Historical Document · 1964
Filed 16 Oct 1958 (Ser. No. 767,699), granted 4 Feb 1964, 16 claims. Covers the coarse decade-stepped scales with unit-labelled number rows and indicator arrows used on the back of the CIE/Pickett N-515-T to locate the decimal point in reactance and resonance problems. Two drawing sheets with worked settings (Figs. 3-5).
Feb. 4, 1964 D. L. GEIGER 3,120,342 SLIDE RULE Filed OCT.. 16, 1958 2 Sheets-Sheet l Feb. 4, 1964 D. |_. GEIGER 3,120,342 SLIDE RULE Filed OCI.. 16. 1958 2 Sheets-Sheet 2 l 5 1 2li lI I F/Gó f,2z. ¿E A rroRNE YS United States Patent O î Ce 1 3,126,342 Darrell lL. Geiger, Bay Village, t?thio, assigner to Cleve K Patented Fe .. d», 1h64 The body members 14 and 15 are secured together in SUBE RULE the spaced and parallel relation just described by suitable transverse connecting means, such as connecting bars land institute of Radio Electronics, Cleveland, Ghia, a corporation of @hier Filed Get.. 1d, 19%, Ser. No.. 767,699 16 Ciaims. áfCl. 23d-7d) or brackets 18 located at the ends of the body 11 and which rigidly connect the body members without ob structing the guideway 16. The slide member 12 is here shown as being in the form of a flat bar slidable longitudinally in the guide This invention relates to calculating devices of the way 16 and being of a width to iill the guideway so slide rule type having relatively movable members carry 10 that the co-operating edges of the slide member and ing graduated scales and, as one of its objects, provides the body members 14- and 15 will lie in a close fitting a novel form of slide rule usable for a quick and easy solution of certain mathematical problems in the field of electricity, and particularly in radio electronics, which heretofore could be solved by the use of a slide rule only with great difficulty and with doubtful accuracy in the result. The expression “slide rule” as used here in is intended to include devices comprising relatively arcuately movable members, as well as devices com prising relatively longitudinally movable members. Another object is to provide a novel slide rule hav ing graduated scales and associated indicia of such form that mathematical problems can be readily solved with out need for conversion from one unit of measure to another for the values being handled. A further object is to provide a novel slide rule hav ing graduated scales and associated indicia of such form that an accurate determination of the correct decimal relation, as is conventional and desirable in slide rules, and which provides for registering cooperation between the graduated scales of the members as will be described hereinafter. The indicator or cursor 13 can be of a conventional form and includes a transparent body or panel 19 carry ing a hairline Ztl. The indicator 13 is mounted on the body 11 for sliding movement longitudinally therealong 20 in opposite directions and is disposed with the hairline 20 extending transversely across the slide member 12 and across the body members 14 and 15. The slide rule 1li carries graduated scales 22 and 23, which are located on the upper and lower body mem~ 25 bers 1d and 15 and extend along the edge portions of these members which are presented to the guideway 16, and indicia also located on these body members and as sociated with the graduated scales thereof as will be de point location is obtainable immediately and directly in scribed hereinafter. The slide rule 10 further includes the solution obtained of the problem being worked. 30 two graduated scales 24 and 25 carried by the slide mem Still another object is to provide a novel slide rule ber 12 and extending along longitudinal portions there having relatively movable members carrying graduated of, and certain indicia associated with these graduated scales and associated indicia and wherein the indicia com scales as will be described hereinafter. The scales 24 prises symbols and numbers, the symbols being conven and 25 of the slide member 12 extend along the edge tionally recognized as representative of different unit values of certain electrical properties and the numbers portion of this member which is presented toward the upper body member 14. Additionally, the slide rule 1€) being representative of diüerent multiples of such unit carries groups of transversely extending indicator marks values. 27 and 28, preferably arrows, located on the slide mem @ther objects and advantages of this invention will be ber 12 at spaced points therealong and having their apices apparent in the following detailed description and in 40 located at the edge of this member which is presented the accompanying drawings forming a part of this spec toward the lower body member 15. iñcation and in which, In the accompanying drawings the graduated scales FIG. 1 is a partial plan View of one side of a slide 22, 23, 24 and 25, the indicia associated with these rule of the construction provided by this invention; scales, and the indicator marks 27 and 2S are shown as FIG. 2 is a partial plan view showing a modified form of the slide rule; and FlGS. 3, 4 and 5 are partial plan views illustrating the use of the slide rule of FlG. 1 in the solution of occupying only a portion of the surface of the slide rule 11i and, if desired, these designations may comprise all or the major portion of the data intended to be carried by the slide rule. Usually, however, and as shown in typical problems in the ñeld of radio electronics; FIG. FlG. l, this data will occupy only a portion of the 3 representing the solution of a problem in which the 50 surface of the slide rule so that various other portions, frequency of oscillation of a resonant circuit is the value such as the surface portions 29 and 31D which are here to be determined; FIG. 4 representing the solution of a shown as having been left blank, can be used for var problem in which the value of capacitance needed in a ious other data. The reverse side of the slide rule 1@ given resonant circuit is to be determined; and FIG. 5 will usually also be provided with other data including representing the solution of a problem in which the 55 desired scales and indicia. Value of capacitive reactance is to be determined. Before proceeding further with the detailed description As representing a practical embodiment of the pres of the scales 22, 23, 24 and 25 and their associated indicia, ent invention, FIG. 1 shows a slide rule 10 having grad an explanation can advantageously be given of the field uated scales and associated indicia thereon, as will be of use for which this slide rule is intended and the type 60 pointed out and described in detail hereinafter, and in of problems to which it is intended to be applied. As tended for the mathematical solution of certain problems has already been indicated above in a general way, the in the electrical field and particularly in the portion of slide rule 1li is usable to advantage in the electrical field the electrical field which relates to radio electronics. The and particularly in the portion of that ñeld having to do slide rule 1d comprises, in general, a body 11, a slide 65 with radio electronics. Radio technicians, engineers and member 12, and a movable indicator 13. others are »frequently confronted with mathematical prob The body 11 is here shown as comprising a pair of lems concerning the oscillation frequency of a resonant flat parallel bars or body members 1d and 15 spaced circuit and concerning the mathematical values of various apart so as to provide a longitudinal guideway 16 there electrical properties of such a circuit or of the components between and which body members appear, in FIG. 1, in a relation such that the body member 14 is the upper member and the body member 15 is the lower member. thereof, such as resistance, capacity, inductive reactance and capacitive reactance. To further illustrate the kind of mathematical problems 3,120,342 er» encountered by radio technicians, and others, and for the solution of which the slide rule 1th` has been designed, three equations are given as follows as being representative of those problems: (Equation l) f numerical value in millionths of a farad, or decimal-wise, by a numerical Value of 10‘6. Likewise, when the value of capacitance is expressed in micromicrofarads, it will be expressed decimal-wise by a numerical value of 10‘12. Similarly, an inductance in millihenrys will be expressed numerically in thousands of henrys, or decimal-wise, by a numerical value of 10‘3 and microhenrys will be ex in which f is oscillation frequency in cycles per second; L is inductance »in henrys; and C is capacitance in -farads. pressed decimal-wise by a numerical value of lO-s. With respect to oscillation frequencies, a designation in kilo cycles represents thousands of cycles, and when expressed (Equation 2) :ce in which XC is capacitive reactance; f is oscillation fre quency in cycles per second; and C is capacitance in farads. in megacycles means millions of cycles per second. ln the case of reactance, the value thereof expressed in meg ohms would be in millions of ohms. From the range of values indicated just above, the seriousness and diíïiculty xL=21rfL 15 of the decimal point location is readily apparent when to convert one or more of the various values from one tical length and have the same num er of gradufartions. (Equation 3) the solution of aproblem involving such numerical values in which XL is inductive reactance; f is oscillation fre is attempted on a slide rule. quency in cycles per second; and L is inductance in henrys. Revel-ting now to FIG. 1 of the drawings, the charac 11n the three equations given just above it will be ob teristics of the` graduated scales, the indicia and indicator served that each equation contains three unknown quanti 20 marks will now be described. The scales 22, 23, 24 and ties. lt will therefore be recognized that in the solutions 25 -all are graduated lineal scales, that is, scales in which of these equations for the unknown quantities thereof the graduation marks of each scale are spaced apart at there will be a possible total of nine different problems _substantially equal distances therealong. ln the case of to be solved. the scales 22, Z4 and 25, the graduation marks 32 thereof ln the usual solution of mathematical problems of the are spaced apart by the same equal distances. These kind represented by the above equations, it is necessary three scales yare here shown as being of the same iden unit of measure to another. Thus, for example, the value of capacitance can be expressed in farads, microfarads, ln the scales 22, 24- and 25 the »graduations comprise main graduation marks 32a and intermediate or second or micromicrofarads. Likewise the value of inductance 30 ary graduation marks 32h. Two of the intermediate grad may be expressed in henrys, millihenrys or microhenries. uation marks 32h are located at spaced points between The value of oscillation frequency may be expressed in Ieach pair of main graduation marks 32 so as to divide cycles per second, lkilocycles per second or megacycles the distance between each such pair of main graduation per second, and similarly, the values of reactance may marks into three spaces whose llengths relative to each be expressed in ohms or megohms. 35 other >are represented by the integers 3, 4 and 3 which One of the important advantages of the slide rule lo, have a total value of '10. The end spaces corresponding as will be explained in detail hereinafter, is that this in value with the integers 3 are of equal length `and the conversion from one unit of measure to another which center space corresponding with the integer 4 `is relatively has heretofore been unavoidable in the solution of prob longer. 40 lems in radio electronics, now becomes unnecessary. The graduated scale 23v of the lower body member l5 ‘It has been conventional in the field of electricity and comprises main graduation marks 33 and intermediate radio electronics to designate units of measure, used for graduation marks 33a. In this case the spaces between various dilferent electrical properties of the ‘kind mentioned each pair of main graduation marks 33 is divided into just above, by different symbols. Since a number of two intermediate spaces of equal length which is accom these conventional symbols appear in the indicia used on plished by Athe use of a `single intermediate graduation the slide rule 10, various ones of these conventional 45 mark 33a between each such pair of main graduation symbols and the recognized meanings thereof are given marks. The intermediate graduation marks 33a are each hereunder. provided with the numeral 3. The numerical designa tions for the intermediate graduation marks 35a arev only Cuf, means capacity in microforads. approximate as to the division of the distances between CMAq means capacity in micromicrofarads. the main graduation marks 33 but is .appropriate and In. means inductance in henrys. suitable for the uses of the slide rule 1t). Lmh, means inductance in millihenrys. Reference has been made hereinabove to indicia pro LM,A means inductance in microhenrys. vided on the slide rule lil and associated with the gradu f means oscillation frequency in cycles per second, fm means oscillation frequency in kilocycles per second. 55 ated scales 22, ‘23, 21t- and 25. This indicia will now be described `and comprises symbols. or groups of symbols )tmcI means oscillation frequency in megacycles per second. and numbers or rows of numbers. ln the case of the XC@ means capacitance reactance in ohms. `graduated scale Z2 the symbol portion of the indicia `com XCMQ means capacitance reactance in niegohms. prises a symbol group 3d located adjacent the left-hand XLS! means inductive reactance in ohms. 60 end of this `graduated scale. This symbol group com XLMSZ means inductive reactance in megohms. prises three symbol rows 34a, 3th and 34C. The numerical In dealing with electrical properties and Values in prob portion of the associated indicia comprises three number lems of the kind referred to above, very large and very rows 35a, 35h and 35C. The associated indicia also com small Values will be encountered. This makes the solu prises ‘groups of directional arrows 36 associated with tion of the problems on a conventional slide rule very 65 the number rows 35a, 35h and 3'5" and preferably located diñicult, particularly with respect to the correct location at the ends of, and in alignment with, these rows. of the decimal point. Another important advantage of The symbols of the row 34a of `the symbol group 3d the slide rule lll is that «the correct location of the decimal comprise -two symbols written as the alternative expres point is easily and correctly determined directly from the sion C„f_ or Lh_. This symbol row 34a is aligned with scales and indicia provided on the slide rule, as will be further explained hereinafter. To further point out the ditliculty presented by the above-indicated problems with respect to the decimal point location, it is pointed out that when capacitance is referred to as being in microfarads, it will be expressed by a the number row 35a and indicates that the numerical values of this number row represent different values of the electrical properties designated by the symbols CML and *Lhl or, in other words, values-of capacity in micro ‘farads cfr values of inductance in henrys. rfhe numbers 5 appearing in the number row 35EL cover a range of deci 3,120,342 5 mal-scale numerical values appropriate for the vvalues of capacitance which are likely to be encountered in the solu tion of the problems when the capacitance is expressed in microfarads, and likewise, are appropriate `for the values of indu‘ctance to be encountered when the induct ance is expressed in henrys. The intermediate symbol row 34h contains only the single symbol Lmh, which represents inductance in mill" henrys and the number row 35h aligned with this symbol provides decimal-scale numerical values appropriate for the problems to be encountered for expressing induotance in the units indicated by the associated symbol, namely, graduations and secondary numbers 2, 3 and 6 located opposite the intermediate graduations and representing proportionate parts of the main numbers between which these secondary numbers appear. The indicia associated with the graduated scale 23 also includes directional arrows associated with the number rows 39e, 39D and 39C. in this case, two groups ¿il of such arrows are provided and are located at the ends of the number rows. The arrows ¿la and 41C located adjacent the number rows 35a and 39° point toward the right to indicate that the numerical values of the numbers of these number rows increase in value progressively toward millihenrys. the right along these number rows. Similarly, the arrows The symbol row 3d@ is similar to the symbol row 34a ¿zlib at the ends of the number' row 39h point toward the but comprises two symbols in the alternative expression left to indicate that the numerical values represented by CIM. or Lßh, and which symbols signify that the numeri the numbers oi this row increase progressively toward cal values or the aligned number row 35° are to be read the lett along the row. as values of `capacitance in m-icromicroiarads or values The graduated scale 24 of the slide member 12 is pro or" inductance in microhenrys. vided with graduation marks of the same number and The directional arrows 36 are provided to visually indi 20 spacing as the graduation marks of the graduated scale cate the direction of increasing values for the number ZZ, and the intermediate graduation marks 32h are also rows 35a, 35D and 35C. All of the arrows 36 associated provided with numbers 2 and 5. The numbers 2 and 5 with these number rows point toward the lettt to indicate serve the same purpose as was described above for the that the values of the numbers appearing in these rows scale 22 but, in the case oi the scale 2d, they are arranged increase valong the rows progressively toward the left. 25 so that the numerical values represented by the intermedi The arrows 36 thus provide a quick visual designation or” ate graduations increase in amount toward the right along the direction along the number rows 35a, 35h and 35C the scale to agree with the direction of value increase for the majority of the number rows described hereinafter in which the hairline 2li, or the scale 24, should be moved as being associated with this scale. The graduated scale for associating the same with numbers of successively 30 2li is of the same length as the scale 22 and, accordingly, increasing numeral value. its graduations will register exactly with the graduations of lt should also be pointed out with respect to the num the latter scale when the slide member l2 is positioned in bers of the number rows 35a, 351° and 350 that the nurn the guideway lo at the location shown in FIG. 1. bers of these rows are located opposite main graduation The indicia provided on the slide member l2 and associ marks 32 of the scale 22, and that the numerical values represented by the numbers of the respective rows are 35 ated with the graduated scale 2d- comprises a symbol group ¿i2 and number rows 43a, 43h and 43C extending decimal-scale values. lt will also be observed that the along this graduated scale. The symbol group d2 com numbers 2 and 5 designating the intermediate graduation prises three rows of symbols 42a, 421° and 42° located in marks 32h ot' the scale 22 represent proportional values a longitudinally aligned relation with the respective num in the number rows for values falling between the num ber rows 43a, @3b and 43C. bers actually shown in the respective number rows. lt The symbol rows 42“, 42h and 42C consist of one sym can now also Ibe explained that Ithe numbers 2 and 5 asso bol each; the row 42a containing the symbol fans. desig ciated with the intermediate grad-nations of the scale Z2 nating oscillation frequency in cycles per second; the sym are shown as increasing in value toward the left because bol row 42h containing the symbol fkc. designating oscilla the numbers of all of the number rows 35a, 35b and 35a tion frequency in kilocycles per second; and the symbol increase in value in Ithat direction. row 42° containing the symbol fm. designating oscillation The indicia associated with the graduated scale 23 of frequency in megacycles per second. The number rows the lower body member 15 comprises a symbol group 3d 433, 43h and d3@ comprise numbers representing decimal located adjacent the lett end of this scale and number scale numerical values likely to be encountered in the rows 39a, 39h and 39C extending longitudinally along the scale. The symbol group 3S comprises three rows of 50 solution ot the above problems for electrical properties symbols 38a, 38h `and 38C located opposite the number designated by the symbols opposite which these number rows 3W, 39h and 39C respectively. ln this case the symbol rows consist of only one symbol each, «the row rows are located. Fthe numbers of the number rows 43a, The numbers of the number rows 39a, 39h and 39s are in the decimal scale and the numerical values of the numbers of the respective number rows are appropriate includes groups of directional arrows 45 located adjacent the number of rows 43a, 43h and 43C, in this case adjacent the ends of these number rows. All of the arrows Lit? 43h and 43C are located opposite the main graduations 3.2au of the graduated scale 24. 33a containing the symbol Xg, the row 38h containing the 55 The indicia associated with the graduated scale 24 also symbol XL, and the ro-w 3S@ containing the symbol f. for the electrical properties represented by the symbols 60 point toward the right to indicate that the numerical Values cal values of the number row 39a are appropn'ate to represented by the numbers of the number rows 43a, 43h and 43€ increase in value toward the right along these designate ìdilierent decimal-scale values or” capacitive re rows. of the appurtenant symbol group 38. Thus, the numeri actance, as represented by the symbol XC of the symbol The indicator marks 27, referred to above as being pro row 3521. Similarly the numerical values of the number 65 vided on the slide member l2, are associated with the row 39h represent difieren-t decimal-scale values of in graduated scale 24 and are used for taking readings from ductive reactance, as indicated by the symbol XL of the the graduated scale 23 or for co-operation with the latter symbol row 33h, and the numerical values of the number scale to indicate a desired setting of the slide member l2. row 39C represent diíïerent decimal-scale values of oscil These indicator marks are here shown as being of the lation :frequency as indicated by the symbol f of the 70 arrow type and disposed with the apex of the arrow point symbol »row 38”'. ing toward the graduated scale 23 and located at the ex The numbers of the number rows 3?@ and 3911’ are lo treme lower edge ot the slide member. In the slide rule cated opposite the main graduations of the scale 23. The it?, the indicator marks 27 are used specifically for read numbers shown in the number row 39C comprise main ing or setting values of reactance on the scale 23 and, numbers ¿il in multiples of l() located opposite the main 75 accordingly, indicia is provided adjacent these indicator entrasse 7 5?: marks for designating different measurement units for the shown and these marks are appropriately spaced along the site ends of the number rows 53a, 53h and 53C, and all of which arrows point toward ythe right to indicate that the numerical values represented by the numbers of these number rows increase toward the right along these num portion of the slide member l2 on which the scale 21t ber rows. value of reactance being read or set on the latter scale. In> this case there are four of the indicator marks 27 is located. The indicator marks 27a and 27h are used for The indicator marks 28, previously referred to as being reading or setting values of capacitive reactance on the scale 23 and, accordingly, these two indicator marks are provided on the side member 12, are located on the por tion of this slide member which carries the graduated scale 25 and consist of the indicator marks 2da, 28h and capacitive reactance. For this purpose the indicator mark l() ZSC. These indicator marks are appropriately spaced apart along this portion of the slide member l2 and are 2‘7à is provided with the value designation symbol X052 here shown as being in the form of arrows disposed with which designates capacitive reactance in ohms. The indi the apices thereof pointing toward the lower body mem cator mark 27b is provided with the value designation ber l5 and located at the lower edge of the slide mem symbol XCMQ designating capacitive reactance in meg ohms. 15 ber l2. The indicator marks 23 are used inco-operation with The indicator marks 27C and 27d are used for reading the graduated scale 23 and the indicia associated with the 0r setting values of inductive reactance on the graduated latter for reading or setting values of oscillation fre scale 23 and, accordingly, these indicator marks are pro quency. These indicator marks are accordingly provided vided With value designation symbols indicating inductive reactance. For this purpose the indicator mark 27C is 20 with designations representing diiîerent measurement units of oscillation frequency. The indicator mark 28e is pro provided with the symbol XLS) designating inductive re vided with the symbol falls. designating oscillation fre actance in ohms, and the indicator mark 27d is provided quency in cycles per second, theindicator mark Zßb is with the symbol XLMSZ designating inductive rea/¿tance in provided With associated indicia representing values of megohms. provided with the symbol fkc. designating oscillation fre If desired, a suitable legend may be provided adjacent 25 quency in kilocycles per second, and the indicator mark 28C is provided with the symbol fmc_ designating oscilla the row of indicator marks 27 to indicate the general pur tion frequency in megacycles per second. pose for which these marks are intended to be used. ln this instance such a legend d@ has been provided and comprises the expression “Reactance Problems” to signify If desired a suitable legend can be provided adjacent the row of indicator marks 28 to indicate the general that this portion of the slide rule is intended for the 30 purpose for which these marks are intended. Such a general purpose of solving reactance problems. legend 54 is shown on the slide member l2 and com The graduated scale 25 carried by the slide member 12 comprises graduations of the same number and spacing prises the wording “Resonance Problems” to signify that right of the graduated scale 24. The scale 25 is provided that when the graduations of the graduated scales 22 With the same indicating numerals 2 and 5 for its inter and 24 are in exact registration, these indicator marks the indicator marks 2S and their associated symbols are intended to be used in the solution of resonance problems. as those of the graduated scale 2d. and is of the same With respect to the location of the indicator marks 27a, length as the latter scale but is located on another portion 35 27h, 27C and 27d on the slide member l2., it is explained of the slide member, in this case a portion located to the will lie at points along the graduated scale 23 which are mediate graduations as the scale 2d, and these indicating numerals are arranged to increase in value toward the right 40 located at 0.159 of the length of the main scale spaces opposite which these indicator marks then stand. Simi the same as the 2 and 5 indicating numerals of the scale Z4. The graduated scale 25 extends along the upper lon larly, with respect to the location of the indicator marks gitudinal edge of the slide member l2 so that, by move 23h and 28° on the slide member l2, it is explained that when the graduations of the graduated scale 25 are in ment of the slide member to the left, this scale can be brought into co-operation or registration with the gradu exact registrationwith the graduations of the scale 22, ated scale 22. these indicator marks will lie at points along the scale 23 The indicia provided on the slide member T12 and which are located at 0.318 of the length of the main associated with the graduated scale 25' comprises a sym scale spaces opposite which these indicator marks then bol group 52 and number rows 53a, 531’ and 53C extend stand. The indicator mark 28a is proportionately located ing longitudinally adjacent the graduated scale. The sym 50 on the slide member 12 relative to the indicator marks bol group 52 comprises three symbol rows 52a, 52h and 52C located opposite the respective number rows 53a, Sâb and 53C. The symbol rows and the individual symbols of the Zöb and 23C but falls outside of the length of the gradu symbol group 52 are the same as the symbol rows and ated scale 23 for the reason that the progression of nu merical values of the number row 39€ has not been ex tended for the distance which would be necessary to serve this indicator mark 28a. individual symbols of the above-described symbol group 34. Thus, the row 52EL comprises two symbols arranged to :form the expression CM, or lah. which designates ca pacitance in microfarads or inductance in henrys. The FIGS. 3, 4 and 5 of the drawings show the slide rule l0 with the movable components thereof in different set tings to illustrate the manner of using the slide rule in the solution of three different typical problems in radio symbol row 52h comprises the single symbol LWL desig nating inductance in millihenrys. The symbol row 52C comprises two symbols forming the expression C/„m or Lm which designates capacitance in micromicrofarads or inductance in microhenrys. The number rows 53a, 531’ and 53C comprise numbers in decimal-scale values and appropriate for designating different numerical values of the electrical properties represented by the symbols of the symbol group 52,. The umbers of these rows are located opposite the main graduations 32 of the scale 25. The intermediate gradu ation numbers 2 and 5 of the scale 25 are used to indicate approximate numerical values occurring between the nu merals shown in the number rows 53“, 531’ and 53C. The indicia associated with the graduated scale 25 also includes groups of directional arrows 53 located at oppo 60 electronics. FIGS. 3, 4 and 5 have been drawn so as to be self-explanatory in regard to the illustrated use of the slide rule il@ for solving these three typical problems, but a brief explanation is given hereunder of the proced ure represented in these views. The problem being solved in FIG. 3 is a resonance problem and, for that reason, the portion of the slide member i2 carrying the graduated scale 25 has been moved into co-operation with the graduated scale 22. The problem here illustrated relates to a situation in which an inductance of 40 millihenrys is connected in parallel circuit with a capacitance of 0.03 microfarad and the problem briei'ly stated is to determine at approximately what frequency in cycles per second this parallel circuit will resonate. As the ñrst step in the solution of this problem, FIG. 3 3,120,342 shows that the indicator 13 has been moved to a position along the graduated scale Z2 at which the hairline 20 is at a setting of 0.03 microfarad capacitance and which setting is determined by reference to the symbol line 34a and its appurtenant number row 35a. The exact setting of the hairl-ine 20 at this value is determined, first, by referring to the main numerical values of this number row and, second, by referring to the numbers associated with the intermediate graduations of the scale 22. This setting of the hairline 20 is designated by the broken-line arrow S5. After the hairline 20 has been thus set at the proper location on the graduated scale 22, the slide member 12 is moved to bring a setting value thereof representing 40 rule l0 in the solution of a reactance problem in which it is desired to determine the approximate value of ca pacitive reactance in ohms of a capacitor of 0.005 micro farad capacitance when used in an oscillation circuit which is resonant at a frequency of 3 megacycles. This prob lem is solved by first setting the hairline 20 at a point along the number line 35a and graduated scale 22 corre sponding with the given value of 0.005 microfarad ca pacitance, as indicated by the broken-line arrow 65. The slide member l2 is then moved to bring the value of 3 mega-.cycles of the number row 43C into register with the hairline 20, as indicated by the broken-line arrow 66. The desired approximate value of capacitive reactance, namely l0 ohms, is then read directly from the number millihenrys of inductance into register with the hairline. 15 line 39a and the graduated scale 23 at the point there This value of inductance is located on the slide member along indicated by the indicator mark 27a. The reading 12 as being in the number row S31’ which is opposite the of the desired approximate value of capacitive reactance symbol row 52h. The general location for this setting as the last step of this solution is indicated by the broken of the slide member l2 is determined from the numerals line 67 and by the broken-line arrows 655 and 69. of the number' row 53h, and the more exact setting is 20 2 of the drawings shows a modified construction determined from the intermediate graduations of the grad provided by this invention for a slide rule 70 of a form uated scale 25. The setting of the slide member l2 as generally similar to the slide rule l0, but in which a com thus determined, is shown in FIG. 3, and is indicated by posite scale and indicia data is provided on the slide the broken-line arrow Si?. member _l2 for solving reactance and resonance problems The final step in the solution of the problem illustrated instead of the two scales shown in FIG. l. in FIG. 3 is to read the oscillation frequency directly ln the modified slide rule 70, graduated scales ’72 and from the numerical values of the number row 39C. Thus, '73 are provided on the upper and lower body members if the oscillation frequency is desired in cycles per second, ld and 315 and correspond with the scales 22 and 23 of the reading is taken from the number row 39e as indicated the slide rule l0. Symbol groups 34- and 38 are also pro by the broken-line arrow 5'7 and at the point designated 30 vided on the members ld- and l5 and comprise the same by the indicator mark 28a. This frequency value would symbols as the corresponding symbol groups of the slide be approximately 5,000 cycles per second. lf the oscilla rule l0. Number rows 74€”, 74E-'D and 74° are provided on tion frequency is desired in kilocycles, the reading is the upper body member ll-d in alignment with the symbol taken from the number row 39C as indicated by the rows of the symbol group 3d and correspond with the num broken-line arrow 58 and at the point thereof opposite 35 ber rows 35a, 351’ and 35C of the slide rule l0. Likewise, the indicator mark 2gb. This frequency value would be number rows 'i523 "í5`n and 75C are provided on the lower approximately 5 kilocycles. body member l5 and correspond with the number rows In reading the value of oscillation frequency from the 30a, 39h and 39° of the slide rule l0. The numerical number row 39", it may be desirable to shift the hairline values, however, of the number rows 74a, ‘71th and 'îfic and 20 to a position in register with the indicator mark being 40 of the number rows 75a, 75h and 75C are somewhat dif used because the hairline will then extend across the num ferent from the numerical values of the corresponding ber row 39C at the point where the frequency value is to number rows of the slide rule lil but still are decimal be read. This relocation of the hairline 20 in register scale values and are appropriate for the composite char with the indicator mark Ztl@ is represented in FIG. 3 by acter of the scale and indicia data provided on the slide the broken line 20a, and the relocation of the hairline in 45 member l2 of the modified slide rule '70. register with the indicator mark 23h is represented by the The slide member l2 carries a graduated scale '77 which broken line 20h. corresponds with the graduated scale 2d of the slide rule FIG. 4 illustrates the use of the slide rule l0 in solving l0 and number rows '73%, 73h and 73C corresponding with a problem where the value of the capacitance of an oscil the number rows 43a, 43h and 43°. The decimal-scale lation circuit is desired to be obtained. A typical problem 50 numerical values of the number rows 78a, 73h and '73° are of this kind would be to find the approximate capacitance somewhat different, however, by reason of the composite value which would be required in an electrical circuit hay character of the indicia provided on the modified slide ing 350 microhenrys of inductance to resonate at an oscil rule 70. lation frequency of 200 kilocycles per second. In the The slide member l2 of the modified slide rule 70 also solution of this problem as represented in FIG. 4, the 55 carries a symbol group 79 which includes all of the sym slide member l2 is moved to a position where the indicator bols of the symbol group 52 and all of the symbols of the mark 23h will co-operate with the graduated scale 23 symbol group d2. The symbol group '79 comprises three of the lower body member l5 to designate on the latter symbol rows 7de, ’79h and ’7%0 in aligned relation with the the desired value of resonant frequency. This setting three number rows 73a, 72d) and 723C respectively. for the indicator mark ill@ is at a point along the number 60 The slide member l2 of the modified slide rule ’70 also row 39@ corresponding with the 200 kilocycles oscillation carries two groups of indicator marks for co-operation frequency value, as is represented by the broken line 60 with the graduated scale 73 of the lower body member lf. and the broken-line arrow 6l. The indicator i3 is then One group of these indicator marks comprises the marks moved along the slide rule to bring the hairline 20 to a point on the number row 35° and the graduated scale 22 at 65 30a, blib and 80C and are provided with the same oscilla tion frequency symbol designations as the indicator marks which the hairline will designate a reading of 350: micro 23e, 28h and 2SC of the slide rule l0. The other group of henrys, as indicated by the broken-line arrow d2. The indicator marks comprise the marks Sie and ‘dll’ which desired value of capacitance is then read directly from the are used in the solution of reactance problems and serve indication given by the hairline 20 on the number row 53EL and the graduated scale Z5. The taking of the desired 70 the same purpose as the four indicator marks 27a, 217D, 27C reading of capacitance from the number row 35° and the and 27d of the slide rule lil. ln this case, however, the graduated scale 22, namely the value of approximately indicator mark Si@ is provided with symbols designating both capacitive reactance and inductive reactance, namely the symbols X00 and XLS). Similarly the indicator mark lilG. 5 of the drawings illustrates the use of the slide 75 Sib is provided with symbols designating both capacitive 0.003 microfarad, is indicated by the broken-line arrow 3,120,542 ri l?, reactance and inductive reactance, namely the symbols spaced first indicia representing decimal scale multiples of said unit values, respectively, and other indicia interme XCMQ and X39. The modified slide rule 7@ possesses the advantage that when the graduated scales and indicia for the solution of both reactance and resonance problems are combined on the slide member l2, there is a saving of space and the slide rule can either be of a shorter length or, if of a full length, a greater portion of its surface will be available for other scales and data. From the accompanying drawings and the