ELECTRIC IGNITION FOR AUTOMOBILE ENGINES 
 
 BY 
 
 YOSO NAITO 
 
 Sendai Kogakushi, Tohoku Imperial University, 1913 
 
 THESIS 
 
 Submitted in Partial Fulfillment of the Requirements for the 
 
 Degree of 
 
 MASTER OF SCIENCE 
 IN ELECTRICAL ENGINEERING 
 
 IN 
 
 THE GRADUATE SCHOOL 
 OF THE 
 
 UNIVERSITY OF ILLINOIS 
 
 1921 
 
IP, 
 
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 UNIVERSITY OF ILLINOIS 
 
 THE GRADUATE SCHOOL 
 
 J une _2_, 1921- 
 
 I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY 
 
 SUPERVISION BY 
 
 ENTITLED , ELEC TRIC IGNT^^IQII FOR AUTO MOBILE iiJJGIHES 
 
 BE ACCEPTED AS FULFILLING THIS PART OF THE REQUIREMENTS FOR 
 THE DEGREE OF MSTSR OF SCIENCE IH LLEGTH I^^AL EIIG IIIEERIIJG 
 
 Recommendation concurred in* * 
 
 Committee 
 
 on 
 
 Final Examination* 
 
 *Required for doctor’s degree but not for master’s 
 
i r I » i 
 
 
 .'-Aitil 
 
 Digitized by the Internet Archive 
 in 2015 
 
 https://archive.org/details/electricignitionOOnait 
 
1 
 
 Contents 
 
 Part I Ignition Circuit 
 
 I Introduction 2 
 
 II Fundamental Principles of Ignition 
 
 Systems 3 
 
 III Phenomena of Closing the Interrupter 5 
 
 IV P’nenomena of Opening the Interrupter '6 
 
 V Internipter Spark 27 
 
 VI Opening the Interrupter Tnen the 
 Secondary Current is Apprecia,ble ,*,.32 
 
 Part II Keat Energy of Various Ignition 
 
 Systems . . . . , .36 
 
 Appendex 
 
 .47 
 

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2 
 
 ELECTRIC IGNITION FOR AUTOMOBILE ENGINES 
 
 Part I Ignition Circuit 
 I Introduction 
 
 Automobile engineering has made great progress during 
 the past few years. The new devices of yesterday to-day 
 are commonplace. 
 
 As for spark ignition, there still exists much dis- 
 cussion about the relative merits of the battery and magneto 
 systems. 
 
 The phenomenon of the electric spark was considered 
 by Faraday many years ago. But a perfect analysis of spark 
 has not yet been given. 
 
 The object of this thesis is to study the electrical 
 phenomena' of the primary and the secondary circuit of ig- 
 nition apparatus. at the instant of sparking. 
 
 For mathematical analysis the battery ignition is 
 taken, but we may apply the same theory for magneto Ignition 
 by slight modific8.tions . 
 
 The latter part of this thesis deals with the heat 
 quantity in a single spark of the various ignition systems. 
 

 
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3 
 
 II Fundamental Principles of Ignition 
 
 Systems 
 
 In developing the theory, the schematic coil shown 
 in Fig. 1 will be considered. 
 
 Af 
 
 Pig. 1 
 
 E Primary terminal voltage 
 
 i, i^ Primary and secondary currents 
 
 Primary and secondary Inductances 
 r r^ Primary and secondary resistances 
 
 C, Primary and secondary capacities 
 
 in Interrupter 
 
 S.G-. Spark Gap M Mutual inducta,nce 
 
 The fundamental equations of the circuit shown above 
 
 are; 
 
 For the primary circuit, 
 
 
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 4 ^ 
 
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 For the secondary circuit. 
 
 
 
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 where 
 
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 The differential equations for the primary and the 
 secondary currents respectively are reduced from equations 
 ( 1 ) and ( 2 j , 
 
 The complete Integrations of these fourth order dif- 
 ferential equations can be accomplished, but is of minor 
 interest . 
 
 To avoid the complication, we shall study the phenomena 
 for definite positions of the interrupter and consider the 
 primary and the secondary resistance, inductance, and cap- 
 3-city constant in most cases. 
 
 (See Appendex I) 
 
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5 
 
 III Phenomena of closing the interrupter 
 
 To speak rigorously, a secondary charging current 
 exists in the secondary circuit in this case, but we shall 
 neglect this current. 
 
 No voltage is impressed on the primary condenser, be- 
 cause the interrupter is closed. So ^ 
 
 / 
 
 are both zero. 
 
 The equation ( 1 ) page3 becomes 
 
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 which is known as the Helmholz formula. 
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6 
 
 The instantanious primary voltage 
 
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 Jz. 
 
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 The following numerical constants are given for the 
 Connecticut Igniter Model- 1 6 : 
 
 L, 
 
 .01 1 
 
 henry 
 
 
 
 
 1 . 1 
 
 ohms r^ 
 
 10,000 
 
 ohms 
 
 c, 
 
 .25 
 
 micro “farad 
 
 smaller 
 
 than • 000 1 
 

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7 
 
 The relation between time and the primary current 
 
 culculated by 
 
 equation( 6 ) is shown 
 
 in 
 
 the following tabl' 
 
 Table 1 
 
 Growth of 
 
 the primary 
 
 current 
 
 
 
 I 
 
 5.2 
 
 amperes 
 
 
 
 r, 
 
 1.1 
 
 ohms 
 
 
 
 L/ 
 
 .011 
 
 henry 
 
 
 So, 
 
 E = I r 
 
 = 5.725 
 
 volts 
 
 
 
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 = / 
 
 
 
 
 
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 log 
 
 e = log 2.72 
 
 = .434 
 
 
 
 
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 JL 
 
 
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 sec. 
 
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 ampere 
 
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 0 
 
 1 
 
 
 0 
 
 0 
 
 4 
 
 .002 
 
 .2 
 
 .834 
 
 
 .166 
 
 .87 
 
 .004 
 
 .4 
 
 .664 
 
 
 .336 
 
 1 .75 
 
 .006 
 
 .6 
 
 .542 
 
 
 .458 
 
 2.38 
 
 .008 
 
 .8 
 
 .441 
 
 
 .559 
 
 2.91 
 
 .01 
 
 1 
 
 .368 
 
 
 .632 
 
 3.29 
 
 .012 
 
 1 .2 
 
 .293 
 
 
 .707 
 
 3.66 
 
 .014 
 
 1 .4 
 
 .238 
 
 
 .762 
 
 3.96 
 
 .016 
 
 1 .6 
 
 . 195 
 
 
 .805 
 
 4 . 19 
 
 .018 
 
 1.8 
 
 . 158 
 
 
 .842 
 
 4.38 
 
 .02 
 
 2 
 
 .129 
 
 
 .371 
 
 4.53 
 
 .022 
 
 2.2 
 
 . 105 
 
 
 .895 
 
 4.66 
 
 .024 
 
 2.4 
 
 .086 
 
 
 .814 
 
 ^.75 
 
 .03 
 
 3 
 
 .045 
 
 
 .955 
 
 4.96 
 
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 3.5 
 
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 .972 
 
 5.05 
 
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 4 
 
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 5.11 
 
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 4.5 
 
 0 
 
 
 1 
 
 5.2 
 
8 
 
 The curve corresponclin^s to Table 1 Is shown in Fig. 6, 
 page 15 . Its oscillogram which is taken by author is 
 seen below. 
 
 Fig. 3 
 
 If we enlarge this oscillogram and plot a curve as in 
 Fig.6,rpage l3, there is seen a certain difference from 
 Curve A. Probably this difference depends upon the fa.ct that 
 magnet! za.t ion curve of iron is not a. strs-ight liner and con- 
 cons equently the prima,ry inductance is not constant. 
 
 T7e will now consider the case when the primary induc-r- 
 tance is not consta,nt. 
 
 Tne values of the follov/ing'table are taken from the 
 oscillogram. 
 
 Table 2 
 
 X 
 
 0 
 
 sec . 
 
 . C 
 
 .0025 
 
 i, 
 
 amxDsre 
 
 C 
 
 .005 
 
 1 .39 
 2.6 
 

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 4.96 
 
 .02 
 
 5.04 
 
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 5.07 
 
 Closing the Interrupter in the Case 
 of Variable Inductance i 
 
 In the former discussion , we assumed that the induct- 
 ance L, in constant, while it is variable with any circuit 
 which contains cin iron core. The variation of inductance 
 depends upon the magnitude of the air gap and the qualify 
 of the iron. 
 
 An example of the saturation curve of an entirely 
 -losed ferro-magnetic circuit is shown in Fig. (4). 
 
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 Fig. 4 
 

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10 
 
 If the magnetic circuit consists partly of air and 
 partly of iron, the saturation curve i:- modified by the 
 Influence of air gap. 
 
 TJhen the air gap is \ ery small, the corresponding 
 curves, are a c.nd b. Fig, 5* If the gap becomes largt.-r, 
 the saturation curve a-pproaches the dotted line, and the 
 hysteresis loop vanishes. 
 
 Fig, 5 
 
 Frolich’s equation for such a saturation curve, which 
 is modified by Kennelly, is shown below. 
 
 
 A ‘ 
 
 "Ihlle 
 
 I = 
 
 / -h k c 
 
 A/ ^ 
 
 c /c? 
 
 where ^ = flux (7) 
 
 v/here N* J number of turns 
 
 -<s 
 
 ' ^ / V- 
 
 A/ A 
 
 If v/e substitute — fo^ ^ > 
 
 /o 
 
 Z = 
 
 / 
 
 ko 
 
 The equation t'.l)’, page 3 becomes 
 

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n 
 
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 ^ 
 
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 -u.i) 
 
 ( 8 ) 
 
 ' , / <=^t ' Jl 
 
 d cj<' _ 
 
 i Ak d{ 
 
 ~ ^ ^ / -t- k< cdt (/-hHi)^ <^t 
 
 The variables are separable in the above equation. 
 
 So, 
 
 ^ ^ 
 
 (€-l tj)(/i-k l)" 
 
 c/ 1 
 
 A 
 
 -t C 
 
 <d L -f- 
 ck-L 
 
 Lc. — dc 
 
 (/+kc)<^^ 
 
 (see Appendex 2) 
 
 
 j_ 
 
 a. 
 
 Log(E-cr) ^ X 
 
 £ ■ VTTtJ 
 
 -t 
 
 When 
 
 (f 
 
 where a r -t Ek, 
 
 = 0 .& i = 0 , 
 
 a 
 
 t 
 
 
 ki 
 
 E -cr 
 
 / -t ki 
 
 -) 
 
 (9) 
 
 ( Eerg s Advanced Course of Electrical 
 
 Engineering) 
 
 The variable Inductance for the corresponding values of ex- 
 citing current i is measured for a certain coil which has 
 an open iron core. Then, we may find the constants k and 
 A. Using these constants, we will study how the current 
 builds up in the coll considered in the previous article. 
 
I> 
 
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By the equation (9), 
 
 12 
 
 Fig. 
 
 i = sr 
 
 Aj— l 
 -J 
 
 £ — cr / ^ A: 
 
 If k .1128 E 5.725 
 
 /\ .01018 V , 1.1 
 
 a =:r -f-Ek = 1.1 + 5-725 x .1128 
 
 = 1 .745 
 
 So, the above equation becomes 
 
 t = 
 
 » a /Q/s> 
 /. 7^S 
 
 {- 
 
 74-S- 
 
 AJ— V — lo'^J-.'/ZSX 
 
 '-} 
 
 /-h 
 
 .*, t - . 00 
 
 Table 3 is calculated by the equation (10). 
 
 
 Table 
 
 3 
 
 
 
 i 
 
 ampere 
 
 
 P — Ac < , 
 
 A+ B 
 
 t 
 
 
 
 L 
 
 sec . 
 
 0 
 
 0 
 
 0 
 
 0 
 
 C 
 
 1 
 
 .202 
 
 .1915 
 
 .302 
 
 .00176 
 
 2 
 
 .433 
 
 . 1815 
 
 .614 
 
 .00358 
 
 3 
 
 .725 
 
 .253 
 
 .977 
 
 .0057 
 
 4 
 
 1.15 
 
 .309 
 
 1 .46 
 
 .00853 
 
 4.5 
 
 1 .52 
 
 .337 
 
 1 .86 
 
 .01087 
 
 5 
 
 2.32 
 
 .36 
 
 2 . 63 
 
 .0157 
 
 The corresponding curve to this table is shown in 
 6, page 13 . 
 

 . V. V; ^ , ;; ■ ,.^;«| 
 
 i PI' 
 
 I mZ ■ . <'» ■''•''» 
 
 I'.'lfV^.' ■ *KJit .,-■ , .. , ■■■ ■.■" ■" - 
 
 ry '‘t • ’i. 
 
 
 ‘t' :4 
 
 *•■(-. ■* . ■•. *'* 4 j. , 
 
 ' 'i O' J 
 
 
 
 
 
 fcO ■iii,^'**i * '' *‘ ^ 
 
 
 ’' ' •• y V .' .'»>■*■ • -Ji <•*.■'*'^^114 >1^ !* 
 
 ..‘^'** /iffli * > 1.C- *■ Xffiw f* ,\rs.JT^K ' ifiSB^. '*J 
 
 a* ■.• •■ "■•■■<V'u/'/i-:'vi 'i- .\--J » •■ S 
 
 * } ' ’,#■ #'i-i 
 
 1 ^(>V 
 
 f *' ' '!v , ! 
 
 /* : 
 
 A s 
 
 ‘V-:- 
 
 »• ,. 
 
 
 V ,. i ' 1 - 4 , ' / -"^ ^ .■> ' ■ V * #. 
 
 ■ <^' 
 
 -m:, ■ ■bt'J fifilvM -.^ V. ' .- >//;?'£..■ ' 7 j Ij gjf 
 
 /^V:: 
 
 A 
 
 ' I, •,_ . ,.■., . 
 
 >*•'•■ ■ ■*'-"i*.i/s'_ 
 
 V-'j 
 
 - ’ V- .• 
 
 ' / ' 
 
 L» V... 
 
 l’ ‘ r. k .'■ ’■*.'/, Cm ' imM 
 
 i jn .. ■ - i •■ 
 
 > •li -4 ■ > I " • 'a^ ^ 
 
 
 
 
14 
 
 Comparing the three cases in Fig. 6, it is seen that 
 curve C which is calciilated by equation (9) is nearer to 
 the oscillogram than the curve A calculated by equation (6). 
 This means that the coefficient of self-induction is chang- 
 ing v/ith the saturation of the magnetic core. 
 
 It is interesting to notice that the time to build 
 the primary current is a function of the primary resistance 
 as well as of the primary inductance. If the resistance 
 is higher, the time is shorter, and if the inductance is 
 smaller, the time is shorter. But, the resistance should 
 not be too large, , because then the primary final current 
 is reduced. The inductance should not be too small, be- 
 cause then the secondary peak voltage will be largely re- 
 duced in the oscillating discharge. 
 
 If xie make the indue ts.nce smaller, it is seen that the 
 time to build the current is largely reduced as in curve B, 
 Fig. 6, 
 
 From the above discussion the following conclusions 
 may be dra\7n : 
 
 I The time to establish the primry current is short 
 when is small or when i) is large. 
 
 II With a closed iron core the inductance L, decreases 
 
 as the magnetizing current inccreases. Hence 
 
 /» 
 
 the so-called time constant becomes larger for 
 higher magnetic saturation. 
 
■^1 .1 I'M 
 
 
 ■ r:. : 
 
 '.V ,, ) 
 
 p» Y ’ 
 
 ■ V 
 
 V .t ■ 
 
 ir- 
 
 
 j^j. • ; 
 
 y/V. J : ■ ■ 
 
 J 
 
 Ci 
 
 ilil , &'» 
 
 
 '^*'7 
 
 iv. ij; 
 
 <?'k 
 
 :■ » 
 
 ■ m; X, 
 
 ' ’ ,.-i' 'tf'.'-^.: ;’l *\i 
 
 
 
 
 t-rr; 
 
 ■ 
 
 ‘ ‘ f*! 
 
 
 vX*-) 
 
 •li ■ -v. ;j, 
 
 ;>• 
 
 v ;..- ; 
 
 ’ , , ■ ' i r 
 
 r. . :h^itz;^kx;r: 
 
 
 .'-• ■'' ' y. 
 
 ••• ' , -7C.t0/- . 
 
 ^Vc*t 
 
 ••' ' .1 
 
 * < 
 
 •'(' . .: ! 
 
 ' :i;h‘ r 
 
 . ,1 , 
 
 ' ; * I 
 
 , i 
 
 0 
 
 I 
 
 .. ."A. 
 
 ' '. J ■ '1 
 
 
15 
 
 Fig. 7 
 
 ripples in the current wave seem to be caused by 
 oscillation of the mirror of the oscillograph. 
 
 The 
 the free 
 
16 
 
 IV Phenomena of Opening the 
 Interrupter 
 
 
 Fig. 3 
 
 Vife assume that the charging current in the secondary 
 is negligible. Then equation (l) becomes 
 
 ^ ^ a 
 
 Oy) 
 
 If v/e differentiate this equation v/ith respect to t. 
 
 
 or 
 
 
 
 c; 
 
 = o 
 
 n di] . t, 
 
 L, dt AC, ~ ^ 
 
 dt^ 
 
 The general solution of this equation is 
 
 hn. t~ 
 
 = A , ^ ' -h ^ 
 
 
 Where m^and m^are the roots of the auxiliary 
 equation. 
 
 7TZ -f- = O 
 
'■c/M tc yt ^ 
 
 A^-sjVlpl’ *^. .H*;’'f^,.’^ ■■^•e'.f.-\ ‘ If «.'■ 
 
 ,x. -.i . -V,’'*: >■ .., ';r -.vjip 
 
 IL - ^,.1 . . _ _ . _sS‘.--L 3 IllS^k _‘_^ 
 
 i ■■ 
 
 T -S 1 
 
 %♦ ; V *»*Y ' ^ * . 
 
 
 <i*- 
 
 -^■•' ? r-.i, 
 
 :-e ’ 
 
 !>• 
 
 .t fTTQ 
 
 '' •' '■ •"if’ ■ " ' ■' ' " '*- • •1 
 
 'f; ,;r.‘ 
 
 '*”■*••■’■ ' «■ ■' 1 -'’ 3 * * ■> ‘ ■' ’ f' =' E * ■ M-'*^ ' V 7 ^;! ‘‘-v ^ 
 
 "..j-i";: ., ' ■• . . . •■ ■ ■'V ^531 -#w" 
 
 
 •iS' 
 
 I *"t'i ■' 
 
 .,./ --i 
 
 &E-f •■%!■ V ' « 
 
 ' !^.(#vi'n:$'^f;,v^' ' ■:!■ -::^w?i ' 3- 
 
 Kr <n ,-»i- «■',;:-'■( yi - if *<» fjywgi^ F^'A i 
 
 El ■■i'^'.r.f* ■■' ■•• ■• ' ', ,■: 'V'"'' 5^' ■ ■ ’'''l.^fcijilHil 
 
 
 
 
 * Vli 
 
 
 '-is 
 
 
 y 
 
 't,v;f:i 4 i- 
 
 ^,-s, "i*, , V ' "'itl ■ ii" 
 
 ^v-- ^ ’sH v'n i?S.!»: ■■ T •^:j 
 
 • 4l‘.i,r t’*).* ■• .:'j” v’-, '<^4 fl!;:.^^ySM 
 
 •1 ji.; hi, i'-'-# 
 
 i:m 
 
 i ^ 
 
 
 r •’ 
 
 r^:h . a'r- I . 
 
 ^ ‘><T V . '^ ' ■ ' 
 
 WISMH 
 
 ? - ,■ ^ f -1 • % 
 
 VV- ‘ ‘'y.-*- ^ ,.« luiiiH •• .•• • b' 7 i-\ 
 
 ■ ’■ . ' '■■-■'>’• • • '■‘' ' 2 rT\ •'■ -. '■‘‘i 
 
 
 &: , ■'■.■ ■ . ■ ■ . I : ^ ^ : -I? 
 
 r ^ -f 
 
 ^■‘^-.r’. L- * J I 
 
 *»Y- '• I V‘^ '■ 
 
17 
 
 So, 
 
 '?T} — - 
 
 Y/here oC =. 
 
 
 / 
 
 / 
 
 ^4 1 
 
 f ^Lf 
 
 
 ' 7 
 
 / 
 
 f 
 
 / 
 
 , and 
 
 jS = ,t 
 
 / J2l / 
 
 
 F 1/ 
 
 cl 
 
 - OC -i- ^ 
 — —OC 
 
 t, = A, 
 
 1:1 the above equation, three conditions are possible: 
 
 (a) 
 
 
 ^L, 
 
 c. 
 
 > 
 
 o 
 
 (b) 
 
 - 
 
 
 < 
 
 Cf 
 
 (c) 
 
 
 c 
 
 ■= 
 
 o 
 
 ^Li 2 . 
 
 — — - is far larger than i; v;ith the primary coil 
 
 under the discussion. So it corresponds to case (b). 
 
 i, = A, 4 
 
 = C A cos ^gt i- B s/n ^c) 
 
 Y 7 here A and B are integration constants. 
 
 The electro-motive force across the condencer is, 
 
 ^c= 
 
 - S - l^^^^J^cos^t■^S>sinpt)-L^|^-o/^^^eos^t 
 fBsinptJ+^t£'*^(-Asin/3t +&cos^t-)J 
 
 ( 12) 
 

 
 . jiiTTi i lri B r • 4 U< W Sitii U a^ ^ ^ 
 
 7 f / 
 
 S*(, 
 
 
 Ji 
 
 ,r.j.- ' « *W irtKPi ' /jjffl' 
 
 i W ^ ' PC'**' %■ "* r* '■ • V ^ , 'Hf ~ 
 
 <•’ 
 
 
 
 m* 
 
 :• .A?*’ >ii, ', M 
 
 '■r 
 
 ! iv ' -■ ; t 'i : ’^' ., ^ f ,' - . . ' >■ ’ 3 BeP>i^ .' '■ ■ ii ’■ ■ ■ ' n 3 ^ •" 3 S 13 W - 
 
 5 "'ii® 
 
 
 
 r.¥ ' ■ 
 
 ^‘' y-'- V 
 
 ''.■^’''♦vSC 
 
 V i 
 
 p... 
 
 ►\ ' 5*'*J| §'r 
 
 
 erffiJSct ' '- y-' ' \‘ i't- ® '■' ’ & ■.'*^ffi' 4 ;'-?X^! 
 
 ' W^:' ''" ‘ '■ W'"! r^-n ■ vi: ' ' ;'cl6 ■^'^P 
 
 »• •’ * .k* ‘ ' S » '' 
 
 -'fy ~i '.' ' •V;*,' 
 
 ■^t”\ i'f-iv ' - ■ .. - ... -'■«* V 
 
 1^3^*.® ■ ;■'# ;.i^.k' O.' .>■• ; • ( .1 >!'-^V iBL- I- 
 
 fA' ■ ^ jUil' :ft‘ 
 
 . •■y'y '. 
 
 Eyy.f.v*-' " y r - K ^ 
 
 ■ '•/ y^ilv l 
 
 ■j' 
 
 V 
 
 
 w . ' " I. 
 
 H* . ' ♦ 
 
 ; ^ ^ K : 5 :, 1:% ,'. ;*i tts^ 
 
 •\ . -Y,y. V'AA'^TiW 
 
 't * ■ ^“ V '' 'v**! -w kk > j t]39 * 
 
 iu. ;-.*' r. '' /#,•■: 
 
 “ a;u ■ ^ 'Sffl- 
 
 Sfc'** * • s ■••rdlMrtkAV.. 
 
 rr w 
 
 ■ ••kJ '- *•■ ... • ' -■> ''■i' *^.'sk4l , V " AV kU. '■ '*’ 
 
 W W'' .' 
 
 1 ■ „ : ^ . ‘ ... , , 
 
 *.''v ..i 
 
 
 r ,** ^ .r) 
 
 ■ ___ - .. ?m'V ...■'i '''• •^ . ' .. • ■.-"i/t. 
 
 ■«' . 1 1 ; ' K‘. 
 
 •yvy 
 
18 
 
 9^ ■= S 005 + 3 c5/'n lp((/i oos^/-^ S^/zi^tJ 
 
 pL^ (-/! >sln/3t -h 8 cosp t)J o^) 
 
 When t = 0 , i, = I where I is the value of the cur- 
 rent at the moment of opening the interrupter. 
 
 From equation (12) , 
 
 I = A 
 
 Prom equation (13), 
 
 0 = E -r^ I +L, 
 
 ]7! — T r» « pi, (^o ^ ^ I Lfl.^ f 3 ) 
 
 " ' ^ - TT, 
 
 So, equation (12) becomes 
 and equation (13) becomes 
 
 -e,. = £ - <Si^2PP . J :sin^f*Ic ( 15 ) 
 
 ( see Appendex III ) 
 
 If E is negligible, 
 
 ^c= -<r 
 
 _ / 
 'eft 
 
 - " ( A S'ospt i- B:5/n/3tJ - /.Of (A co5^ti‘35thptJ 
 
 ^-4 sinpt -f- 3 o.o5^i)J 
 c,- s 2T°^^C A co'spt -hS^f'npt) 
 
 When t = 0 
 
 , i,= i. 
 
 I = A and 3 = - — I 
 
 f 
 

 - -A. 
 
 
 
 -.-\-uL'u . Jiiil — 
 
 ■ • r 
 
 ► /!'• C' *X J ■' . . ' ^ * 
 
 •( 
 
 ^-i I - 1 
 
 F*’ 
 
 rwif- 
 
 K?^'. 
 
 ? , * 
 
 I •'• 
 
 - > ,> Vi 
 
 
 
 '-ij; 
 
 V,- - ■ 7^ • - *. »7-'« » 
 
 V- < {< 
 
 \ '*'-,V Si^V'.c 
 
 
 . ^ 
 
 1 * . ' '^ 
 
 ''' '■'■'^ 41 ^ ■' 
 
 
 
 
 ■■ 
 
 
 
 \ 
 
 ♦s. A* 
 
 s . ■■.'r 
 
 mm 
 
19 
 
 i ^ X a ^ ^/n/St) 
 
 (16) 
 
 and -€T^ = coSiQt-h ~x:L^o( czo^^t 
 
 +■ Io(^L ^/P^St-L^^x 3 In pt -Xo<l^ cos^t) 
 
 ^ m { 
 
 -o(C- / 
 
 L^/ ^ 
 
 ^J=L 
 
 ) slh^t 
 
 = Z e 
 
 
 (17) 
 
 Equations (16) and (17) are reduced by R. Colly in the 
 
 Wiedemann Annalen, vol.44, page 109* 
 o< , . . 
 
 in equation (16) is very small in our case. 
 
 So , 
 
 -C, = Z 
 
 4 = ^ ^ S^n/3t 
 
 It is evident that the current and voltage are oscil- 
 latory and damped. 
 
 Their period of oscillation is 
 
 -2 TT 
 
 y _ ^ n _ 
 
 ■ ' /■ 
 
 
 The da-mping coefficient is equal to o (= — 
 
 •■• T = £tt /JX, 
 
 (xt^ y . 
 
 (18) 
 
 S/r7-X=^ 
 ' =/ /4C, 
 
 ( 19) 
 
r sti^- ,v‘- ' ''’■ ■-L '^ i^&m - 
 
 '■ BP.; ?'V ■ ■xfe.-tj?*'? i-4 *' ' 
 
 4' . «'■ '-'’Wii-pgfe 
 
 k-I^Sh' , ; ■■ - ^4; ’” •;■ -i \i'^S'%.^!ii^ 
 
 ' , } ■ ^ • ■ '\ ' ‘ ia. ' ' " .•■• 'jIV® h 
 
 
 ■ - . ■ i' 
 
 
 
 ■" ;;J 
 
 i : ' n•'V^ V ’ K ?■' ! • I'u r 4^ r olil 'J f* *• f -0 
 
 '(.f 
 
 ■ M- 
 
 V ^ ^ 'V t: ' »^•'^^ V ’ K ?■' ! • i'^r 4^ r olil 'J f* *• } 
 
 ' *>■ .r .*■■•. K'; , ,j^ _ '■ ^ ' Cl ' 
 
 '■ '-llt'i ■ ** ' 
 
 JSuSl., 
 
 :*5i j**.. 
 
 ; j|. 
 
 '5 SS"v ''4 “ ^ ■' ^ 
 
 jAupt !>t -itMftnt ■»si^*|ii»&h.«4K 
 
 ■Cv 
 
 
 , r A » 
 
 '■ ' V i ^, 
 
 
 
 09 r»„j|'' ?!. K ' ■ ', ,<L>- ■‘■.xi^'i- 
 
 ii, !i'-'»l,j 
 
 , ^ ' ^•- ffi 
 
 
 
 V. ^ 
 
 lit 
 
20 
 
 If there is some magnetic leal^age in the primary and 
 secondary, 
 
 j J =. A n n 
 
 5 / X 
 
 where n, , n_ are number of primary and second- 
 ary turns. 
 
 If there is no leakage between primary and secondary. 
 
 M = L L, 
 
 / ^ 
 
 and 
 
 from equation (19) 
 
 because the secondary induced e.m.f. is =r s/>? 7 ^=: 
 
 neglecting the damping effect. 
 
 From the above discussion, we may conclude ; 
 
 I The secondary e.m.f. is proportional to the prim- 
 ary current at the moment of rupture. 
 
 II ^ — J L% . ~ 
 
 if there is no leaks-ge flux. 
 
 Taking as example an ignition coil which has following 
 constants . 
 
 
 .01 1 
 
 henry 
 
 
 1 . 1 ohms 
 
 
 20 
 
 m. f . 
 
 E 
 
 5.725 volts 
 
 
 5.2 
 
 amperes 
 
 
 

 • % ®'' ^ ^ ■ 
 V4. -^fc- -ii^A 
 
 
 T»V„V fc" 
 
 i^ » 3 (ii \ i *# 
 
 
 v-f- ',: , „ . : iTt - . - , '*■ ; 
 
 '• iW'*^ ‘Vv».*'*‘1k ■>' » "' . ’ »•.• ’■"» 'v-V^ 
 
 ■■■’ y 
 
 L». ■ ' ' \ -(H -w 
 
 ? ■■ :• p .T". - • •: ' ,' - ■ ' v .»r x 
 
 '^■■' t* ' 'SkS^^/ ^ ' .' '^" 
 
 
 -.'.<-’Q /f'USjivs . 
 
 I j, - w 
 
 r ‘' • , -• ,* ' 'Jr< 
 
 f 'ft . 
 
 ir'. ■ ','*.T‘’:V:; 
 
 } BRKf..;; 
 
 f »fcji '.■^ *• fj ' ,; 
 
 /’♦ 
 
 I . . ,.j^i^ :^L. ' *^ j ' \ jiB^'V. SiSifej 
 
 « iJJ; ’■'■•. *‘{a» -»^J 
 
 ./," fT V <|. .*-.> 
 
 I c 
 
 «d xi “ \ . K"* 
 
 ' '• V**}! 
 
 /.uii 
 
 f 'w, 
 
 
 
 '. *' gipK^*J^'''''''^*^r''''‘'*' fe'f 
 
 , ^ • fi-Xi*; 4cf^< . • ,l4J <^aer ijiijrii f»A?EZ*«Bl \?i* V/_' 
 
 vi \ A ' . '.i*.vt»1i .jl;: '; ^ 
 
 I ^■'s-'r-? . 
 
 B’ /?.v.;i:r._ 
 
 i‘ ' ■ 
 
 Jf 
 
 nv^' ' '* '* 
 [Tv v.Vy 
 
 \ ' 
 
 ,A 
 
 : /•*. l ipjKi " •' ■' ^ 
 
 i^ N-% "iT 
 
 ‘V’' i 
 
 
 
 i '■ • ■ ' '• i» 
 
 'f>^ SUi 
 
 ■ .,-!• .;»•*•■ I 
 
 
 t»»'d )t(T», .'ry, r-;„^ .^■.’-M 
 
 
21 
 
 .'. C,' 
 
 ^ _ /. / 
 
 
 
 
 
 ^ X >0// 
 
 
 
 
 / ^x.o// 
 
 /./JL 
 
 > 2.4 / > 0 // ^ ^c?X / 0 ^ 
 
 
 - . 022 )/ 
 
 - ^ /(OG 
 
 
 
 = I , equation (14) becomes 
 
 
 / 
 
 
 ^fh pi) 
 
 (1 
 
 / 
 
 = ^ S.zx fcas^/oot- a) 
 
 
 
 = S.Z X '^“‘^<205 x./ooi 
 
 
 t 
 
 sec. 
 
 Table 4 
 
 -sot 
 
 e 
 
 cos2100t 
 
 1 
 
 ampere 
 
 0 
 
 1 
 
 1 
 
 5.2 
 
 .00025 
 
 .987 
 
 .866 
 
 4 .44 
 
 .0005 
 
 .975 
 
 .5 
 
 2.53 
 
 .00075 
 
 .962 
 
 0 
 
 0 
 
 .001 
 
 ,951 
 
 -.5 
 
 -2,45 
 
 ,00125 
 
 .939 
 
 - . 866 
 
 -4.2 
 
 .0015 
 
 .927 
 
 -1 
 
 -4.81 
 
 .00175 
 
 • 917 
 
 - ,866 
 
 - 4.13 
 
 .002 
 
 .904 
 
 -,5 
 
 -2.35 
 
 .00225 
 
 .383 
 
 0 
 
 C 
 
 The corresponding curve is 
 
 shown in Fig. 9 
 
 , page 24: 
 
 If = I , equation (15) becomes 
 
 ^ ~ s/n -h r cos ^tj 
 
. 1 u ' ' ' '■ m 
 
 ’?:. ( 
 
 if- 
 
 MK,v iiT-^ ' ■ 3.VA ™V.- tB ' S!i-,'''«^ 
 
 ^®-V ’®^ '•■ S^nT. e'^T^ 
 
 > 
 
 %'Jrs I'l i . 
 
 
 ^ -^r- 
 
 
 
 Kt *^. ;t'- 
 
 
 / , i “^*1* 
 
 • H 
 
 » <;?s: 
 
 ^ R.C. . -'' - W '- ' •■ '.^.'^W’^'^ 
 
 ' Rilf . .V/%i '■ ^O' '^'■'■^VATik'A -vi,t,;i;- ■■i.^Sk. >';:•’?«&' 
 
 I 
 
 ' J ' iO’^l •' 
 
 ■ ■■ 
 
 P* ., ‘i.; ;.;‘v ' ■ 
 
 t 
 
 
 
 SI . 
 
 -/ ;. * ^ '•f.: 
 
 . , S'! 
 
 • 'Tm '’^> 3l '.V 
 
 ■ <, . 
 
 * '^ra- 
 
 _1_ f' ; '. .t 
 
 s^iH ' * i ‘ 
 
 ^ 
 
 Ivl 
 
 «- ***• 
 
 
 ■ '?< 
 
 \Kf.i 
 
 '/i’ W ',■ . .v'f: -i^*; 
 
 : xtim 'd 
 
 '■ ^'i \y \ 3^ 
 
 1 , 
 
 -.-v' 
 
 1 V 
 
 ^ ^ * 
 
 : 
 
 < ■* 
 
 * f -, 
 
 t - , *,;■ 
 
 :.r [ f _ 
 
 
 
 
 k' w ■ 
 
 
 ^ , ■* 
 
 ■ - ■ 
 
 \ '^ ■ ^ ■ I tl > -T 
 
 
 ■‘ Vi; 
 
 • it' ^ . 
 
 O'' 
 
 
 rx T 
 
 fv_ V. r 
 
 
 J. 
 
 '•'®^ 'C«- ■'.'ill' 
 
 , 'VV' ■ f ■ - :, * . 
 
 
 ^ ■ >J'*'.f \li. i'C 
 
 
 & 
 
 fl , ■ », , 
 
 L/-''-.i?<?:‘'.?’! !‘iWv '■ ,;X-V* 
 
 ^ •T'^ 
 
 
 
 ;rr . *arw r < » » \ji a fn, l y 
 
22 
 
 = Sf ] ZS ^~ sJn Z/oot + S']Z CCS 
 
 By calculatlns the terminal voltage at the interrupter 
 for each instant, we may determine how the voltage rises up 
 and down at the Instant of interruption. 
 
 Table 5 
 
 t 
 
 sec . 
 
 ^-sot 
 
 sin2 1 OOt 
 
 cos2 1 OOt 
 
 e 
 
 volt 
 
 0 
 
 1 
 
 0 
 
 1 
 
 0 
 
 .00025 
 
 .907 
 
 .5 
 
 .866 
 
 60 
 
 .0005 
 
 .975 
 
 .866 
 
 .5 
 
 107.4 
 
 .00075 
 
 .962 
 
 1 
 
 0 
 
 121 
 
 .001 
 
 .951 
 
 .866 
 
 -.5 
 
 111 
 
 .00125 
 
 .939 
 
 .5 
 
 -.866 
 
 66.7 
 
 .0015 
 
 .927 
 
 0 
 
 -1 
 
 -11.1 
 
 .00175 
 
 .917 
 
 -.5 
 
 -.866 
 
 -45 
 
 .002 
 
 .904 
 
 -.866 
 
 -.5 
 
 -89 
 
 .00225 
 
 .883 
 
 -1 
 
 0 
 
 -ICO 
 
 .00375 
 
 .825 
 
 1 
 
 0 
 
 105 
 
 .00525 
 
 .769 
 
 -1 
 
 0 
 
 -86.7 
 
 .00675 
 
 .714 
 
 1 
 
 0 
 
 91 .5 
 
 .00825 
 
 .662 
 
 -1 
 
 0 
 
 -73.8 
 
 .00975 
 
 .614 
 
 1 
 
 0 
 
 79.3 
 
 .01 125 
 
 .57 
 
 -1 
 
 0 
 
 -62.7 
 
 .01275 
 
 .53 
 
 1 
 
 0 
 
 69.2 
 
 .01425 
 
 .49 
 
 -1 
 
 0 
 
 -53.1 
 
 •01575 
 
 .45 
 
 1 
 
 0 
 
 59.7 
 

 ,**.>-• ,-» .^ •■ ■ r>i»UI '■->'<- * 'S', ' ■ ,.•>•■ a'' '’>■•.1 
 
 
 
 
 ■ , r.-*' -■ “ 
 
 sr^o 
 
 » - ■ - .V-*, ^ ,- 
 
 /I . :*ra 
 
 .♦* ■ 
 
 .: ;?>»>% i 
 
 • V- 
 
 - ■ 7crrcito, y 
 
 'H > :., 
 
 1 *• • i 
 
 • j. 
 
 
 ‘1/ 
 
 I,'.. 
 
 
 .i 'fjLt,- 
 
 f- 
 
 
 <V, 
 
 
 ./> * I • « .( «■ >, i' » 
 
 
 4, I ♦ I i » I I I 
 
 ' 1 
 
 '■ - ;s '* 
 
 '• ;, ^ • ■ '■' .i_ 
 
 ■ O'" 
 
 
 *SI 
 
 
 i 
 
 i ■ .'T 
 
 > ,:. - 
 
 
 • ^ ; -* • i ‘ *w •'‘'>"^ 
 
 • ■ :.’'/J 
 
 ^ , ’ 7 fc-' ^VM 
 
 '■■f 
 
 
 
 ' .' V-‘^’ 
 
 
 It* -t 
 
 !C . , ^ - ~v ‘ ’V^'‘ ''® lilfl'K 
 
 4- ':- ^'^’’7 
 
 ^ <^11 . sbA^isL II' " '"S I , ' 
 
 
 frrr’ rf f *^.v *-g> >/ w h ' w» in n y ti . 
 
 
 
 0 
 
23 
 
 01725 
 
 . 422 
 
 -1 
 
 0 
 
 ’ -45 
 
 01875 
 
 .393 
 
 1 
 
 0 
 
 52.9 
 
 02025 
 
 .362 
 
 -1 
 
 0 
 
 -37.8 
 
 The corresponding curve is shown in Fig. 9 , page 24 . 
 

24 
 

25 
 
 An experiment to check this calculation was made by 
 inserting a variable capacity into the interrupter terminals 
 or the Connecticut Igniter. 
 
 The connection diagram for the experiment is shown 
 below. 
 
 The voltage at the terminals of the primary coil 
 e oscillates, by charging and discharging the current to 
 the condenser after opening the interrupter. 
 
 The oscillogram taken when =: 20 m.f. 
 
di » A' * /. * 
 
 
 *v ■ NS^J 
 '*' mil 
 
 if<' 
 
 p: .•■ 
 
 f • % . 
 
 ■^64 
 
 *r - Jf 
 
 
 \ r.^T^ 
 
 . ' V ‘ 4 :'W. 
 
 > -'ll,, 
 
 ^ T”' .<>;,„ i: 
 
 ^ . ' ■' J'‘ f—-*" ' W iyii>>iW| i *''<%P W | » »l<.i » ^ 
 
 . i '"n,4^i’ 
 
 mr‘\’ ■ 
 
 .■■•'. A 
 
 
 1 K^.--' s ■• ■■(. ~ 
 
 
 
 I 
 
 J .jErTj. '* 
 
 i I - T 
 
 »kC,< : ■ .', ■' ’ ■ V ’/ 
 
 V ’.*••, v^ 4 . '. m 
 
 ■v’V ■, ]■} ' ®’ • ,. H* ■? 
 
 r«ar t *. ■' .,'1 ( ■ ' . r^'- . t 
 
 liF j>’ * • ' '•'>:.< < 1 . ' 
 
 -"'■M'j' :>, . f ' • ■ 
 
 hf 
 
 
 ' f c».t . *•< 3<f I'J . ftftc , Ik 
 
 k'lC; ' ■•■ '‘V- , ■',', ■'.'. :.’i ''‘ 
 
 fcTf^,.i'’ .'■ . - e' ■,'! -i? , ■ "'■ ' ^ ' ^ 
 
 '■ ■'.". '■ 4 . W-. •.’*■<-' 
 
 V 
 
 f > 1 t 
 
 * . ■•' * j *i t 
 
 
 |T'> . . ■ V 
 
 '•*' 1 ^'" 
 
 ■M 
 
 X " *■ 'S*'" “' 7 '! « • •?*'>iV|» oHMHaMi 
 
 '4 
 
 r- A*- *- /. ,f-. ^.-v••^)<i•.^•■;^.^ 
 
 I''',, • ■' 
 
 t' ■ <<?,.i,"'“’ 
 
 /.V ,v •■, ■»- . 
 
 
 
 • '* |‘•'^Vi 
 
 Yl '■ * ■ M,. .iV ^ ,’IjISS 
 
 U'» 
 
 ■ .<■ W' 
 
 P/. -■ V: 4 ■ ^ ' •'• 
 
 'S' ' ■' ' -’ - 
 
 ■ M tli r 
 
 
 ' W'v#w.^ *sr*^ 5 H 
 
26 
 
 The maximum peak volta2;e of the oscillogram is aboi^t 
 85 volts. 
 
 Comparing this voltage to the voltage wave of Fig. 9 
 which has 120 volts in the maximum of the first oscillation, 
 we may perceive some difference. It is considered that 
 this difference is due to the fact that the energy stored 
 in the core is dissipated by the interrupter spark and is 
 greatly reduced, while we have not considered this in the 
 calculation. 
 
 The period of oscillation agrees in the calculation 
 and the experiment. The period is .003 second per cycle 
 by calculation, and the experiment shows us about .0029 
 second. 
 
 It is very interesting to notice that if the capacity 
 of the condenser is increased, the oscillating voltage 
 induced in the primary coll, as well as the secondary, is 
 is’’ lower and the period of oscillation is larger. 
 
 The following experimental data shows this fact. 
 
 The current at the moment of opening the interrupter was 
 always kept constant, that is 5*2 amperes by making the 
 speed same, and in Fig. 10 was changed. 
 
 Table 7 
 
 Cx Maximum spark length 
 
 Condenser capacity at secondary 
 
 1 5 m. f . 1.2 m»m. 
 
 12 3 
 
 9 
 
 10 
 
• ■’iMWp t .. . 
 
 
 
 
 
 ' ' K.; 
 
 J,rr 
 
 
 «Y^Mv< 4 V 
 
 -.•( 
 
 
 ■-f 
 
 n .^• 
 
 3 <- 
 
 , u !„.*v,‘' 
 
 •1 
 
 ^ Ov ''y-r,;, . :„ ; '.'ITIf' ,-• 
 
 ^, ■='- 
 
 jfTjt ^!jfi.' 
 
 ii ' 
 
 : ' . AO . T : 
 
 
 : I'r • ’ ' . ' '' 
 
 ' %’ ■'■ 
 
 
 ■• ?♦’ ,'ipit .■' 
 ■ 
 
 
 F yr* 
 
 , '•‘- 'S. 
 
 • »A1(A^C''V 
 
 V ' * »* '• 
 
 . JL. 
 
 
 
 
 S y* . 
 
 4 . ..<. ' '.vcta:' 
 
 ‘ ■ . :> '■!*■ 
 
 43 
 
 -V’ N>vC. . 
 
 1. 
 
 i U - 
 
 cV 
 
 . .. '.-Cl" 
 
 ^ ;.^V. 
 
 ■• •''' .- 
 
 ' > 
 
 •1 . 
 
 
 '/ 
 
 . . 
 
 
 .,.: -'n _ '• 
 
 ‘.f .\ ■ 
 
 
 ' ■'^ ' 
 
 t 7r ■^■' ' 
 
 ^•‘'i , .!' .' •■'•*’ -. '.' f J 
 
 V ’ ;■ 
 
 
 
 
 ‘ 
 
 ^ ■ ' .. rtyi. ..;■' 
 
 
 
 •V 
 
 .;: M;; ' " ' 
 
 -,J.tv..- '''I f 
 
 ' K: ,. iF:v:c *1' 4-jnMcr';^ 
 
 , v.A 
 
 
 
 
 ;j 
 
 
 
 
 r.. 
 
 y' 
 
 . .'*t 
 
 t' 
 
 
 
 # • 
 
28 
 
27 
 
 V Interrupter Spark 
 
 We have so far neglected the interrupter spark v;here- 
 a,s such a spark always exists with interruption of the 
 primary current. This spark does not occur at the in- 
 stant when rupture takes place, but a little later. 
 
 This fact was proved by H.Armagnat in Eclairage electrique 
 ( vol.XX!II, Jan. 27 , 1900, page 121 )• 
 
 When v;e break an inductance circuit which is connected 
 in Fig. 1 la, the voltage induced at the interrupter terminals 
 does not exactly follow equation (17). 
 
 The capacity between the contacts of the interrupter 
 must change from infinity to zero in very short instant. 
 
 Tjien the capacity/ is infinite, the voltage curve in 
 Fig. 11 b must be tangent to the absissa. If the contacts 
 open wider, the capacity diminishes gradually and the vol- 
 tage curve rises along the dotted line. 
 
 The disruptive voltage between the contacts E^' is 
 proportional to the distance between contacts. We assume 
 that it rises proportionally to time. 
 

 , W >« TC''Xrr lo ^ 
 
 a ; .'^ V . . .' .., , ;\_. , ,^/ ) 
 
 • » » •'■‘ti * . I ■ • (, 
 
 ^ J ;■> . ^t .'■' ■0''; l 0 V'.' 5 > -S? • -0/. ’ I : .■'•^ 
 
 / 
 
 lij ■•. '* Tt; :■•;» rj ’ ‘.roY .-(Sji^ 
 
 ,u^: ilJ'iiJui-'/ Q'i.tj /.U 
 
 
 '■'i tj ..'"' 
 
 . t ; 
 
 ■■ k 
 
 ,, - tW 
 
 : 0f :, i 
 
 f ^ r : 
 
 > . • • i * 4 • 
 
 ■■ 
 
 1 * ' ' 
 
 “-"'-■ '<■■'-1 ■ ■■ • ..-■. ■, ,7 7 . v ; .: 
 
 ••' •... * ff -’ ■'«••••• •■. ,V • ic Vi .;., -. V-.-7 
 
 , . ,. ^ ' I ' • ' I , * ■ ' 
 
 *. ‘ - • ■*• ■.■<:'/» !> Jl ^ ■ ■••• 
 
 * ’ ’• 4 ^ V loiiJ ’j; j f ,! ** 
 
 1 
 
 
 !(■ . 
 
 ,■ « ■ 
 
 ■ f '- l - • 
 
 
 
 
 ifCl 
 
 - , 
 
 
 
 ’« ‘-“ ID ' 
 
 
 
 
 
 
 . *;'V . '0€»\7v.^' ,^.." Xa^I ;.,t*X^C''t4l' '44 
 
 "kXH Vn .- . 
 
 t-v*’- „.*.r a; ../".' i 
 
 L U ' 
 
 • I 
 
 M - * 
 
 r 
 
 ■# 
 
 
 r 
 
 I 
 
 
 ) 
 
 
29 
 
 The primary spark starts at the intersection of curves 
 E^’ and e^ , but soon disappears. The terminal voltage 
 will still rise until the secondary spark appears. 
 
 The voltage continues as. long as the spark exists, 
 and drops down when the ionization of air become iins table 
 Fig. 12(c) shows this phenomenon. The secondary 
 spark starts a.t A and is sustained a short period of time. 
 
 In Fig. 12(b), we can not see any spark voltage at 
 the secondary which continues a short period as in (c). 
 
 The oscillogram corresponding to Fig. 12(c), is shown 
 
 below. 
 
 Voltage variation at the terminals 
 of the primary coil with no addition- 
 al capacity. 
 

 rY-vA’ ' 'V - ” v"'lff'-< -' 
 
 k «iu<> 
 
 L, . ' .* ,' . '■** '*''. '!*’-f'' 4 U'‘ "."'t •• '<i(^. ^'• 4 } ••*’ ' ' ■?'*' 
 
 pv . ;,;' C* ' V ■ •*.-'^^’*.»''<i-' '■■ '“ M • .-K 
 
 
 f .' ■* '• '■y 'ijV' • « jh'w.w .’ ■ 
 
 B» 5 -', ■ , ,; ' v'W't 
 
 » • / J'\^ flw 
 
 . b V.,... -'^‘ 'fS^M^:.y ^ 
 
 :.''•! ■ V'.’JS^V.r ’’V'''''f'V'. ■- ;' v'j ■ '' ■/'V.‘^'’viii4ii 
 
 *., . 
 
 ^1 
 
 
 V 
 
 %7^, , _. w 
 
 t I.xt At It 
 
 ■■"••'•' 'VVlOI-At 
 . •- , ■ 1 ., ■ (',•■ <^^ 02 '^ 
 
 .'»' •, <■( ' -vj 
 
 '," -.■: ' , V- j4‘P < 
 
 I 
 
 
 
30 
 
 Voltage at the terniina,! of the primary coil 
 when there is 20 m.f, capacity parallel with 
 the interrupter 
 
 If we connect a large capacity in parallel with the 
 interrupter, we see that the duration of the spark is very 
 long, but the disruptive voltage a.t the secondary is very 
 is very small. 
 

 r„ 1 
 
 , .. -i;^ r; ;•■ ' ' , -V" v; 
 
 W?K"'V 
 
 '■:.■■ . -.yr. 
 
 V '■•sV ' ■' 'T'-PK':1' ■ ■' ■ ■ ' •’“'V ■*’■' ' ^-V T' ‘ 
 
 ■ .'. ■ '• f »v . s‘'*’r''' -.7 ' «v .t.'i*/4: ;■ •t,>"i ,.. a.'i -• ■v'‘ 
 
 ‘- 'jjffvfl )" V ■■■'>■• .. >.-:;i ■' v • 
 
 t *' - • ,•■;;,•'* . ■ •"■■■ t '••'•'•'^ v* . ' 
 
 ^ r‘ ' t • *i . . ‘ V ■ t .V ' I ^ Tt‘ '■ ‘1 
 
 j».Vi i '•'' ■' 
 
 7^ ',>y iftiy . '*■ ■ '■ ^ < ■■ h' % 
 
 
 r»4?'W 
 
 i: 
 
 ' ■ ■■:< ■,*. '1/ '^ ' I* ■;•• ■• • ■ i , v.-^' ,1 ■. if 
 
 •' /-* •' ‘ ' • * V * .'. ■‘’* * » '■‘' ■' •<*• ' ■■•^'^‘•'.i'^^.w' 
 
 •' . - ,> • •'■ • * • r •• . ./I./' .’■• •”• 
 
 ;.'44; • .. ..' . . *•,♦■• . •*■ 
 
 ‘■^ ^vV». 
 
 4-- 
 
 al-' J... , .r f. .* 'f • .;,4»* •. . ••;. ; J- ^ 
 
 r T*" ■" *'■; 2.' * . f -v*-^ j , ' " ■, 'I®-. ■ '■ i'* 
 
 H^' 
 
 ,f. ■ 
 
 '‘»4 ■■'‘y W ' 
 
 ;.jki 
 
 
 a' ■ 
 
 .. ., , ,, „, , ,. 
 
 ^i*'* . ;.^ •■'. ' '*, . . ,Vj^- . ■■ *• 'aT ' \ ' _;. * :► , ■•■*> ta^' »1 
 
 I^BaP* 'jif ill \/*v r* Iv.' r-. .iiii .!*i f ^v/ A 1*^ iL /.. 
 
 L '■’ 
 
 •#' 
 
 : '..a*:vU>vl: . ■ ■■'; :,;•£' i ' 
 
 Kik 
 
 • - ‘ ~ -. - I— ... ■ . r 
 
 
 
31 
 

 I . '■ 
 
 • f’-rsr- ■-. 
 
 
 w-S] 
 
 
 : i'., " :'U': ' 
 
 V ■ i,] -(^ 
 
 < ■ ' ;t 
 
 J 
 
 ry ■■■ 
 
 » ' 
 
 '::■ \\:M .'-'T 
 
 . ’i 
 
 fc-r'- 
 
 y ' 
 
 If 
 
 t 
 
 1 '- 
 
 ■ j>t 
 
 :f 
 
 
 ■•<•"•' 1 • ■ •>■* 
 
 w- If 
 
 ':-^|rj. 
 
 
 :{' :ty 
 
 ■ * • Hi 
 
 4 U ■. '. ■■ -if ; ::f 
 
 'tlf- 
 
 -V. '• • -‘* 1 .:;:- f'r'n-VH 
 
 , *'i 
 
 '''''’' h'-. 'H;-; ■ 
 
 ■f ?i|f: ■ 
 
 ■* 
 
 
 ,v- 
 
 t;,t '4-"..if ' * \<J 
 
 '1. ■ 
 
 ii,-: .; 
 
 
 
 
 
 /:• 
 
 r 
 
 r if 
 
 . T.* ;'i" 
 
 \ .'• 
 
 4 -..-;. aci:. 
 
 I . T ■ 
 
 ■’■ :? -• ■ •’•K-rV 
 
 ' 1 : Si 
 
 t 
 
 ’ ■ , ' . , . ■ : f'Va/ 
 
 - '■■ ■ >■ ■ . :' . ;j',- • 
 
 "v- \S "■•’■'* 1 “ 
 
 - -igBa" '* 0 - 
 
 * • . 
 ^ - 
 
 !•: ! 
 
 . - 
 
 ., j- , '; 1 ;! - 
 
 
 'r': 
 
 ^ • • 
 
 7 T 
 
 ■'« . 'ir 
 
 ''. ■*<) «'l •- _- 
 
 . jT,.r i 
 
 \ 'r I 
 
 f 
 
 I < . '<f I j . . ' • i • ' ■' » -i ■ 
 
 ' •-* <.-i»..-^ 
 
 t 
 
 
 M '"7 . S.1?75P . ■■ 
 
 m; t'-i . ■■* 
 
 'lu; 
 
 r’^ >■’{ 
 
 s*.>^ 
 
 ■ T* ■ ■ . ' "'ij;. . V»,I 
 
 
 -. ;j'M 
 
 'S .p tv -r» Ml.. ,.^ 
 
 . '■ -i f ’. i .• ■•'■»• jafi • ' 5 ' ■ ' , 
 
 .,. 4 . , - -l- . 4 HP-* .T<r-^: -' -‘J^* 
 
 .,:.; 7 {ns f 
 
 j.^‘ 
 
 ■• . ' ■ * ’ ' 1 V 
 
32 
 
 VI Opening the Interrupter When 
 
 the Secondary Charging Current 
 is Appreciable 
 
 From the oscillographic study, the secondary capacity 
 seems to be negligible. But if we consider this capacity 
 the developement of the differential equation is as follows 
 From equations ( 1 ) and (2), 
 
 dt^ 
 
 -t 
 
 /7 d 6 ^ ! lA _ M CsL cJ lAx, 
 
 L, dtr 4 ^ L,C, dt^ 
 
 ^ c / ^ ■ M d^i// 
 
 — dt- 
 
 
 dt^ ' dt 
 
 d^ 
 
 ^ dt^ 
 
 dt^ dt 
 
 where 
 
 J. = 
 
 / 
 
 2L 
 
 c/ - 
 
 2 — 2L J 
 
 
 
 (a) 
 
 (b) 
 
 
 
 - _ ^<^2 
 
 
 
 
 - 4 <r, 
 
 The solution of the above simultaneous equations 
 
 are : 
 
 =. A e 
 
 V =: Be 
 
 z 
 
 /wjf’ 
 
 mi 
 
 where 
 
 m 
 
 (c) 
 
 = -J^± 
 
 From (a), (b), and (c), 
 
 A ( x“^2/x +y^+J^ ~ p^^ x^B 
 
 B ( x't 2cTx^ =p Y?'k 
 
 ■2 Z Z * ^Zl 
 
 (I) 
 
 (II) 
 

 < 1 .. '« 
 
 ■*<y : V 
 
 
 
 
 </' I J a'sS^.v^’ futjv^ '^'i- 1% Aw' ft 
 
 
 
 .,i 
 
 "V",: 
 
 
 !^ ■' ' " " * * ' i ' ~" '’'*'■ *• 'i ' ^ 
 
 ^' ',■ sjv/oXX^fV ti.. fn/ 
 
 • • I •..>*■;' -.v., • '‘ ■ .' ■ .. ' V '• . .C 
 
 « ife '.:: * :..;t 
 
 7 vAi') V ^ ;ia ^ ■, 
 
 
 r: 
 
 
 
 ft j ji i, 
 
 V. li- I 
 
 r ® 
 
 
 : I 
 
 
 iU 
 
 '.‘VW 
 
 
 • '-i'^’C’ " *r ^-"' ‘-ft Iv *vvv A " ' 
 
 "■ 5 f '■ . . ft ^ ';■ 
 
 hr ; 
 
 
 
 " -‘ ‘ • ' * ^ i'‘J£im 
 
 m 
 
 '•' < V ' ®KJr 3 ' ''■ Ai ' '^’■" 7 * ' ’ i ' '^•^' 
 
 r,,.- ." *I ?i 
 
 "'''i ' '■- 'Ji ^ 
 
 '.'V 
 
 
 ^** ■*’'■, 'wt'' 
 
 ■ r 
 
 ■ 'r : 
 
 
 
 
 •W 1 
 
 ‘■iiid 
 
 f. ., ' Hi a'*.; •-• !|i',>,.A|ft®,| 
 
 ' * 'Auk A' <ft . 'f^Ki 
 
 ':M 
 
 P(i*V 
 
 
 /' .•'5 
 
 ‘»f 4 • K • ; 
 
 ^■■■h'~ ' '■^i' 
 
 ‘•■k*'.-i^^; ■ '\ ■^- 
 
 4 ^ ^ < 
 
 
 
 
 U) 
 
 ' 7 . ■■ .■;■ -’ 
 
 ur. 
 
 .Ti'g 
 
 ■) ~i 
 
 ■ ...^m 
 
 _ V • •’ .. / ■ J ' ' « 
 
 
 
 . . V- A. , 
 
 '_- .; . •■ • * 
 
 ;• y-K.t. : 
 
 ’> '‘''' ' 
 
 f^' ft-/'.;^*,^';i'^ 
 
 - 7^5 
 
 
 '} i>.fc .;!*■■'' ■'..'iiat 
 
 . yi i ^.V ■ — r ’ j ’T i Bf tti.. 
 
 
 
 g- 3 1 ‘ i'g » 
 
33 
 
 The solution of equations (a) and (h) is 
 
 K, = /!, 4, 
 
 =. 4 . e.'^^ 
 
 = /»?4, e'”''^+ 
 
 where in^ is the four roots of the auxiliary 
 equation. 
 
 = - <=n ± 6 u ,m^ = -cr^±ii^ 
 
 and A and B are constants. 
 
 When 
 
 t = 0 
 
 V,- 0 
 
 0 
 
 i = I 
 
 i = 0 
 
 z 
 
 
 
 0 
 
 
 0 
 
 
 
 B m^Af, 
 
 
 
 ?.= 
 
 c? 
 
 
 
 
 where ] 
 
 t 1,2,3 
 
 ‘,4 
 
 
 
 (II), 
 
 substituting 
 
 m for 
 
 X , 
 
 
 
 
 
 
 
 ; = 
 
 
 
 
 
 
 
 
 '?n, 
 
 
 
 
 
 — C/ 
 
 (11), 
 
 substituting 
 
 m for 
 
 X , 
 
 
 
 4r '' 
 
 / + 
 
 2. <^ 
 
 * ' 
 
 
 ) = 
 
 A/ 
 
 
 -f- 
 
 
 + 
 
 
 
 io ^ - 
 
 977^ 
 
 / 
 
 
 
 
 
 
 
 = 
 
U ^ . - ’ ' ,. ” A’/, . la -•' '^? At j ;-• - . .|J 
 
 
 
 ^ f i. S^ .' 
 
 •;. 7i'x'.', ■' '■ • >7i'J \.yi«6^;;': 
 
 £eh^ • ;.'■ ''7~--'-' ■ *^' * si'.' ?>^5^liwK4 ; f.fi/Jfp 
 
 ■H'- * ^ , *1. A fff , "v 
 
 ■P»'' ^ •!...► "■7./'; 
 
 - ,’ a',. „■ , , -'^ '• i*': ^ t . , ■ ''•** =,_ ’ . 
 
 :V'^. I' 
 
 
 
 ■■ „ >. -'Ia ,%• «( 
 
 
 
 ,..-i 
 
 . t; , . ^v.^- - 
 
 P’V” V''-' . ■X’ V ^. . \j, 'V''*” <2^'' ' '■' 
 
 
 , ,X' 'Wi 
 
 < • 
 
 J^‘ * 
 
 
 C<r >(' 
 
 ■ v> ■ ' *' » Al .*''• A rWyiiilR ;a ji- • ■% ,,j, , '■ ..'Vf ‘Writ.L 
 
 r* ’ ■'- ■ * ' 7 "' ' .' *&*■ ■ i'j&w ■ ■ ‘ ‘ '’ipiM 
 
 • . ,*■> ^ •*;? , ;>9l,: 7 V. 
 
 
 V * 
 
 ' ' rz -f -.' •'•■ t' . 7_ • : 
 
 ■ .-/.. > -■ '■ •^.•^.7fi», '--A -'M-' ■ ■' ■' '- 
 
 ■>.■••• o'-' K V' « ,<v " 
 
 •it: 
 
 a ■= :.; ! 
 
 if t 
 
 
 ... -'.'lA 
 
 ' ‘.1^ A T *■“ - ft. 
 
 '- ^ .:V^- Vt..^ 
 
 -7a^7 ' 
 
 .Q. 
 
 jy 
 
 ■^vV 
 
 T «F|K^i 
 
 5^ 
 
 ( f- 
 
 
 ; '7 !^k.: jl 
 
 'I ii , n ».i|». , i ia j i u i ^L ^ 
 
 Ri 1 
 
 ISi'i 
 
 
34 
 
 3y the following four equations v/hlch are derived from 
 the boundary conditions, we may find constant 3 . 
 
 
 -h 
 
 &2 
 
 -h H- - 
 
 
 : P 
 
 / 
 
 
 
 ^3 
 
 '?r?J^ 
 
 
 3, 
 
 -h 
 
 Sx 
 
 ^ 3b 
 
 
 - <D 
 
 
 
 
 
 
 
 
 -h 
 
 
 '*■ 3^ -t 
 
 
 — O 
 
 
 -t 
 
 
 1- t 
 
 
 — o 
 
 1 
 
 2 
 
 J_ 
 
 J_ 
 
 
 
 
 J_ 
 
 J[_ 
 
 mf 
 
 m* 
 
 m* 
 
 m* 
 
 — 
 
 P 
 
 m*- 
 
 m^ 
 
 
 
 X 
 
 3 
 
 -» 
 
 
 
 •«- 
 
 3 
 
 2. 
 
 J_ 
 
 J_ 
 
 J_ 
 
 J_ 
 
 
 o 
 
 J 
 
 1 
 
 _1_ 
 
 Dl, 
 
 
 m 
 
 
 
 
 
 m_ 
 
 m 
 
 
 2 
 
 3 
 
 
 
 
 
 3 
 
 2. 
 
 1 
 
 1 
 
 1 
 
 1 
 
 
 0 
 
 1 
 
 1 
 
 1 
 
 III/ 
 
 m 
 
 HI, 
 
 m 
 
 
 0 
 
 Hh 
 
 m 
 
 m 
 
 / 
 
 2. 
 
 3 
 
 
 
 
 4 ^ 
 
 3 
 
 2 
 
 f z -i ^ 
 
 m. 
 
 m 
 
 m' 
 
 
 3 
 
 m. 
 
 m. 
 
 m 
 
 m 
 
 1 
 
 1 
 
 m 
 
 Ill 
 
 rn^ m^m^ 
 
 — P 
 
 
 P 1 1 
 
 0 
 
 
 
 
 
 K 
 
 m^ 
 
 3 
 
 
 
 
 
 m^ 
 
 ■3, 
 
 
 3 
 
 m 
 
 z 
 
 
 1 
 
 1 
 
 1 
 
 
 “3 
 
 m 
 
 z 
 
 .r, * 
 
 m 
 
 m^ 
 
 3 
 
 m^ 
 
 X 
 
 1 
 
 m^ 
 
 z 
 
35 
 
 While, 
 
 
 
 
 1 
 
 1 
 
 1 
 
 1 
 
 =- ( 
 
 
 
 “3 
 
 
 ( 
 
 mf 
 
 °C 
 
 “3 
 
 
 
 3 
 
 Di, 
 
 K 
 
 < 
 
 < 
 
 
 B, (m, -m^ 
 
 )(m. 
 
 -m^ )(m, -m^) 
 
 
 K-“, 
 
 )(m^ 
 
 -ni^)(m^-m, ) 
 
 3, 
 
 (in -;n 
 
 ) (ra. 
 
 -m )(m -in ) 
 
 
 3 ^ 
 
 3 
 
 t 
 
 3 ^ 
 
 
 (m -m 
 V / 
 
 )(in 
 
 1 
 
 1 
 
 s 
 
 — 
 
 - P 
 
 m^rr^m^ 
 
 
 1 
 
 1 
 
 
 
 
 
 
 in 
 
 m 
 
 m 
 
 
 
 
 
 2. 
 
 3 
 
 
 
 
 
 
 2. 
 
 m 
 
 3 L 
 
 in 
 
 in*' 
 
 
 
 
 
 X. 
 
 3 
 
 <f 
 
 m, - 
 
 
 1 ( m^- 
 
 m 
 
 ,) ( 
 
 in, - 
 
 m^) 
 
 m - 
 
 3 L 
 
 m^: 
 
 ( n^- 
 
 m.) ( 
 
 in - 
 3 
 
 m^). 
 
 = -P 
 
 ■in^m^m^m^ 
 
 — «p 
 
 in, mt’rn vi 
 
 
 f X. -i 
 
 =. -? 
 
 m, m,,m>. 
 
 = -P 
 
 
 
 -*■ -e ^ e~^ 
 
 /4 cos i ly^t + aj + B cos(!/^t- -4-c^) 
 

 ' . ■■ ■■ ''iv' ,'t.-^;. ■^Jfi.trir, 
 
 . , ^ ^ pv, .>, V, ^ . )^ ( ^,„ , . ^':, 5,4: ,;* 
 
 ki- • lEJ?^'^^' ■'':*.^v-v‘ ••' ■■•■.^*^3i# .'•>■■•'' ' S‘... N ■; 
 
 fc''^"' B®''i’ -' ' 'H'"- .‘V'lW'SI ’i” ' '•'^'■ Vt" ^ . *'■ '■‘*.1^‘& ' ' 
 
 KA-'K»-i^:.-, ^ ;»• 
 
 '' ) ' 
 
 IX i 
 
 ■ I 
 
 '•> -F ' ■■ »♦ 
 
 -■ 
 
 ??i/5 ". 
 
 Kjjo* ** 
 
 
 
 ■'• ii-:J 
 
 ' ^ ,'*^•-*‘ 1 , /r^^tSiUTfS 
 
 - .- - ■ : „ V ^ F V“^r>t, - > 
 
 i ■*' V'V.- \;> i/'"' , .'. JSP'.ft - ■"■ ' ■ '^. 1 
 
 r. \ u* \ '5 o V ''•^ . 4 ^ /S % +■ '^wV.v.v 
 
 jr-’-. t r’ .■.“ 
 
 kli- ■■•4i=*->' '^ 4i a/.f HWB^ 
 
 l-'' ' ^ ■■ ■ '■ ?v5v 
 
 ,..^.4^ ^ «; ' ■ :,i.: .4 r 
 
36 
 
 Part II Heat Energy of Various 
 Ignition Systems 
 
 The opinion is held by ma,ny engineers that if s.n en- 
 gine runs s.t good speed, the gas can be ignited by a sparh 
 with comparatively low heat quantity. However, at start- 
 ing of the engine the heat quantity in the spark is an im- 
 portant factor in igniting the mixture. 
 
 The American Bureau of Standards has measured the heat 
 in unit sps.rks for various ignition apparatus of aerons.utic 
 engine by a calorimetric method. (Report No. 56} 
 
 A simplified form of heat measuring apparatus has been 
 used by the writer in studying this problem. 
 
 General Principle 
 
 T7e introduce a knomi constant heat energy into s. cer- 
 tain apparatus and note the rate of temperature rise caused 
 by this energy. For this purpose, heat created in a re- 
 sistance unit by direct current is accurate. 
 
 Next, we note how ignition sparks in the same apparatus 
 raise the temperature of that appratus. 
 
 Comparing the above two effects, we may compute the 
 heat quantity in a single spark from the following formula. 
 
 watts X 60 
 
 Joules per spark 
 
 Spark per rev. x r.p.m. 
 

 
 I ■'''''■ fi»' ni' '*■'■ 73»"-k»V*, WcU^t 
 
 '4- , -, ♦ 
 
 
 
 S» (f I » 
 
 ^., '^ .. ff\ A I .-v '•*» ^ . i . V , , ^ , Ty. !..\Lfflri>ifi{ #kTWI,' JlLw 
 
 > • 
 
 u 
 
 
 
 ■ ».■* 
 
 ■ a 
 
 
 
 \\ '-S'- tW«Vn;^ ^ 
 
 |iS!‘V:, .^ 210^' ■: 
 
 r‘ « _„ ’. '■ •'- ■ ■ >•- -*;...«“'j' ■■ . <'.'• '*;■.. - . 
 
 A'^ • . «rF U A. -I - V — ,....•_ .. i_ ^ * j ^ j,i#- ■ '« . ■- . . j,-,*/*. ' ' t* :. -B r^. vi 
 
 
 ■ ‘ 1 ^ 1 : ■■' 
 
 . ’ -.i» ki'ur 
 
 ■ ' •rx!!>‘ses rt r^ ^i^i ‘ j > jy^ >- ^ . 
 
 
 >J.v 
 
 .» 
 
 - '9 _ ., ... • 1 if • ' ■ , \ 
 
 ^'(?jiwf.9iwfc, .■t'riiiiwiii^ 
 
37 
 
 Construction of Calorimeter 
 
 The main part of the calorimeter used in this test 
 was made of brass piece set in a double-wal] ed box as 
 shown in Fig* 13. 
 
 Thin aluminum plate forms the inside wall and saw- 
 dust is stuffed between the walls so that we may keep in- 
 side temperature uniform. 
 
 The difference between this method and that of Bureau 
 of Standards is that the temperature of the '’brass wall was 
 measured by thermos -couple in the latter, while in the 
 former temperature of cavity inlthe brass piece was measured 
 by thermometer* 
 

 
 
 I*!*;-- 
 
 It 
 
 J^i' ^ »t/- ' .‘^■•f" . ‘'vr_ •.-‘•TJ • *!> ^ 
 
 .,*in xoll?' /iai'/ ^.'Xr ^ •ilV.'*l a .^>»’^ '• “' 
 
 ;■ L-V''" ’ ' ’ • . 4 ' ' ■ "K ^'r::,.' _ _‘‘^ 
 
 '■■ tWr*/' •' ' y J < jt-* •■/ >'. .■ .fta'.-: 'k ''t . ‘f ■ c''<iW^^ 
 
 . ' V' . , ■ • '. .'C ♦Ai -^X^L ;4 
 
 V ■ ^ •is^t ■.• vv irv-' ■ fe’ ■ 'Si 
 
 «. \.y:.:r^:i. ■ ... - .-/SPii* ;■■»■ 
 
 “' life;.,..,. 
 
 v^. . ; V 
 
 ^ V x' • • . . 
 
 
 
 
 • ■*¥*#,/ 
 
 k .j. '."’> 
 
 
 
 '.- .4 
 
 
38 
 
39 
 
 Process of Experiment 
 
 First the calorimeter was calibrated. For this pur- 
 pose, constant energy was introduced to the cavity for fif- 
 teen minutes, readings of the thermometer v7hich measures 
 the temperature in the cavity being taken every minute. 
 
 The same initial temperature, 35*^C, of the calorimeter 
 was always chosen for beginning either a calibration test 
 or a spark test. 
 
 The rise of temperature is irregular during the first 
 three or four seconds. 
 
 It is vSupposed that this comes from the fact that the 
 initial temperature of the cavity is 35^0, while the tem- 
 perature of the brass piece is not exactly the same as that 
 of the cavity. 
 
 To avoid this Irregularity, we consider the reading 
 at the fourth second as our zero and get ca,llbration of 
 the apparatus as shown in Fig. 13; page 40. 
 
 Several experiments were conducted for different ig- 
 nition systems. 
 
 Two different spark gap lengthes were used, 
 
 and J. 
 
 8 
 
 The results of the experiments are shown in Figs. 1,2,3, 
 
 4 , and 5 • 
 
t 
 
 I 
 
 J 
 
 i 
 
 ( 
 

42 
 

 
 tlr".. 
 
 "i ■',!«»;•. y, : .."^ :i_ ,r.- IX':.^^.. .^‘ • 
 
 • T-.' . ■ -■ '■ •■' • rr(-“ ,- ;r - ■■ ' 
 
 V‘ '"■; 
 
 •■ "in: •: w‘ 
 
 ■J t-- 
 
 -r^i- 
 
 ■i:. 
 
 
 1 I ' 
 
 JH . 
 
 
 
 'fe ix:''! 
 
 j’-V’ ’! . l-^.— ^••r*;:.-i..-.C.‘fc.;' ;f:, _:’ 
 
 K.'VJ: ;;; ,.4 .;:■ /i,- =; ' [-’‘S { 
 
 Fiti 4 rS ■• ....: 
 
 
 
 
 , V i 
 
 ^ io* . v~« • 
 
 ^•*X5-# -> j . 
 
 nr 
 
 
 ' .->T- - ^ /-^ik ■ 
 
 -i ... . .^w., 
 
 
 ^ ■ L -iii : 
 
 r-i 
 
 ;,: ' ;-■ .-:jT?. ■ *; •• 
 
 . . .^ J »44«'.|-: . 4 - .. :^i. 
 
 J- 
 
 r.-f'-.- 
 
 
 tE'-rr" H-.l 
 
 I. ,v- •_ 
 
 r*„', .'.-j: 
 
 •' ' -^' i ''V . * '>■' 
 
 ■ . • . ■ ’ ... f ‘ ; ' , l.»5 . . ■ X ‘ ' 
 
 • 'V .:■ -*7 . • . c; , ^ " ' 
 
 : VS»>4' ■ ' 
 
 . iL.- i n : = 
 
 ■ .r.-...'^ r : '_ • -;.n. n$r.V.;'*’S ^■fl-■7 :,'n^.. "J :' -,• .n: 
 
 • * " ■ ’■' r* ■ ' — •■* *'■ '^■ ~ . • * *■ ^ fr f *- -¥*>» “ •— t — w 
 
 ■ ■■ ■ I' . ‘ ^ ‘ !'‘“'s :;u ■'■'7 
 
 ’ ’ ' . V .-■ -r„ ;,; ‘i^'„ ’ ' '' 
 
 -X.:; 
 
 X,. if.v. »...i,.j v-:^*; LT^nvr- • ir.:rt* — 
 
 
 
 }rtt 
 
 71..:^^. 
 
 
 
 ■' ■* ‘ ' 'i ' : ’ ’: ■ ‘.li^ i' ‘ ~7 '.tJ*lL ' ' ! • • ' ' Jj 
 
 ■'^7 nln.:. 
 
 — J- -f-~ 
 
 n. . 'ilvk- 
 
 
 n ■; :i >-r:|n:fn;,Tfr'':u: ; - n :n 
 
 . .:• -V. ;- - ' .f - •■ ’ . '• . v J. -.'■?.‘nlfi^- 
 
 ■ ■ ■ ---Ttn^nr , ■ .:.,:|'r^- . 
 
 ^'- ■ I, _ 
 
 .• h.. n 
 
 
 
 \ ■ ' 
 
 
 
 -* •- --4 . , 
 
 - . ■ 'f ' :'; u . 
 
 i 
 
 ■ ',U ,. •;...•{* ' ■ •■* • ; 
 
 -J ,, ;.^ t , •., '*7'‘-r! 
 
 
 :rr 
 
 - . ■ I \'tA^ t V 
 
 
 
 
 -!.T 4 .Vr. '-> .'. ■■.-v^'Hr.irl-" 
 
43 
 
 The energy in unit spark depends greatly upon the 
 primary current at the moment of interruption. Theoretic 
 ally it is proportional to the square of the current at 
 interruption, because the energy stored in induction coil 
 is 
 
 W =• I 
 2 
 
 where I ; current at interruption. 
 
 We have already seen that the time to build up the 
 current in the primary circuit is very slow for the Con- 
 necticut Igniter, but very fast for the Atwater Kent system 
 If we close the primary interrupter permanently, the 
 final current, which depends upon the resistance of t]ie 
 primary coil, is larger in the Connecticut system. 
 
 The following oscillograms shows this relation. 
 
 Primary current of the Atwater Kent system 
 
D 1 
 
 ■ I 
 
 , . ■ ->v" ) ' 1 1 if ■ ■‘^- >'-!-■ — 'v^ (S h ^ 
 
 
 ..J ■ *»'•* -o;6'WflftiSi»5'‘e^$,;,rt<%i''B]f!ti;as^ 
 
 f ; ' . ' ' • • - ' n r ■ lfo4 
 
 
 ■W' 
 
 <c 
 
 ^ > 
 
 
 * i 
 
 '#f. ^." Vh;!'' 
 
 >.* . ^c:^*' 
 
 
 r '3 
 
 
 
 
 l^i r"'£!'*' r » •'■ < 
 
 ^ dBk. ' » V 'i’ ■' . ,’**■• 
 
 dfc*? 3 r^ t* ■ ■*■ ■'* jf- 
 
 fl- . 
 
 
 
 W 
 
 
 ' '■. ■ J'i; , 
 
 '#: 
 
 \ 
 
 ■".,.? ' Jif ,»t ,y<^:i'" 
 
 
 
 
 1 ^,-:^/ :-‘ '"' T'.".: ■ 
 
 ii&iilki:: ^■rm ' ■ ; 
 
 ■ 4 i^ 
 
 1 * <' 
 
 F ...^ :r -.v-f^ 
 
 •■’fe , ■'■» 
 
 ■J 5 ', 
 
 *ii^ ■ •;* '•<'* . ;»* '■•: •■ ,' • ” '^' 7 ^’^' ♦ 
 
 MT ' ' i'. ':f^ ' ‘ ; ' ' ' ■'■ ..%/,i. ’■ 
 
44 
 
 Prinarv current of the Connecticut Igniter 
 
 The Connecticut Igniter must have more energy in unit 
 spark at low speeds than has the Atwater Kent. But at 
 higlier speeds, near 1000 r.p.m. of interrupter shaft (cof*- 
 responding to 30 to 40 miles per hour of car speed), the 
 latter yields more energy per spark. 
 
 In the Connecticut Igniter, we can get no spark at 
 
 A 
 
 all at more than 1000 r.p.m, (interrupter shaft) for 4. 
 
 8 
 
 spark gap, while in the Atwater Kent system, we may clearly 
 
 see a spark at 1200 r.p.m. or higher and — spark gap. 
 
 8 
 
 If we change the spark gap length, it seems that at 
 
 low speed the energy is little larger for the larger gap 
 length and smaller for the smaller gap length. 
 

 ■■ » vV' 
 
 
 
 
 
 
 
 
 >. ? '* v 
 
 ^.r 
 
 3 »^f ■' 
 
 \ 3 !^ , ’ •> 
 
 \ 
 
 V 
 
 .■M-y,:, 
 
 ■ ..it'i.'- 
 
 j S tV • ^ 
 
 
 
 
 
 M- ^ 
 
 ■ *'* . I •' ’ . 
 
 
 ■' .;t ‘-^ 
 
 ^■,Xys 
 
 ■ iW'-»:' 
 
 - :. ^ ..*{•• 
 
 . » . V ■-. ,> „ .►■ 
 
 ■ ., i 
 
 , -f 
 
 , ':•■■/ iv ' . 
 
 ,- » ^*S,^ “t 
 
 
 <ir- 
 
 r-. A.- 
 
 
 .* iVl- 
 
 f ^j'l-.'r.'^O.* hi 
 
 
 
 FV 
 
 
 '■A-'V vV-;{ i (•';, 
 
 '»^<iiTi^X' .d '■ v / 
 
 3 i;% 
 
 4 'X.f 
 
 
 >nr.'. .'. i 
 
 
 » >Wl.v 
 
 .T,-' ^:^y?'r. -;i , ;r ;n: 
 
 ® M ' -j-f-* 
 
 .'? -— iV •’•, '' ''^ "’ ■ 
 
 ' ■* 
 
 '• " '■ ' ., , . -V 
 
 * .X/f ■ 'i' 
 
 ■'it'* — '• .ri'j'., - '■, tii**-^'Mt ' <”?1 ^'\- ; J 
 
 \mfs . ^ ’• ’■ L, *7 
 
 • y ■•<-/ 
 
 i ';i '--rT-;.,„l ^ 
 
 -1 - 
 
 ('■‘a 
 
 > ■ i-:. 
 
 '-4 • >; ):: '• *• . f.-,:h 
 
 .'■; •>•- '-v- --<i-'" ■ r?i a;,i 
 
 ' ■■ r ' ' ' ' 
 
 ■>:, .r ! , ^ \ 
 
 '.-f' .t ' , / r' : 
 
 . .. ."i < 
 
 
 
 
 ■ ,<'■'•■) ■■ ■/■•■‘r’- '■,' .'ii< 
 
 ■' Jtr.. 
 
 / I" 
 
45 
 
 In the Phil Brin Igniter, the heat energy in unit spark 
 is large with the high fre luency system. But the high 
 frequency system seems not to he good for the running con- 
 dition of the engine, when we need a rather snappy spark. 
 
 If we use single spark in tnis system, the spark energy 
 is so small that we can not measure It accurately by the 
 calorimeter mentioned above. 
 
 e 
 
 current 
 
 Jlo0iy=>m 
 
 ; Ifrutn SJSiaed 3^o»joM 
 
 
 Single spark of the Phil Brin system 
 
?■ K at. \#/^ \i ft . ^ ' '4».f* "I aoi^w'i^ «>'.5t.J.^aii»- 'ji ^liL, '• ,. I.tll^' _ 'iL^ i' - ^?j ^ 
 
 ' %>' -\ ' -mjLas. .r 'I. h 
 
 
 
 
 »,.v:r 
 
 
 
 
 
 
 , ■ t 
 
 .i' 
 
 ■ ' ■ ■'< ‘ .' ■ tf<^ ' ■<' 
 
 . ,Y>. f/ i '■ I'f^- '^v''^-~i$’ ' ■4*’’' *■ -. 1*','^ *1 ^yviSp^'i'’ *'.% 
 
 r'i 
 
 '^.V: 
 
 
 
 ,. i f. ’j^ 
 
 ■\- - ,_ 
 
 
 
 ' ■■ w -^;^v ■.■-■•* '4«i ' ■ 
 
 ■' is&i/ 
 
 ^ . 'V'.'' :i 
 
 .lt;va, ffXri' ,,ii.fJ!|; 
 
 . - ■ ■ irttv •■ ^ ■■ ' / '*• • V . , :fM 
 
 ■ 4ii 
 
 i<- : ' .v..f;- r ' ./< ‘ ■■ ' iiJ&ffPs'' w‘. ' M ^ 
 
 Kfes! ' . . ■" A‘.'''«i‘'^’’ '■ * -*‘‘T«. < '•■ il ' . '‘’ ' Wi&‘v ■ ‘ r L'” V’'- 
 
 fly* ' V. ' ' - W, ' '• 
 
 
 V'**^ /’"<0 '-l»PW-i 
 
 Ipp 
 
 *...A* »;V^ 
 
 
 lajik « 
 
 
 ■ • / -'.Vvy « ' 
 
 .„ -..r-p .■ - 'Vt,'> " V,.,- ■•,. . 
 
 ' ‘ i jl/V'a. X**-*" •■ *^?v‘' ’ V ’ A iflMfidI 
 
 
 _:. i-^- » . . |> '4* 
 
46 
 
 High frequency sparlc of the Phil Brin system 
 
 Prom the oscillogram for single spark, we see how small 
 is the duration of the interrupter contact. 
 
 The primary current of the high frequency spark has the 
 same nature as that of the ordinary induction coil with 
 magnetic interrupter. 
 

 'ft 
 
 
 
 : i 
 
 
 
 Jti' 
 
 ■V ' *.'•. ^- '- :'r ii'iTCif'.'' ' '■'■‘“i 
 
 
 
 : /? 
 
 ■V-rJ 
 
 ^♦ 1 : 
 
 ^ ^ 1 « 
 
 a 
 
 M? 
 
 ■p;-; 
 
 *L. 
 
 4 
 
 
 ' 1 
 
 
 ^'r. 
 
 '*%y iimmi:^ - " 'jmM "■ ^ ' " : * 
 
 
 
 ■■ ■■*'',. 
 
 0 
 
 
 
 X 
 
 /«.m .XXii!^,.: to' , X-;l 
 
 If. ill 
 
 
 H 
 
 
 
 
 
 i<‘ 
 
 V . 
 
 '■'jt: 
 
 _j^ry, *7 
 
 
 XTt'i 
 
 
 
 } • /. , 
 
 .if 'V V ’ff*."^'-' 
 
 ^"'lisp-St'lBfflE -7 
 
 * -'./X r^. i 
 
 
 '^M 
 
 
 
 ('■' LI 
 
 
 
 Li*.*-: 
 
 
 M ;' ': J ' V" ^ 
 
 iii 
 
47 
 
 
 Appendex 
 I 
 
 n ~ r /' -t- / + M 
 
 ^ '^-3f + cr^ 
 
 Differentiating (1) and (2) v;ith respect to t , 
 
 o = ^ ^ 
 
 <=tt ' cCt^ 
 
 £> =. n + L ■— + M-^' + -i£ 
 c^t ^ c/t^ dt <r^ 
 
 (3) and (4) are rewritten the following way, 
 o = ( /.^ D/+ n Dt--!--^ ) <, + MD^ 4 
 
 ^ = H t. ^ (l^Py tp ^ -^) 4 
 
 ^ 2 
 
 / ^ -o 
 
 ( 1 ) 
 
 ( 2 ) 
 
 (3) 
 
 (4) 
 
 (5) 
 
 ( 6 ) 
 
 (7) 
 
 ( 8 ) 
 
 The equation for the primary current:! (7) 
 
 o = -/h ^/ h 
 
 : 3 ) 
 
 
 
 
 / 
 
 ( 9 ) 
 

 ■- » 
 
 \l^ 
 
 
 
 
 
 
 '• to ' V^ 
 
 V ?y' 
 
 :iiH 
 
 fj 
 
 <5 ••+ 
 
 't 
 
 , <<>' > *?■ V'^-*'isj ■»51 .^¥,i T .> 
 
 gi('/.i^ iif r „>^” T.. V. :4*^'- 
 
 ^ if * -\Q^'> V ■■>^;.w\\;,?!; 
 
 r'-tl--: 
 
 
 '/i "i v' ■ „ ‘ 
 
 
 If 
 
 I: 
 
 '■ 3S 
 
 C^\- ■ 
 
 MM a 
 
 ,‘ftj^,i)^’rt "■ ■ -/■I-' ■■'’ '■:\>|A's#^’'|; 
 
 ^ '■%■ » .. ' ' fA #K« ¥A V* .$t'''i>^ • t I' 
 
 li’^; -■..iM! 
 
 7 .' > .', '>^r. 
 
 
 ' . A , ':' '(, -:,' •;iO ‘;^‘' 
 
 '< ,„_4.; 
 
 ■ , 'r- "T 'i •!**.'_ '^''’,-\a" ' ‘v ' -<'■ lar ■..,. 
 
 ifTiV*'.. ; i ft ■ ^ '^ ■ ' ^ »4 ■ 4‘"<\ '• ■ 
 
 ; .« .3'^X 
 
 , '■'■• / ‘ 4 
 
 
 V. V C „• i"Miiicffr': 
 
48 
 
 Similarly, for the secondary current 
 
 O = { + rc 4 -4 ^^ 4 "^ ^nrjD,^ 
 
 -i / 
 
49 
 
 II 
 
 (e ~t>J{ /-i-kc) 
 
 A 
 
 cr 
 
 < r / -f- Ac 
 
 0 -t~kc)^ 
 
 A ^ 'j-kt) j- dCE-ir) 
 
 (€- ^‘r) C/ -f- 
 
 A C/-hkc)^^ 3 ( / ~hUc)(s~ik)-hCCE-/r) = / 
 
 If ^ , the above equation becomes 
 
 A C/ + A / 
 
 r 
 
 A = 
 
 (TTJe) 
 
 If 
 
 C cs ^-^) =/ 
 
 C - 
 
 A 
 
 r ~hkB 
 
 If i = o , 
 
 E 5 -h 
 
 f r -t-kE )■ 
 
 E 3 ^ / - 
 
 k E 
 
 ^ / 
 
 r-hk B 
 
 (k-f k£j^ 
 K k E 
 
 (r -h keJ-^ 
 
 
 A = 
 
 cr'^ y 
 
 / 
 
 r A 
 
 
 
 
 r + k E for 
 
 a , then 
 
 PI ^k 
 
 and 
 
 Cf 
 
 
 A r _ 
 
 i 
 
 (b - i.rjad 
 
 (/ 'tkc)a^ 
 
 k 
 
I'**’' 
 
 ' <r 
 
 -■»■' '■*' • ■., ML^ • _:' VjIi--»«-iK' • 
 
 ' .. .■ : wybHW ’ *':''■ ,f:'-.fi^ ''”:^k'‘ 
 
 ' ■*: ' T •< w^f , 
 
 
 it’!. 
 
 r- ■» 
 
 
 
 
 
 ■1^. ,;:■> 
 
 
 
 r ' “£?!*.,FS i. 
 
 r?T *v.: ■■ tofV'uil'''' ■ ■ '■•" ■ J 
 
 
 
 ., ,., /■ 4 ’ , ■>**., ••'• — — - '•■- 't '■<*?'... » ■• ' 
 
 i'.^ 
 
 V ' '■• M. 4^- 
 
 ■ • =^r >1 
 
 * - f 
 
 1, , :"t. 
 
 
 ^'A 
 
 % ~ ^ ■* V" 
 
 :MA --> f■^^^ - 
 
 : ./ 
 
 ' -iC 
 
 tr 
 
 :m 
 
 '. '■ 7 ^ A , V.'.s^'i'^ ^ li:"- 
 
 “ ■ . . ^ jaMv , ■ \ .. 
 
 
 m' ... - - 
 
 
50 
 
 III 
 
 C A cos^t -h3 :5>//^^0 
 ^ ^ -V- 3 c:os^tJ 
 
 iv/)er^ A = -3 -c?rjd^ 
 
 p, - Cr^~2:)r-h L.l<^ 
 
 4 
 
 r^ I <=os^t y- s/n^^ ~ L^o(Z aosyt 
 
 L,Io<r 
 
 — Sihst — ^ 4 -^ s/hst -t I o'', Cos^i' 
 
 — czo5^^~ -i- L ^Zo< 
 
 ^ -f- — s//)^t — Sitnpt 
 
 3/>7^zf- - '3//7^ty3 X 5/yst -t-X^C c:€P^^t 
 
 = (k^-^^o'nj <„h/> /■ coyt 
 
 Put 0( ^ J2,, 
 
 X,L. 
 
 _Z“ Z' 
 -*-o '/ 
 
 ('of 
 
 >2 /I 
 
 
 
 ■+ x^r; czosyst