oscil- lations to be set up in the two semi-circular rods PP'. This induces an oscillation into the circuit aEb which was directly below PP 1 sepa rated from it by mica, both circuits being immersed in kerosene. The S Zeit. ^hys. Chem., 40, p. 635, (1902). 9 resonating circuit is acb and it is tuned with the primary by decreas- ing or increasing its inductance by pushing in or pulling cut the telescoping tubes. The point of resonance was determined by the maxi* mam glow of a G-iesler tube pieced between c and ab at a point of maxi- mum potential. The capacity to be studied was c. Tris method is similar to Thwing's with the exception +hat tun* ing is accomplished by varying the inductance instead of the capacity. In general the distance ac is not long and therefore the difficulty it of obtaining accurately brings a considerable per cent error into the result. Drude concluded that under the working conditions the error might be from 2 to ofo. VI E. S. "PERRY'S METHOD 9 In \Q97 E , S. Ferry devised a modification of Thwing's method, by which dielectric cons bants could be determined by a null method. His method consisted in getting two circuits of equal self inductance in resonance with a third oscillating circuit. The three circuits are shown in Figure 5. Fig. V 9 Phil. 7 ^a.g., 5:44, p. 104, (1.897). 10 The oscillating circuit was mh and the two resonating systems were pa'b and ga"d. When all three were in resonance the capacity C', Whid I was a variable parallel plate condenser, in ph must equal the capacity C" , which was the capacity under consideration with air as the dielec- tric, in gd because the period and inductance of the two circuits were the same. Thus C" could be determined by computing C. Then when the dielectric to be measured was in C w , changing its capacity to C^, and C' had been changed to C-[ in order that the three circuits be in resonance again, it could be said that C| (which was computed) was equal to C" . Then by definition K = 21 (13 ) C In theory this method seems simple for the working formula con- sists only in the ratio of two computed capacities but the method of tuning is not so simple. The principle of th9 bolometer was used to detect resonance. The application of this instrument can be shown in the following figure. The set u"o is the familiar k Wheatstone Bridge sot up. If r Q equals r. the galvanometer will shov; no deflection when the key k is close if rj equals r_. If rj and r^ are made of the same material, that is, have the same temperature resistance Doefficient and are of equal resistance at one temperature they will j be of equal resistance at all temperatures. Under these conditions If rj and are raised to any temperature the balance of the bridge j is not disturbed as long as the rest of the bridge is kept under the ; ] J conditions original. Ref erring again to Pig. 5, the side a*b of the secondary circuit pb was inserted as a part of the branch ab or p., (Fig. 6) and the side a w d of the other secondary circuit formed part of the branch ad or r„ (Fig. 6). r and t were exactly equal resistances, coils in this case, b'c and d'c. First it was necessary to tune individual- ly each of the secondary circuits with the primary. The condenser to be studied, with air as the dielectric, was placed in one of the sec- ondary circuits, say pb, and the condenser removed from the other sec- ondary. Then when the primary was set into oscillation the induced currents in pb heated ab, or part of r^, Fig. 6, and the Wheatstone Bridge balance was disturbed and the galvanometer caused to deflect, when the t'.vo circuits were in tune, and tuning was accomplished by changing the capacity in the primary, the maximum current oscillated through ab and this caused a maximum deflection of the galvanometer. Then this condenser was removed from the secondary pb and placed in the secondary gd. Since the two secondaries have the same inductance the deflection in this case would also be a maximum, but in the op- posite direction and perhaps not of the same magnitude., because the two secondaries were not equi-distant from the primary. If this was the case gd was moved until this second maxima was just equal to the first, Then the variable parallel plate condenser was placed in the other secondary circuit (ph) and adjusted until the galvanometer showed no deflection. When this point was reached the two condensers in the secondary circuits could be interchanged and the deflection remain zero. The capacity to be measured is now equal to the capacity of the parallel plate condenser which could be computed. The above operation were repeated with the dielectric to be measured in the condenser. jThis operation gave the final data needed to substitute In equation 11 , J.2 It can be seen that the manipulation in this method, is not so simple. Great care har also to be taken to protect the bolometer fron temperature changes. Quoting from Ferry "all parts of the bolometer must be carefully screened from heating effects. Air draughts and similar sudden changes can be guarded against by thick coverings of cotton wool." While this method is a null method the zero deflec- tion is produced by the effects of the two maxima counterbalancing each other, and each of the maxima had to be determined, in other wordji the errors in determining each remain in the result. Ferry computed the frequency of his oscillations to be about 33,000,000 per second. VII C. NIVEN*S METHOD 10 Niven determined dielectric constants by a resonance method us- ing a Fleming cymometer as an instrument to detect resonance. Thwing's arrangement was reversed and the capacity to be studied was put in the primary in series with inductance. The Fleming cymometer was the secondary. Instead of determining resonance by the maximum glow of a Neon tube the cymometer circuit contained a small coil, inside of whid vas a thernoelectric junction. The current from the junction caused a sensitive galvanometer to deflect. The set up is shown in Figure 7. C 1 i < 1 1 1 1 1 i 1 1 i i 1 1 1 u 1 1 1 1 1 1 1 1 i s WWWWWWWWWWWWWWWTH ^ Fig. 711 JOProc. Roy. Soc, 85, p. 1M, (!9I'J). I o Circuit I is the primary with the capacity C and the inductance of the rectangular wire. The spark gap is excited by an induction coil The secondary is the cynometer which consists of the wire C'XE in se- ries with a variable inductance LL' and the variable tubular condenser C'C". When the handle H is shifted both the inductance and the capa- city are changed. The oscillation in the cymometer heated the coil X and some of this heat was radiated to the thermo junction which was placed within X. For this experiment that particular scale was used which calibrated in terms of VOL. The condenser C was a spherical condenser of capacity, with air as the dielectric, of J7.8 c.g.s. units as computed by the formula C = t rr ' (12) r' - r with water in C the cymometer tuned, that is, the galvanometer deflec- tion was a maximum, when the scale reading was I4..R. k 17.8, where k is the dielectric constant of water, would be the capacity of C with the water in it and if T is the period T = 2ttVL k 17.8 = 2tt 14.5 (15) Then an air leydedfof computed capacity 11047 cm. was substituted for C and the cymometer tuned at 11.7. Then Tj a 2ttVL 1047 = 2tt 11.7 (14) Dividing (15) by (14) and squaring k J7.8 , J4.5 . g (15) J047 " K 11.7 ) jknd solving for k k = 90.36 (16) This particular case for water shows how dielectric constants can be ietermined by using a cymometer. Niven found that conducting liquids such as water, alcohol, etc. 14 would not permit a discharge to take place. To avoid this difficulty he put in series with C a condenser of large capacity. This forced the conducting capacity into oscillations while it did not change the resulting capacity of the primary. This can be seen to be true from the formula c = C ' C 2 (17) Ci + C 2 which gives the capacity of two condensers C, and Cg when connected in series. If Cn is very large compared to Cj equation (17) becomes, to a very close approximation C = Cj (18) However, because of the large condenser more energy was used and the condenser was heated to a considerable extent. A constant temperature was maintained by allowing the liquid under consideration to continu- ally flow through C, and also by immersing C in a large tank of water Which could be kept at the desired temperature. Fleming"^ has shown that in many cases the capacity measured in this way depended to a considerable extent upon the length of the <_ 12 spark gap m the primary. Anderson , working in this laboratory with a cymometer decided that 2. \<fo wrror in dielectric constant determin- ations was unavoidable by this method. VTTT HERMAN ROHMANN'S METHOD 13 Rohmann developed a very interesting resonance method for study- ing the variation of + he dielectric constant of gases with pressure. VI. J. A. Fleming, Principles of Electric Wave Telegraphy and Telephony, p. J 80. IS S. H. Anderson, Phys . Rev., 34, p. 34, (19 12). .13 Ann. dPhys., 4:34, p. 979, (J9J0-J1). 15 Circuit 1 is tne primary, and II the secondary. The oscillations in I are induced in it from the circuit III. It has been shown by Diekmann 14 that when the specially constructed dynamometer sfcows a zero Reflection °I L 1 = °8 L s ' (19) where and L represent the capacity and inductance of circuit I and C Q and L B are the total capacity and inductance of circuit II. F.ohmann was able to study the CQ ausius-Mosotti relation as applied to cases without directly determining dielectric constants. He claims to be able to measure capacity changes to an accuracy of I in 100,000. It is interesting to see if this accurate method can be extended to s+udy substances which have dielectric constants greater than those of ^ases. His accuracy comes from the fact that the inductance Lg is 3r.aH compared with Lg. Suppose the circuits were in tune when the capacities in II were C and C . Let C 2 be changed by an amount den fad let C^ represent the value of C 3 necessary for resonance. Tnen it can be shown, to a close approximation, that 14 ::. Diekmann, Ann. d Phys., 24, p. 77!, (1907). 16 s dC 2 L 3 (20) C 3 - L g Now if the inductances L 2 and L 3 were in such a ratio that the right hand member of (20) had a numerical value of .00! equation (20) would become = -.001 ^ J ' C 3 " G 3 Suppose the absolute value of - 65* ware 10 cm., then dC« = .0 1 cm. (22) Thus by this arrangement if C 3 could be changed by an amount of JO cm. and practically this could be done very easily, it would be possible to measure a change of capacity in Cg of .O'J cm. This example shows how the accuracy was obtained. To apply this method to determine dielectric constants one of two plans could be used. ] L and L_ must be known, as in the above example, and then the change of capacity, when the dielectric was added, could be com- puted and from this the dielectric constant determined. 2. Co could be changed by various known amounts and C 3 calibrate* ,o read these changes. Plan (1) does not seem feasible because of the difficulty of accurately determining small inductances. Any per cent error made in determining the small inductance L„ is doubled in the result because • is squared according to (20). Plan 2 is but slightly more favor- able. C, would have to be calibrated against condensers placed in C 2 whose capacity could be computed. A guard ring could not be used and that means that the computed values might be in error as high as if,* There is a further objection which applies to either plan. To measure a. dielectric constant even as low as 2 means that would have to be 17 changed an enormous amount in order to offset the doubling of Cg when the dielectric was placed between the plates. This is a cs.se where the method of obtaining accuracy leads one to a design of apparatus which is impossible to obtain practically. So while this method is a very accurate one to study gases, whose dielectric constants are low, it seems to be impractical for the study of substances which have higher dielectric constants. The spark gap in circuit III was such as to produce a quenched spark. This has the great advantage of giving a constant uniform os- cillation. It seems that this improvement could be applied with prof- it to any of the previously described methods. PART II EXPERIMENTAL I GENERAL DESCRIPTION OF THE METHOD It was decided to try to develop an accurate method by modifying Thwing's method and to use as a detector of resonance a Duddell theme galvanometer. Figure 9 shows the essential features of the final ar- rangement of the apparatus. Circuit I, the primary, contains a capacity Cp -• •- <5> ■c — ' ii 3T i 1 1 I — | L J and the inductance of a coil Lp. Cir- cuit II, the secondary, contains the inductance L and a variable Korda con- denser C. The thermo-galvanometer is shunted across the capacity as is shown The primary oscillates with a definite Fig, IX period determined by its capacity, in- ductance and resistance. By varying the Korda C to some value, say 0* the secondary will have the same period as the primary; that is, it will be in tune with it and then the maximum current irill oscillate in G. . IS the secondary, and the thermo-galvanome ter will give a maximum deflec- tion. Then T = 2TVLCf r (23) where T is the period of both the primary and secondary and L and 0* the inductance and capacity of the secondary. Then the condenser un- der consideration, a conical condenser with air as the dielectric, was placed in parallel with the Korda as is shown by the dotted lines. When placed in parallel its capacity is added to the Korda, therefore to produce resonance the Korda had to be reduced to some value, say 0" Then since the period is the same as before T = 27rvL(C n +C a ) (24) where G & is the capacity of the cone with air as the dielectric. Then the liquid to be studied was poured into th^ cone and the Korda tuned at, say C m . Then T = 27rVL(C" + C x ) (25) where C x is the capacity of the cone with the liquid being studied as the dielectric. By comparing (23) and (24) C" + C a = G ' (2C N Therefore a = C - C M (gy) 3y comparing (23) and (25) C"» + C x = C» Therefore C x = 0' - Then by definition of the dielectric constant k v = = C - g£ (30) C a C - C" A calibration curve was plotted for the variable Korda C which gave its capacity in cm. for any reading of the scale. So the C's in the right hand member of the equation were obtained very easily. It was (28) (29) J9 found to be more accurate to use instead of the denominator of (30) C-j , the capacity of the cone with air as the dielectric as determined by the electrometer*. Then the formula became o Nf (33) In determining the dielectric constants of solids a slab of the solid was obtained and placed between two pieces of tin foil. The tin foil was kept close to the slab by the pressure of sheets of lead. The capacity of such a condenser was determined by the above method. The capacity of the condenser with air as the dielectric was determine from the formula c = -A.. 47Td (32) where A is the area of one of the sheets of tin foil and d the thick- ness of the slab. Then by definition the ratio of these two capacities gives the dielectric constant. II DESCRIPTION OF THE APPARATUS The Spark Gap .- When the spark was a simple one as is shown Ik Figure 9, the induced oscillations in the secondary varied greatly. This was shown by the galvanometer readings jumping back and forth so that the maxima could not be determined at all. Many combinations of spark j v .aps were tried. The most successful arrangement is shown in Fig. JO. The induction coil was T7i connected to the zinc balls B and C. The spark between B and C oc- curred under kerosene. The ca- pacity and inductance of the pri- mary were connected as is shown. The oscillations of the primary F 20 took place from A to B to C. The energy in the primary was so small that the discharge was in the form of a very faint glow between A and B. With this arrangement the induced currents in the secondary were nearly constant and therefore the galvanometer deflections were nearly constant . The Galvanometer .- The galvanometer was a Duddell thermo- gal vanometer . In principle it is very similar to Professor C. V. Boys radio micrometer. A loop of one turn, C, suspended by a fine quartz fiber, P, hangs between the poles of a permanent magnet. The loop is closed at the bottom by a thermal junction of Antimony Sb and Bismuth Bi. Just below the thermal couple is a small wire re- sistance which serves as a heater. The heat radiated from the heater, produced by the current in it, causes the thermo- couple to send a current through the loop C, and then it tends to place its plane perpendicular to the line of force. Deflections were observed by means of a lamp and scale and the mirror m. This galvanometer seems to be one of the most sensitive instruments for detecting high frequency currents. For this experi- ment ore could not ask for a more sensitive detector. Condensers . - The primary was a variable Korda-*^ condenser. It consisted of two sets of semi-circular plates. The sixteen plates in the set S were connected together and held stationary, while the fif- teen plates in the set M were connected together and arranged so that Pig. XT <xte r. 15 Korda German latent, No. 7£447, Dec. J 3, IS93. 21 they could be moved about a central axis. By rotating the moveable set M the y,rea of the plates interlapping could be changed and thus ^ \ the capacity could be varied at will. The amount of the interlapping area could be read on a six inch circular scale, reading from 0° to 100°, placed on the box in which the plates were mounted. The secondary variable condenser was a simi- lar Korda with the exception that there were only eight fixed plates and seven r oveable ones. The Test Condenser .- The condenser in which the liquids were studied was a conical condenser similar to the one used by Fleming and Dewar'^. Figure 12 shows a cross section. GGIZD C fiK. XTT The distance between tne con- denser walls was about 2.5 mm. and the taper was very slight. The cone was centered and held rigid at the top by a three legged ebon- ite spider and at the bottom by a small ebonite pin. The spider was fastened to the outside casing by three small screws. With the spider off and the bottom of the casing removed by unscrewing, the apparatus could be cleaned very asily . >v**-$ v fi lrr***s ^LtU^ v>v*k jdL&L^t* < — * •£-«•> *** ^ajl^^jL cci^^vy^ The Inductances .- The primary inductance L p was a coil of six burns of rubber covered copper wire 0.9 mm. in diameter. The coil was 16 J. A. Fleming and Dewar, Proc. Roy. Soc, Vol. 61, p. 279,0897 r 22 wound on a wood disc 14.5 cm. in diameter. The secondary inductance L s was simply one turn of the same a ize wire wound on a similar disc. The Induction Coil .- The coil used was a Max Kchl 30 cm. induc- tion coil. Such a large coil was not needed however, for only a small amount of energy was consumed. The variable Korda condensers had such small capacities that they could not be calibrated by the ordinary method with a ballistic galvanometer, by comparing the quantity of electricity on them when raised to a s;iven voltage to the quantity on a standard condenser when raised to the same voltage. So an electrometer method was resorted to, The electrometer was set up in a lar,;e grounded iron box with a glass window. Within the iron casing it was protected from extraneous static effects. To be sure that the needle was placed symmetrical with respect to the quadrants it was adjusted so that when the needle was charged and the quadrants grounded the 3cale reading was Just tbe same as when the needle and the quadrants were both grounded. Since the capacity of the electrometer was comparable with the capacities to be calibrated its capacity had to be determined. This was done by a method of mixtures. The needle was charged to 50 volts, one pair of quadrants grounded and the other charged to a potential V (about 4 volts) causing a certain deflection, say d. Then the quantity of electricity Q, on the electrometer would be where C x is the capacity of the electrometer and k is the constant of proportionality between the potential and the deflection. Then this charge was allowed to mix with the inside of a cylindrical condenser III CALIBRATION OF THE CONDENSERS Q = C X V C x kd (33) 23 of capacity C, while the outside was grounded, causing the deflection to reduce to d'. Then q = (c v + C)V» = (C Y + C)kd' From (33) and (34) (C x + C)d' = G x d which solving for C x gives C x = C-AU- (35) x d-d r C, the capacity of the cylindrical condenser was computed from the formula c = rr: ^ (se) 2 log e jrr where r' is the inside radius of the outside cylinder and r is the outside radius of the inner cylinder. The variable Korda was calibrated by mixing the quantity on the electrometer and two cylindrical condensers in parallel with the Korda set at every J0° position between 0° and J80°. The formula can be de- duced in an exactly similar way to the one above. It is Pk = < 37 > where Cj is the combined capacity of the electrometer and the two cy- lindrical condensers, d the deflection when the electrometer and cylin ders are charged and d 1 the deflection when the Korda had been added in parallel. The capacity of the test condenser was also determined by this method. The charge on the electrometer was mixed with the cone and a cylindrical condenser connected in parallel. The formula in such an arrangement is (37) where Cj is the capacity of the electrometer, d the deflection when it alone is charged, and d f the deflection when 24 the two condensers were added. Then the determined capacity minus the capacity of the cylinder gives the capacity of the cone. All of the apparatus was placed in a grounded metal box to pro- tect it from outside static effects. The connections were made by raising or lowering contacts into mercury cups. These mercury keys were operated by long silk threads go the body never came near any of the apparatus. The calibration curve for one of the Korda's is shown in Fig. 13 IV PLATINIZING THE CONDENSER It was discovered that many liquids reacted chemically with the brass condenser and so it was decided to platinum plate the cone. The solution used was one prepared by Mr. Randolph of this laboratory. . . 17 Langbem gives the composition of the bath as : - Platinum chloride 0.245 oz. Sodium phosphate 4.94 oz. Ammonium phosphate 0.99 oz. Sodium chloride 0.245 oz. 3orax 0.087 oz. These were dissolved in six quarts of water and boiled for ten hours, the evaporating water being continually replaced. Before plating sach piece was polished and carefully cleaned by repeated washings in iilute hydrochloric acid, then water, then alcohol to remove all greas a,nd finally rinsed thoroughly in distilled water. The platinum had to be deposited hot, so the beaker containing the solution was surrounded Dy nearly boiling water. The object was connected to the kathode and ompletely immersed in the bath. The anode was a piece of platinum 17 G. Langbein "Electrodeposition of iietals," translated by W.I. 3rannt, 3rd. Edition, p. 320. foil placed symmetrically with respect to the piece to be plated. The current was obtained from a battery of storage cells consisting of two cells in series and two sets in parallel. This arrangement produced a copious evolution of gas at the anode. Each piece remained in the bath for about fifteen minutes. Then it was removed,- polished, cleaned and the process repeated. V DETERMINATION OF THE FREQUENCY The frequency n of the oscillations in the secondary was deter- mined by substituting in the formula T = — = 2ttVLC" (58) n when the secondary was in tune with the primary the variable Korda registered 969 cm. of capacity. L, the self inductance of the loop I 8 computed from Kirchhoff 's ' formula L = 4ira(log e - .1 .75) (39) was 473 cm. Then since (38) calls for inductance and capacity in Henries and Farads n = = . =7.03 • JO 7 27TV 969 * 475 • lo""^ \ 9 or the frequency is about seventy million. VI DISCUSSION OF THE METHOD AND THE ACCURACY The final error in any method depends upon the errors made in determining each term of the working formula. This formula was ' m C"' k = — cTj — (40) The accuracy in each term of the numerator depends upon the accuracy of tuning. For each trial the apparatus was tuned several times and the average capacity taken. The following figures show how the severa 1.8 See Bulletin U.S. Bureau of Standards, p. 55* (1908-09). 26 readings agreed. 169.5° 170.0° 171.0° Mean 170.4 170.0° Maximum possible error 0.9 17 1.0° 17 1.0° The sharpness of the maxima can he £"een from the curve on the follow- ing page. The denominator was determined from formula (37). Pour independent determinations of this capacity gave numbers which were proportional to 48.6 48.7 48.6 48.6 The error in data as accurate as the above leads, in the case of a di- electric constant of about 3, to a maximum possible error of approxi- mately 2.4$. Under* favorable conditions maximum data could be ob- tained which was a little more accurate than the sample given. It seems reasonable, in the case of low dielectric constants, to estimate the maximum possible error as about 2</c. The reading of C f seemed to change slightly from day ""O day, as if it depended to 3ome extent upon the batteries to which the induction coil was connected. If tbis coul be avoided, and it probably would be by using a quenched spark, C 1 could be determined a great many times and the mean taken as accurate. If this were done the maximum possible error would be about \fc. In these error estimations the calibration curve has been assumed correct The electrometer was working perfectly when the calibration data was taken. The curve being an average of many points is probably more accurate than any one of the individual points. Errors due to the liquid being conducting and thus decreasing the maxima were avoided by placing a very large capacity (! micro- farad) in series with the cone. This overcame conduction entirely and did not change the capacity of the cone, as has been shown by equation ( I" 7 ) . The maxima were kept large, never less than 50 cm., to insure their accurate determination. The intensity of the maxima could be regulated by advancing or withdrawing the secondary inductance from the primary coil. In general the coils were never closer than 5 cm. I The method is very sensitive to capacity changes. The near presence of the body would change the maximum points very noticeably. To avoid such errors all the apparatus except tha induction coil and galvanometer was placed in a grounded metal box. So protected the maxima were independent of outside influences. To measure substances of higher dielectric constant more capacity had to be put in the secondary and in order to tune with the primary the inductance of the primary had to be increased. It was found under these conditions that the maxima could not be determined as accurately as with the lower capacity. Thu3 this method fails to give accurate esults for substances which have high dielectric constants. The study of a sulphur slab brought out an interesting phenomena In attempting to tune, two distinct maxima were observed. The first was small but very noticeable and the second large. The curve on the next page represents the data taken upon this slab. Overtones in 3lectric resonance have been demonstrated. In this case the dielectric constant computed from the first weak maximum is the proper value for 3ulphur and the one computed from the large maximum is much too low. To justify taking the small maxima as the fundamental it must be as- sumed that the first harmonic is more intense than the fundamental. 28 Similar resonance phenomena are known in sound. Sulphur is the only substance which showed this double resonance. VII STATEMENT OF RESULTS Experiments have not been made with a great variety of substanc- es but enough liquids and solids have been studied to show that the method is accurate and convenient. It is a very sensitive method when the substance ^as a low dielectric constant. The following table shows the results that have been obtained. Substance Dielectric Constant Results By Other Observers Kerosene 2.0J 1.99 - 2. JO Turpentine 2.26 2.28 Cotton Seed Oil 2.97 3.00 Castor Oil 4.60 4.49 - 4.65 Alcohol 95^ 26.0 23.0 te 2C.3 Sulphur (II axis) 3.38 3.5-4.6 Paraffin . J .98 1.70 - 2.10 VIII SUMMARY The maximum possible error for substances of low dielectric con stant by this method is about 2%, but under favorable conditions the probable maximum possible error is about K?. High dielectric constants can not be accurately determined with the available capacities. The necessary measurements can be easily and quickly taken. Computation is a minimum, being simply a ratio. The method is one that can be easily applied to the study of the variation of dielectric constants with temperature and pressure. Only a small amount of the liquid to be studied is necessary - I 29 about 20 c.c. It seems that with a proper arrangement of capacities the method can be made sensitive for substances of higher dielectric constants. It is bopecl that the method can be extended and improved, making one applicable for accurate study of the variation- of capacity with fre- quency . In conclusion the author wishes to express his appreciation to Professor A. P. Carman for his valuable advice and many suggestions so freely offered throughout this investigation. Laboratory of Physics University of Illinois. May, 19 14 mBm.