Densitometer
United States Patent Schlatter Apr. 15, 1975 DENSITOMETER 3.772.915 11/1973 Stamler 235/151.34 x 3.775.597 ll I973 N b 235 lSl.3 X  
 [75] Inventor: Gerald Lance Schlatter, Boulder. Ovem er Colo Primary Examiner-Eugene G. Bot: [73] Assignee: International Telephone and Assistant Exam1&#39;ner-Edward J. Wise Telegraph Corporation. New York Alrorney. Agent. or Firm-A. Donald Stolzy 221 Filed: Dec. 10, 1973 [57] ABSTRACT Appl. No.: 423,409  
 A vibration densitometer including a closed loop electromechanical oscillator for vibrating a fluid immers ible vane. A digital output directly proportional to density is achieved through a unique digital squarcr.  
 [52} US. Cl. 235/l51.3; 73/32; 235/l5l.34;  
  235/1505?J The densitometer is an all digital system. in the loop. [5 1] Int Cl G06 15/34; Gm 9/00 a tracking filter is provided. Separate search and track [58] Fwd 0&#39; Search 235/1513 [5134 92 MT automatic gain control feedbacks are provided. A 235/92 CP 92 R 197 73/30 threshold detector controls clamps and a gate to cause v [94 M the voltage controlled oscillator of a first phase lock loop to search or track the vane resonant frequency. [56] References Cited The threshold detector also effects the search feedback. A phase adjustment circuit and a second phase UNITED STATES PATENTS lock loop are employed to impress a sine wave voltage h 33 3; :2 component on the vane driver of a phase which crelfetfl... 3,769,500 10/1973 Schlatter 235 15134 x mmmum emclency&#39; 3,769,831 1 [H973 Schlatter 73/32 41 Claims, 22 Drawing Figures TENTEHPR. 5am  
 SHEET 5 BF 9 FIGJI.  
 FIG. I2.  
 [)ENSITOMETER BACKGROL&#39;ND OF THE INVENTION This invention relates to vibration densitometers. and more particularly. to an improved densitometer and a digital function generator therefor for producing a digital output directly proportional to density.  
  \&#39;ibration densitometers are essential digitally inclined instruments because the density they indicate is a function of their ibrational frequency. Howe\ er. thc present time. no highly accurate or inaccurate digital linearization circuit has been employed with such in struments.  
 SUMMARY OF THE INVENTION In accordance with the present invention. the abovedescribed and other disadvantages of the prior art are overcome by providing a digital function generator for very accurately lincarizing the output of the electromechanical oscillator of a vibration densitomcter.  
  Other features of the invention reside in the use of a search or sweep feedback and an automatic gain control (AGC) feedback.  
  Still another feature of the invention resides in the use of a threshold detector for search. track and feed back control.  
  A further feature of the invention resides in the use of a phase adjustment circuit and phase lock loop to ef fect ma\imum drive efficiency.  
  The above-described and other advantages of the present invention will be better understood from the following detailed description when considered in connection with the accompanying drawings.  
 BRIEF DESCRIPTION OF THE DRAWINGS In the drawings. which are to be regarded as merely illustrati\e:  
  FIG. I is a block diagram of a densitomcter constructed in accordance with the present invention;  
  FIG. 2 is a block diagram of a loop circuit shown in FIG. I;  
  FIG. 3 is a schematic diagram of an input circuit. an AGC amplifier. a tracking filter. two zero crossing detectors. two phase detectors. two low pass filters and a clamp shown in FIG. 2;  
  FIG. 4 is a block diagram of a phase lock loop shown in FIG. 2;  
  FIG. 5 is a schematic diagram of a phase adjustment circuit. an AND gate and an inverter shown in FIG. 2;  
  FIG. 6 is a block diagram of another phase lock loop shown in FIG. 2;  
  FIG. 7 is a schematic diagram of a low pass filter shown in FIG. 6:  
  FIG. 8 is a schematic diagram of a driver amplifier shown in FIG. 2;  
  FIGS. 9. III. II. I2 and 13 are graphs of a group of waveforms characteristic of the operation of the loop circuit shown in FIGS. 1-8. inclusive:  
  FIG. I4 is a more detailed block diagram of the digital function generator shown in FIG. 11;  
  FIG. is a more detailed block diagram of a square low digital computer shown in FIG. 14;  
  FIG. I6 is a still more detailed block diagram of a divider and rate multiplier shown in FIG. 15;  
  FIG. 17 is a front elevational view of a set of lamps conventionally used to. when gated on at appropriate (ill intervals. display selecthely one of the ten digits l-9 and (I:  
  FIG. I8 is a block diagram of alternative embodiments of a divider and rate multiplier shown in FIG. 15:  
  FIG. I) is a switch matrix which may be employed with a counter shown in FIG. 18 to produce serial pulses in serial groups where the number of pulses in a group is directly proportional to the binary setting of the switches in the matrix of FIG. I9;  
  FIG. 20 is a block diagram of an alternative embodiment ofthe digital function generator shown in FIG. I;  
  FIG. 2I is a block diagram of a conventional off-set digital computer; and  
  FIG. 22 is a graph ol&#39;a group of waveforms characteristic of the operation of the digital function generator shown in FIG. 20.  
 DESCRIPTION OF THE PREFERRED EMBODIMENTS In the drawings. in FIG. I. a vibration densitomcter probe is indicated at 34&#39; having a driver coil 23 a \ane 24. a piezoelectric crystal 25 and a preamplifier 26.  
 Probe 34&#39; has an input lead 27 and an output lead 28.  
  Other blocks shown in FIG. I are a loop circuit 1 a digital function generator and utilization means SI. Loop circuit 29 has an input lead 32 and output leads 33 and 34. Digital function generator 30 has an input lead connected from loop circuit output lead 34. The output of digital function generator 30 is connected to utilization means 31.  
 The output lead 28 of probe 34&#39; is connected to the input lead 32 of loop circuit 29. The input lead 27 of probe 34&#39; is connected from the output lead 33 of loop circuit 29. Probe 34&#39; and loop circuit 2) form a closed loop electromechanical oscillator. \ane 24 is submerged in a fluid. The density of the fluid is a function of the frequency at which vane 24 \ibrates.  
  Digital function generator 30 may have its input lead 35 connected from lead 33 or at other points in loop circuit 2). Loop circuit 29 impresses a square wave voltage on input lead 35 of digital function generator 30 having a mark-to-space ratio of I11.  
  Utilization means 3] shown in FIG. I may be a density indicator. a specific gravity indicator. a process controller or otherwise.  
  Throughout this description. reference will be made to the text ofcertain L&#39;.S. patents and LS patent applications. These patents and patent applications are listed for convenience forthwith.  
 Reference is hereby made to the following patents:  
 l. LS. Pat. No. 3.677.067.  
 Z. L&#39;.S. Pat. No. 3.706.220.  
 3. L15. Pat. No. 3.738155.  
 4. US. Pat. No. 3.74I.tltlll.  
  The foregoing patents of paragraphs l l. (1].(3) and (-l) are hereinafter referred to as patents PI. P2. P3 and P4. respectively.  
  Reference is hereby made to the following L&#39;S. patent applications:  
 I. LYS. Pat. application Ser. No. 161.025 filed July 9.  
  I97l. for DENSITOMETER COMPONENTS by G. L. Schlatter.  
 2. ES. Pat. application Ser. No. INS-l8 filed Oct. l2. l97l. for FLLID SENSING SYSTEMS by G. L. SchIatter-C E. Miller.  
 3. US Pat. application Ser. No. 270.335 filed July It). I972. for DENSITOMETER by G. L. Schlatter.  
 4. I15. Pat. application Ser. No 2S9.77U filed Sept.  
  l6. I973. for \IBRATION DENSITOMETER AP- PARATLS h G. I.. Schlatter. L&#39;.S. Put. application Ser. \o. 299.638 filed Oct. Ill. I972. for METHOD OF AND APPARATL&#39;S FOR RESOLYING A COMPLEX A.C. \&#39;OI..T- AGE OR CLRRENT INTO ITS VECTOR (&#39;O.\I- PONENTS h N. A. .\larshall.  
 6. L5. Pat. application Ser. No. 3()9.I6tfiled .\&#39;o\. 24. I972. for DENSITOMETER AND PROBF. THEREFOR h C. E. Miller 7. [5. Pat. application Ser. No. FII LZFU filed Nov 24. 1972. for FLL&#39;ID SENSING SYSTEMS h G. L. Sehlatter-C. E. Miller.  
 6. LS. Pat. application Ser. No. 318.836 filed Dec.  
 27. I972. for FLL&#39;ID DENSITY DIGITAL COM- PI&#39;TER h M. H. Nmemher.  
 9. CS. Pat. application SCI. No. 321.662 filed Jan. 6.  
 19173. for PILSE TRAIN MODIFICATION CIR- CI&#39;IT h) P. 7. KalotayG. A. Fitzpatrick.  
 II) US. Pat. application Ser. No. 332.74l filed Fch I5. I97]. for METHOD OF MAKING A VIBRA- TIO,\ DENSI&#39;I&#39;OMETER h C. Ii. Miller.  
  The foregoing LIS. patent applications listed in para graphs t l l-l Ill). inclusiie. are referred to hereinafter as applications Al-AIU. respectivel v Prohe 34&#39; shown in FIG. I ma} he comentional. Alternatnel probe 34 ma he similar to or identical to a prohe shown in an of the patents PI P4. Prohe 34&#39; ma} also he similar to or identical to the prohe shown in applications A2. A6. A7 or Alt).  
  Preamplifier 26 shown in FIG, I mav he conven tional. Preamplifier 26 ma) also he similar to or identical to either one of the preamplifiers shown in application A4 or A5.  
  Loop circuit 29 is shown in FIG. 2 including an input circuit 36. an AGC amplifier 37. a tracking filter 38.;1 zero crossing detector 39. a one-shot multiviln&#39;ator 40. an in\erter 41. a clamp 42. a phase lock loop 43. a squarer 44. an AND gate. an inierter 46. a phase lock loop 47 and a drive amplifier 48 connected in succession as serial stages from input lead 32 of input circuit 29 to its output lead 33 and connected respectnel from the output lead 28 of probe 34&#39; to the input lead 27 of probe 34.  
  In FIG. 2. other stages are a zero crossing detector 49. a phase detector 50. a low pass filter 51. a phase de tector 52. a low pass filter 53. a threshold detector 54. an inierter 55. a clamp 56. a sweep oscillator 57. an emitter-follower 58. a sawdooth generator 59 and a phase adjustment circuit 60.  
  AGC amplifier 37 has an AGC input lead 6] connected from the output of clamp 56.  
  Tracking filter 38 has two output leads 62 and 63. Tracking filter output lead 63 is connected to the input of mm crossing detector 49. The output of Zero crossing detector 49 is connected to one input 64 of phase detector 50. A junction is provided at 65 from which an output lead 66 of AGC amplifier 37 is connected. Tracking filter 38 has two input leads 67 and 68. Tracking filter input lead 67 is connected front junction 65.  
  Phase detector 50 has a second input lead 69 connected from junction 65. The output of phase detector 50 is connected to the input of low pass filter 51. The output of low pass filter l is connected to the input lead 68 of tracking filter 38.  
  The purpose of Veto crossing detector 59. phase de tector 50 and low pass filter 51 is to cause tracking filter 38 to track the frequenc of output signal of AGC amplifier 37. The signal on the tracking filter 68. thus. causes the passhand thereof to straddle the frequenc of the input to tracking filter 38 over input lead 67.  
  The output of tracking filter 38 on output lead 62 thereof is 90 out of phase with the signal on the output lead 63 thereof. The signal from the tracking filter output lead 62 is impressed upon zero crossing detector 39 and phase detector 52. The output of zero crossing detector 39 is impressed hoth upon phase detector 52 and one-shot 40. The output of phase detector 52 is impressed upon low pass filter 53.  
  A junction is ro\ided at 70 connected from the output of low pass filter 53. A lead 71 is connected from junction 70 to input circuit 36 to the AGC input of an amplifier therin for automatic gain control.  
  Threshold detector 54 has an input 72 connected from junction 70. Input lead 72 of threshold detector 54. when below a predetermined potential. causes the potential of the output lead 73 of threshold detector 54 to go either high or low. The output lead 73 of threshold detector 54 is. thus. for example. either ground or +15 \olts or +\&#39;l. as defined hereinafter. When the output of low pass filter 53 is below the predetermined potential. output lead 73 of threshold detector 54 is at ground.  
  Threshold detector 54 operates both of the clamps 42 and 56 and the sweep oscillator 57. Clamp 56 and sweep oscillator 57 are operated through the inverter Imerter 55 has an output lead 74 which also assumes potentials of \&#39;l or ground.  
  Clamp 42 either passes the output of inverter 4I to the phase lock loop 43 or in the other state of the threshold detector 54. clamp 42 ha\ ing an output lead 75. is operated to clamp the output lead 75 to ground. The output of imerter 55 is simply the reverse of the output detector 54. When the output of inverter 55 is high. sweep oscillator 57 receives power. When the output of in\ erter 55 is low, the output of sweep oscillator 57 is at ground.  
  Emitter follower 58 is connected between sweep os cillator 57 and phase lock loop 43. Phase lock loop 43 has an output lead 76 which is connected to squarer 44. Junctions are provided at 77 and 78. Squarer 44 has an output lead 79 connected to junction 78. Junction 78 is connected to junction 77. Clamp 56 is connected from junction 77 to AGC amplifier input lead 6].  
  When the output of threshold detector 54 is high. loop circuit 29 is tracking and opens clamp 42 to unground the output lead 75 thereof. Conversely. at the same time. inverter 55 grounds the input to sweep oscillator 57 and disables it. During tracking. inverte 55 also disables the output of clamp 56 by a connection 80 from inverter output lead 74 to clamp 56.  
  During searching. threshold detector 54 holds the output of clamp 42 at ground while inverter 55 operates sweep oscillator 57 and clamp 56 passes the output of squarer 44 to the AGC input lead 61 of AGC amplifier 37.  
  In FIG. 2.junction 77 is connected to digital function generator 30 shown in FIG. 1.  
  AND gate 45 receives an input from junction 78 and from an output lead 81 of phase adjustment circuit 60.  
  Saw-tooth generator 59 has an input lead 82 connectd from junction 78. and an output lead 83 connected to an input of phase adjustment circuit 60.  
  Circuit 60 is manually adjustable to manually adjust the sine wave component of the output \oltage of driver amplifier 48 through the use ofcertain structures including the phase adjustment circuit 60. itself. and phase lock loop 47. This adjustment makes the electromechanical oscillator oscillate with ma\imum effi ciency.  
 OPERATION In the embodiment of the invention shown in FIG. 1. probe 34&#39; and loop circuit 29 provide an electromechanical oscillator which oscillates at a frequency dependent upon the density of the fluid in which vane 24 is immersed. The same is true of the pulse repetition frequency of the square wave voltage applied to the input lead 35 of digital function generator 30.  
  Digital function generator 30 may be described as a digital linearization circuit. It produces a digital output directly proportional to density from the input signal thereto impressed upon the input lead thereto.  
  In FIG. 3. input circuit 36 is shown for connection from preamplifier 26 in FIG. I. Input circuit 36 has input leads 84 and 85. Input circuit 36 has various junctions 86. 87. 88. 89 and 90. A capacitor 91 is connected from input lead 84 to junction 86. Input lead is connected to junction 87. A resistor 92 is connected between junctions 86 and 87. A transformer 93 is prov ided with a primary winding 94 and a secondary winding 95. Primary winding 94 is connected between junctions 86 and 87. Secondary winding 95 has leads 96 and 97. lead 97 being grounded. A potentiometer 98 is proided having a winding )9 and a wiper I00. Winding 99 is connected from transformer secondary lead 96 to ground. Wiper 100 is connected to junction 88. A diode 101 is connected from junction 88 to ground and poled to be conductive in a direction toward ground. A diode 102 is connected from junction 89 to ground and poled in a direction to be conductive toward junction 89. Junctions 88 and 89 are connected together.  
  A capacitor 103 is connected from junction 89 to the non-inverting input of a differential amplifier 104. Junction 90 is connected from the inverting input of amplifier 104. A capacitor 105 is connected from junction 90 to ground. A resistor 106 is connected from junction 70 to junction 90.  
  All of the blocks shown in FIG. 2 may be entirely conventional except phase lock loop 43 and phase adjustment circuit 60.  
  In FIG. 3. a calibration frequency may be provided over input lead 107. if desired. and impressed upon junction 65 through a circuit 108. Circuit 108 includes junctions I09 and 110. A resistor III and a capacitor 112 are connected in series in that order from lead 107 tojunction 109. A diode 113 is connected from ground to junction I09. and is poled to be conductive in a di rection toward junction 10). A diode 114 is connected from junction to ground and is poled to be conductive in a direction toward ground. Junctions 109 and 110 are connected together. Junctions I10 and 65 are also connected together.  
  AGC amplifier 37 has junctions I15. I16. I17 and 118. A capacitor 119 is connected from an output lead 120 of amplifier 104 in input circuit 36 tojunction 115. A resistor 121 is connected from junction 115 to I25. Diodes 123 and 124 are connected in succession in that order from lead 80 to lead 61.  
  A junction is shown at 126. The anodes ofdiodes I23 and 124 are connected to junction 126. The cathode of diode I23 is connected to lead 80. l&#39;he cathode of diode 124 is connected to lead 61.  
  Junction 77 is connected from junction 78. as described previously.  
  In FIG. 3. in AGC amplifier 37.11 resistor 12) is connected from lead 61 to junction I16. Junctions 116 and 118 are connected together. A resistor I28 is con nected from junction 118 to ground. A resistor 12) is connected between junctions I17 and 118. Amplifier 122 has an output lead connected to junction I17. A capacitor 131 and a resistor 132 are connected in series in that order from junction 117 to junction 65.  
  Again. in FIG. 3. junctions are provided at 133. I34. I35. I36 and 137. Junction 133 is connected from lead 67. A resistor 138 is connected from junction 133 to ground. A resistor 13) is connected between junctions I33 and 134. A capacitor 140 is connected between junctions I34 and 136. A resistor 14] is connected between junctions 135 and 136. A differential amplifier 142 is provided having an inverting input connected from junction 136. a grounded non-inverting input. and an output lead 143 connected to junction I35.  
  Tracking filter 38 is connected to Zero crossing de tector 39 and phase detector 52 via a lead I44 con nected from junction 135 in tracking filter 38 to a junction 145. Zero crossing detector 39 and phase detector 52 are connected from junction 145. In FIG. 3. track ing filter 38 has a field effect transistor 146 including a source I47. a drain I48 and a gate 149. Source I47 is grounded. A resistor 150 is connected from drain 148 to junction I37. Junctions I34 and 137 are connected together. A resistor 151 is connected from junction 137 to ground. A resistor I52 is connected from gate 149 to lead 68.  
  Zero crossing detector 49 has junctions at 153 and 154. A capacitor I55 is connected from junction 137 to junction 153. A third junction 156 is also provided and maintained at potential +\&#39;2. A resistor 157 is connected between junctions I53 and 156. A resistor 158 is connected from junction 156 to the non-inverting input lead of a differential amplifier I59. Junction 153 is connected to the inverting input lead of amplifier I59. Amplifier 159 has an output lead 160 connected to junction 154. A resistor 16] is connected from junction 154 to potential +\&#39;2.  
  Lead 64 connects junction 154 to the input of a conventional amplifier 162 in phase detector 50. Phase de&#39; tector 50 also includes a conventional electronic or transistor switch 163 which is connected from and o erated by amplifier I62. Switch I63 is connected by a lead 69 from junction 65 to low pass filter 51 at junc tion 164 therein. Low pass filter 51 has various other junctions 165. I66. I67 and 168. A resistor 16&#39;) is connected from junction 164 to ground. A resistor 170 is connected between junctions 164 and 165. A capacitor 171 is connected from junction to ground. A resistor 172 is connected between junctions I65 and 167. Junctions I66 and 167 are connected together. A potentiometer is provided at 173 having a winding I74 and a wiper 175. Winding 17-1 is connected between +\I and I. A resistor I76 is connected from wiper I75 to junction I66. A differential amplifier I7I is pro- \ided having an output lead 178 connected to junction I68. A capacitor 179 is connected hetween junctions I66 and I68. Junction I67 is connected to the imerting input lead of amplifier I77. &#39;lhe non in\erting input lead of amplifier I77 is connected to ground. Lead 68 and resistor I52 are connected in series in that order front junction I68 to gate I49 of field effect transistor I46.  
  Zero crossing detector 39 includes four junctions I80. I8I. I82 and I83. A capacitor I84 is connected from junction I45 to junction I80. A resistor I85 is connected between junctions I80 and H ll. An amplilier is provided at I86. A resistor I87 is connected from junction 181 to the non-inverting input of amplifier I86. Junction 180 is connected to the imerting input of amplifier I86. Amplifier I86 has an output lead I88 connected to junction I83. Junctions I8I and I82 are connected together. A resistor I89 is connected from junction I82 to potential +\&#39;I. A resistor I9&#34; is connected from junction I83 to potential +\&#39;2. A letter diode I9I is connected from junction I82 to ground and is polcd to he hack biased between potential +\&#39;I.  
  Phase detector 52 may he identical to phase detector 50 and. therefore. will not he described except that phase detector 52 has an input lead I92 connected from junction I45 to a switch 193 \ia a resistor I94. Switch I93 is connected to lo\\ pass filter 5. to a junction I95 ia a diode I96 poled to he conductive toward junction I95. Low pass filter 53 also has junctions I97. Wis and 199. A resistor 200 is connected from junction 195 to ground. A capacitor 20] is connected from junction I97 to ground. Junctions I95 and 197 are connected together: A differential amplifier 201 has an output lead 203 connected to junction I98. Junction I97 is connected to the non-inverting input of amplifier 202. l&#39;he imerting input of amplifier 202 is connected from junction I99. Junctions I98 and 70 are connected together. A resistor 204 is connected between junc tions I98 and I99. A resistor 205&#39; is connected from junction I99 to ground.  
  In FIG. 4. sweep oscillator 57 is again shown with emitterfollower 58 and phase lock loop 43. Emitterfollower 58 includes a transistor 205 ha\ ing an emitter 206 connected from the output of sweep oscillator 57. a collector 207 and a base 208. Collector 207 is connected to potential \&#39;I. Emitter-follower 58 has a junc tion 209 connected from emitter 206. A resistor 210 is connected from junction 209 to ground.  
  Junction 209 is connected to a junction 21] in phase lock loop 43. Phase lock loop 43 includes a phase detector 2I2. a low pass filter 213. a resistor 214. a resistor 2I5 and a \oltage controlled oscillator YCO) 2I6.  
  VCO 2I6 ma) or may not produce a sawdooth output \oltage and may or may not he comentiomtl in each case. If the output \oltage of \&#39;C() 16 is a saw tooth. squarer 44 and saw-tooth generator 59 in FIG. 2 may he omitted and lead 76 connected directly to junction 78 and connected directly to the input of phase adjustment circuit 60.  
  Phase lock loop 43 has an input lead 2l7 connected front clamp output lead 75 shown in FIG. 2. and the output lead 76 connected to the input of squarer 44.  
  Phase detector 212 has an input connected from lead 217 and a second input connected from the output of \&#39;C() 216 which is also connected to lead 76. During tracking. the output of phase detector 212 is impressed upon the input of \(O 2I6 via a low pass filter 2I3. resistor 214 and resistor 215 in succession in that order. resistor 214 being connected from the output of low pass filter 213 to junction 2II. Resistor 2l5 is connected from junction 2]] to the input of \&#39;CO 2I6.  
 During tracking. transistor 205 of emitter-follower 58 is cut off and the output of sweep oscillator 57 is grounded because of the grounded output of imerter During searching. lead 2I7 is grounded in clamp 42. The output of low pass filter 2| is then grounded. &#39;Irunsistor 205 is no longer cut off and the output of sweep oscillator 57 passes to VCO 2I6 \ia emitterfollower 58.  
  In FIG. 5. phase adjustment circuit 60 is shown connected from saw-tooth generator 59 o\er lead 83. Phase adjustment circuit 60 has two junctions 2ll-l and 219. A capacitor 220 is connected from lead 83 to junction 218. A resistor 22] is connected from junction 218 to ground. A resistor 222 is connected between junctions 2I8 and 219. Junction 219 is maintained at potential +\&#39;I. A potentiometer 223 is shown liming a winding 224 and a wiper 225. Winding 224 is connected hetween junction 2I9 and ground. Wiper 225 is connected to the imcrting input of differential amplifier 226. The nominverting input of amplifier 226 is connected from junction 213.  
  In FIG. 5. AND gate 45 has junctions 227 and 228. A resistor 229 is connected from potential to junction 228. In phase adjustment circuit 60. amplifier 226 has an output lead 230 connected to junction 228.  
  In AND gate 45. a resitor 231 is connected from junction 227 to potential +\&#39;I. A resistor 232 is connected from junction 227 to ground. AND gate 45 has a differential amplifier 233 with an output lead 234 connected to junction 228. Amplifier 233 has an inxerting input connected from junction 227. and a noninverting input connected from squarer junction 78 o\ er a lead 235.  
  Inverter 46 has junctions 236 and 237. Inverter 46 also includes a differential amplifier 238 ha\ing an inrerting input lead connected from AND gate junction 228 and a non-inverting input lead connected from junction 236. A resistor 239 is connected from junction 236 to potential +\&#39;1. A resistor 240 is connected from junction 236 to ground. A resistor 24] is connected from junction 237 to potential +\&#39;I. Amplifier 238 has an output lead 242 connected tojunction 237. Junction 237 is connected to the input of phase lock loop 47.  
  Phase locls loop 47 may or may not be entirely conventional. as desired. Phase lock loop 47 is shown in FIG. 6 including a phase detector 243. a low pass filter 244 and a \&#39;CO 245. Phase detector 243 has input leads 246 and 247. and an output lead 248. Low pass filter 244 has an input lead 249. and an output lead 250. \&#39;CO 245 has an input lead 251 and an output lead 252.  
  Phase detector input lead 246 is connected from the output lead of inverter 46 at junction 237 shown in FIG. 5. In FIG. 6. the output lead 248 of phase detector 243 is connected to the input lead 249 of low pass filter 244. The output lead 250 of low pass filter 244 is connected to the input lead of \&#34;CO 245 at 25L Both leads 252 and 247 are connected to a common junction 253. Junction 253 is connected to the input of driver amplifier 248.  
  Low pass filter 2-H may be entirelv conventional. Alternativel low pass filter 2-H ma v be that shown in FIG. 7.  
  \&#39;(O 245 is entirely comentional and ma v or mav not produce a sine wave output. as desired.  
  In FIG. 7. the input and output leads 2-89 and 250. respectively. of low pass filter 2-H are again show it. Low pass filter 2-H has three junctions 254. 255 and 256. resistor 257 is connected between lead 249 and junction 254. A capacitor 258 is connected from junction 254 and ground. A resistor 259 and a capacitor 260 are connected in series in that order from junction 254 to junction 255. A resistor 261 is connected from junction 256 to potential +\&#39;I.  
  A resistor 262 is connected from junction 256 to ground. A differential amplifier 263 is pro\ ided with an output lead 264 which is connected to junction 255. The in\erting input of amplifier 263 is connected from junction 254. The Ittilt-IIH erting input of amplifier 263 is connected from junction 256. Lead 250 is connected from junction 255.  
  Driver amplifier 48 of FIG. 2 is also shown in FIG. 8. In FIG. 8. \arious junctions are illustrated at 265. 266. 267. 268. 269. 270. 27I. 272. 273. 274. 275. 276. 277. 273. I79. 280. ZXI. 282. 283 and 284.  
  Driver amplifier 48 has an input lead 285 connected from the output lead of phase lock loop 47 shown in FIG. 2. The output lead of phase lock loop 47 is illustrated at 286 in FIG. 6.  
  In FIG. 8. a capacitor 287 and a resistor 288 are connected in series in that order from lead 285 to junction 265.  
  Svmbols at 289 and 290 indicate that a resistor 29l ma v be replaced between junction 266 and potential -\&#39;I. A resistor 292 is connected between junction 267 and potential-Y1. Junctions 265. 266 and 267 are connected together. A differential amplifier 293 is pro- \ided with an output lead 294. Amplifier 293 has an in- \erting input lead connected from junction 267. A resistor 295 is connected from the non-inverting input lead of amplifier 293 to groundv A transistor 296 is proided having a collector 297. an emitter 298 and a base 299. A resistor 300 is connected from amplifier output lead 294 to base 299. Emitter 298 is connected to junction 299. A resistor 30] is connected from junction 269 to ground. A junction 302 is connected from junction 269. Junction 277 is connected from junction 302.  
  Collector 297 is connected to junction 268. A train sistor is pro\ided at 303 having a collector 304. an emitter 305 and a base 306. Base 306 is connected to junction 268. Emitter 305 is connected to junction 270. (ollector 304 is connected to junction 27]. Junctions 271 and 272 are connected together. A resistor 307 is connected between junctions 268 and 270. A capacitor 308 is connected between junctions 272 and 302. A resistor 309 is connected from junction 272 to potential \&#39;3. A resistor 310 is connected between junctions 272 and 274. A transistor 311 is illustrated having a collector 312, an emitter 313 and a base 314. Base 314 is connected from junction 27!. Collector 3I2 is con nected to junction 273. Emitter 313 is connected to junction 274. Junctions 270. 273. 275. 278 and 280 are all connected together.  
  transistor 319 is pnnided having a collector 320. an emitter 321 and a base 322. Base 322 is connected from junction 27-1. Collector 320 is connected to junction 278. Emitter 32I is connected to junction 279. A capacitor 323 and a resistor 324 are connected in series in that order from junction 28] to junction 282. A resistor 325 is connected between junctions 282 and 284. A resistor 326 is connected from junction 284 to ground.  
  As shown in FIG. 8. drive coil 23 has leads 327 and 328 connected from junctions 281 and 284. respec tivel v.  
  A transistor 329 is provided in FIGv 8 including a collector 330. an emitter 33] and a base 332. A resistor 333 is connected from junction 280 to base 332. A re sistor 334 is connected between junctions 280 and 283. Emitter 331 is connected to junction 283. (ollector 330 is connected to junction 268. Junction 282 is con nected to junction 265.  
  In FIG. 9. waveforms are illustrated at Fl to F8. The signal at F] appears at the output of preamplifier 26 shown in FIG. I and ma \ar from it] to ltltltl mil|i- \olts. peak-to-peak.  
  The output signal of zero crossing detector 49 in FIG. 2 may be as illustrated at F2 in FIG. 9.  
  Waveform F3 and FIG. 9 ma v be the output signal of phase detector 50 shown in FIG. 2.  
  The output signal of tracking filter 39 appearing on output lead 63 thereofshown in FIG. 2 ma v be as illustrated at F4 in FIG. 9.  
  The output signal oftracking filter 38 on output lead 62 thereof shown in FIG. 2 ma v be illustrated at F5 in FIG. 9.  
  The output signal of phase detector 52 shown in FIG. 2 ma v he as illustrated at F6 in FIG. 9.  
  The output signal ofzero crossing detector 39 ma v be as indicated at F7 in FIG. 9.  
  The output signal of one-shot 40 show u in FIG. 2 ma v he as indicated at F8 in FIG. 9.  
  The output signal of sweep oscillator 57 shown in FIG. 2 ma v alternatively be an v one of the waveforms G1. G2. and G3 shown in FIG. 10. Sweep oscillators for the purpose of providing the waveforms G 1. G2 and G3 are entirely conventional. Waneform GI is a triangular waveform. Waveform G2 is a saw-tooth wmeform.  
  The waveform G3 is fairly linear during periods TI and T2 and fairl v curvilinear during periods T3 and T4. The waveform G3 is produced b an RC (resistancecapacitance) circuit.  
  The output lead 79 of saw-tooth generator 59 in FIG. 2 ma v have a signal thereon as illustrated in FIG. I]. The waveform of FIG. 12 is alternative to that shown in FIG. I I. Saw-tooth generator 59 and squarer 44 maj be entirel v conventional. Alternatively. saw-tooth generator 59 may produce the waveform of FIG. I2 in- \erted or not b an inverter to the waveform shown in FIG. 11.  
  In FIG. 5. amplifier 226 mav produce an output pulse as indicated at HI in FIG. 13 when the potential of junction 218 reaches the potential of wiper 225 of po tentiometer 223 (assume FIG. II waveform I.  
  In FIG. I3. H2 is the output pulse on output lead 234 of amplifier 233. In FIG. 13. H3 is the output pulse which appears at junction 237 in inverter 46 shown in FIG. 5.  
  One embodiment of the digital function generator 30 is illustrated in FIG. 14. In Fl(i. 14. junctions are pro- \ided at 335. 336 and 337.  
  Herein. junction 335 may be described as a -terminal junction.&#34; Junction 78 in FIG. 2. and other junctions therein. may be described as an output junction.&#34;  
  ln H0. 14. a di\ ide by-twenty di\ider 338. a di\ idcby-ten di\ ider 339 and a di &#39;ide-by-tcn di\ider 340 are connected seriatim from an input lead 341 of digital function generator 30 to junction 335. NAND gates are pro ided at 342 and 343. The output of NAND gates 342 and 343 are impressed upon a square law digital computer 344. A burst oscillator 345 ha ing an output lead 346 connected to junction 336 provides one input to each of the NAND gates 342 and 343 o\er leads 347 and 348. respccti ely. Each of the NAND gates 342 and 343 has tw o inputs. The other input to NAND gate 343 is supplied o\ er a lead 349 connected from junction 337. The other input to NAND gate 343 is connected oier a lead 350 from junction 335. An in &#39;erter 351 is connected from junction 335 to junction 337. A difl&#39;erentiator 352 is connected from junction 337 to square law digital computer 344. If desired. all of the differentiators disclosed herein may or may not be identical to differentiator 353 shown in FIG. 18. Howe\er. other dil&#39;ferentiators may also be employed.  
  An ol&#39;fset digital computer 354 and a display unit 355 are connected in succession in that order from square law digital computer 344. Off-set digital computer 354 may be entirely comentional or as disclosed in application A8 or as disclosed herein Off-set digital computer 354 receives serial groups of serial pulses. the number of pulses in each group being directly proportional to the square of the period ofthe square wa e appearing at terminal junction 335. This is likewise directly proportional to the square ofthe period of the square w a\c appearing on input lead 341 of digital function generator 30 shown in Fl(i. 14.  
  The number of output pulses in a group impressed upon off-set digital computer 354 may be described as being either equal to or directly proportional to 41&#39; where &#39;I&#39; is the period into di\ider 338. Offset digital computer 354 then takes a group of these pulses and produces an output continually updated either equal to or directly proportional to In the abo\e. .4 and If are constants.  
  Display unit 355 is entirely conventional. A different display unit may be employed. if desired. Display unit 355 includes a logic circuit 356 connected from off-set digital computer 354. and an indicator 357 connected from the output of logic circuit 356. Indicator 357 can read in binary or decimal numbers directly the density of the fluid in which \ane 24 shown in H6. 1 is im mersed. Alternati ely. indicator 357 may read in specific gra\ ity or otherwise.  
  Square law digital computer 344 is illustrated in FIG. 15. Square law digital computer 344 shown in FIG. 15 has a di\ ider 37&#39; which is merely a counter that counts the output pulses front NAND gate 342. Dil&#39;ferentiator 352 sets the count of di\ ider 37&#39; to zero upon the lead ing edge of the pulse appearing at junction 337 and shown at E6 in FIG. 21.  
  A rate multiplier 38&#39; is connected from NAND gate 343 and produces on its output lead 358 a number of serial pulses in a group which is a fraction of the total oil input pulses in a group such as a group shown at E8 in FIG. 2| dependent upon the number stored in the register of the counter of di\ ider 37&#39;. The output pulses in a group on output lead 358 of rate multiplier 38&#39; is then directly proportional to the square of the period of the square wa e either at junction 335 in H6. 14 or at input lead 341 therein.  
  In Fl(i. 15. a switch matrix 33&#39; is connected to a rate multiplier 359. Rate multiplier 359 is also connected front rate multiplier output lead 358 to off-set digital computer 354. Rate multiplier 359. thus. has an output lead 360 which produces groups of pulses directly proportional to or equal to 4F. Switch matrix 33&#39; has a set of manual operators 361 to produce binary or decimal switch settings. Binary switches may be employed. Al ternati ely. binary coded decimal IBCD) switches may be employed. The factor A is set by setting the switch matris 33&#39;. The number of pulses in a group on the output lead 360 of rate multiplier 359 is less than the input thereto. in part. depending upon the setting of the switch matris 33&#39;.  
  hi FIG. 15. the counter of di\ ider 37&#39; maybe entirely conventional. As stated pre\iously. switch matri\ 33&#39; may also be entirely con entional. The same is true of rate multipliers 38&#39; and 359.  
  In accordance with one alternati e embodiment of the present in ention. di\ider 37. rate multiplier 38&#39;. switch matrix 33&#39; and rate multiplier 359 may be as shown in FIG. 16. Divider 37&#39; includes diyide-by-ten di\iders 362. 363. 364. 365 and 366. Rate multiplier 38&#34; has rate multiplier decades 367. 368. 369 and 370. respecti &#39;ely. connected from BCD outputs of di\ideby-tcn di\iders 363. 364. 365 and 366. respecthely.  
  Note that di\ide-by-ten di\ider 366 carries the most significant decimal digit. Rate multiplier decade 370. on the other hand. has the highest frequency output. Thus. in order to produce the desired multiplication of the decimal number contained in the registers 363-366. as a fraction. i.e.. less than unity. it is necessary to weigh di\ider 366 against the highest frequency rate multiplier decade 37&#34; and so forth.  
  Switch matrix 33&#39; contains four BCD switches 371. 372. 373 and 374 ha ing adjustable knobs 375. 376. 377 and 378. respectively.  
  Rate multiplier 359 is identical to rate multiplier 38&#39; and. therefore. will not be described further. From the foregoing. it will be appreciated that BCD switch 371 carries the most significant digit.  
  Typically. the square wave appearing at junction 335 in FlG. 14 has a period of 0.5 second. Typically. the pulse repetition frequency of the output signal of burst oscillator 345 in FIG. 14 is ltlt) kilohertz. Further. typically. the number of pulses in each of the groups at E8 and E9 in FIG. 21 are about 25.000.  
  Di ide-by-ten di\ ider 362 is employed in di\ider 37&#39; to make sure that the number of pulses impressed upon rate multiplier 38&#39; by NAND gate 343 is about ten times the number stored in di\ide-by-ten di\iders 363-366.  
  Display unit 355 shown in FIG. 14 is entirely eonrentional. and for each decimal digit. it may appear as in FIG. 17. Display unit 355 is. thus. sold with logic circuit 358 to illuminate neon lamps 379 of the indicator 357. Such display units are sold by many companies. For example. one such display unit is sold by the Burroughs Corporation under the trademark PLANAPLEX.  
  Rate multipliers 38&#39; and 359 may be entirely comer tional. Any one including. but not limited to. those sold by Motorola Semi-conductor Products. Inc. and &#39;I&#39;esas Instruments Incorporated may be employed. The l\Iotorola model numbers are MC I4527AL and MC I4527CL. The Texas Instruments rate multipliers are described as synchronous rate multipliers with circuit types SN7497 and SN4lo7. The foregoing Motorola and Texas Instruments model numbers are generally given for what is described herein as a rate multiplier decade which may be connected seriatim ad infini tum. if desired.  
  As stated previously. off-set digital computers 354 shown in FIG. 15 may be entirely conventional. One or many such computers may be employed. One such computer is sold as an MOS by Hughes Aircraft Company. This MOS is described further as a counter/latch- !decoder/driver HCTROl07D/HCTRO107F.  
  Alternatively. divider 37&#39; and rate multiplier 38 of FIG. 15 may be combined in a changed form as shown in FIG. 18. Counters are provided at 37&#34; and 38&#34;. Counter 37&#34; has a conventional logic circuit 380 and flip flops K1. K2. K3 KN forming a register 381. Dift&#39;erentiator 352 is connected to logic circuit 380. NAND gate 342 is connected to logic circuit 380 through a divide-by-two divider 382.  
  Counter 38&#34; has a logic circuit 383 and flip-flops L1. L2. L3 LN connected therefrom to differentiators 353. 384. 385 386. respectively.  
  AND gates 387. 388. 389 390 are respectively connected from differentiators 353. 384. 385 386.  
 and respectively from flip-flops K1. K2. K3 KN.  
  The output of each AND gate shown in FIG. 18 is connected to the respective input of an OR gate 391. the output of which is irnpreseed upon rate multiplier 359 shown in FIG. 15.  
  Note that flip-flop KN contains the most significant digit and the output frequency of flip-flop LN is the greatest. the output of differentiator 386 being impressed in common with the l output of Hip-Hop KN on the two respective inputs of AND gate 390.  
  The outputs shown from all the flip-flops in register 381 from the flip-flops L1. L2. L3 LN in counter 38&#34; are from the l outputs of the corresponding flipflops.  
  The differentiators shown in FIG. 18 produce positive output pulses when the l output ofthe corresponding flip-flop goes high.  
  As stated previously. the flip-flops of register 381 in counter 37&#34; are weighted in binary fashion according to the frequency of the output pulses of the differentiators. None of the pulses at the outputs of the AND gates in FIG. 18 are coincident. This feature and the method of operation of all the structures shown in FIG. 18 is fully explained in application A9.  
  Counter 38&#34; and logic circuit 383 receive an input from NAND gate 343 shown in FIG. 14. and as shown in FIG. 18.  
  Ifdesired. the square law digital computer 344 shown in FIGS. 14 and 15 may be further modified by changing rate multiplier 359 to that shown in FIG. 18. but by omitting counter 37&#34; and substituting therefor a switch matrix 392 as shown in FIG. 19.  
  An alternative embodiment ofdigital function gener ator 30 is indicated at 30&#34; in FIG. 20. Digital function generator 30&#34; has an input lead 393. A divide-bytwenty divider 394. a divide-by-twenty-flve divider 395. a divide-by-two divider 396 and a divide-bytwo divider 397 are connected in succession from input lead 393 to a terminal junction 398 corresponding to terminal junction 335 in FIG. 14.  
  Digital function generator 30&#34; has a burst oscillator 30&#39; which may be identical to burst oscillator 345 shown in FIG. 14. AND gates are provided at 399 and 400 with their outputs connected respecthely at the points indicated in divider 37 and rate multiplier 38&#39; of square law digital computer 10&#39; shown in FIGS. 15 and 20. dividers 37&#39; and 38&#39; being the same in both the cases of FIGS. 14 and 20. For example. the output of gate 399 is connected to the input of rate multiplier 37&#39; and the output of AND gate 400 is connected to the input of rate multiplier 38&#39; shown in FIGS. 15 and 20.  
  In accordance with the foregoing. square law digital computer 10 in FIG. 20 may be identical to square law digital computer 344 shown in FIG. 14.  
  AND gate 400 receives one input from junction 398 and another input from oscillator 30&#39;. AND gate 399 receives one input fron the output of burst oscillator 30&#39;. and another input from the output of an imerter 401 connected from junction 398. A lead 402 connects a junction 403 with a junction 404. The output of in verter 401 is connected to junction 403. One input of AND gate 399 is connected from junction 403.  
  As before. a differentiator 405 is connected from junction 404 to the divider 37&#39; in square law digital computer 10&#39; to reset the same. as before.  
  Digital function generator 30&#34; shown in FIG. 20 has various other junctions 406. 407. 408. 409 and 410.  
 Differentiator 405 is connected to di\ider 37&#39; of square law digital computer 10&#39; through a oneshot 411. The output ofone-shot 411 is connected to a junc tion 412. Junction 412 is connected to square law digi tal computer 10. The output of AND gate 399 is con nected to square law digital computer 10&#39; through an AND gate 413 having a second input from an inverter 414 connected from junction 412.  
  An inverter 415. a differentiator 416 and a one-shot 417 are connected in succession in that order from junction 406 to junction 409. AND gates 36&#39; and 39&#39; are provided. each of which receives an input from the output of one-shot 417 by a respective connection from junction 409. Junction 406 is connected from the output of divider 395 and to the input ofdivider 396. Junc tion 407 is connected from the output of divider 396 and to the input of divider 397. Junctions 407 and 408 are connected together. AND gate 30&#39; has one input connected from junction 408.  
  Junctions 404 and 410 are connected together. AND gates 36&#39; and 39&#39; both receive an input from the output of inverter 401 by respective connections from junction 410. An inverter 418 is connected from junction 408 to another input of AND gate 36&#39;.  
  Off-set digital computer 31&#39; receives an input from square law digital computer 10 and from the outputs of AND gates 36&#39; and 39&#39;.  
  An indicator 27&#39; is connected from the output of offset digital computer 31&#39;. Off-set digital computer 31&#39; may be decimal or binary. The indicator 27&#39; may be a simple indicator with one lamp for each binary stage or a decimal indicator as described hereinbefore and hereinafter. Indicator 27&#39; may be entirely conventional. Off-set digital computer 31&#39; may be conventional or of the type illustrated in FIG. 22 and disclosed. described and illustrated in application A8.  
  Oft set computer 31&#39; in FIG. produces a hinary or a lunar coded decimal tBCDt otttput so that indicator 27 may he read directly. hinary or decimal. in density or specific grtnity d. where d KIT 1- If and K [f /4f) where.  
 f is the pulse repetition frequency of hur t oscillator 2 ll) (although need not he a multiple of Ill) where n is a positi\e integer large enough to make A], less than unity. .-l is a constant less than unity determined hy the setting of su itch matri\ 33&#39; in FIG. 15. B is a positi\e integer determined hy the setting of switch matriy 33&#39; in FIG. 15 or the switch matrix A shown in FIG. 2|. 1&#39; is the period of square \\a\e E5 Ill FIG. 21.  
 K l li, l&#39;,,,l(  
  &#39;1, is the maximum expected value of 7 over the operating range of the instrument.  
 For]; Illll kilohertz and 00.1 second &#39;1&#39;, l.ll  
 second. is. thus. 100.000 to make K,, I U5. Thus. K may he Iitltlt). This gi\es:  
  Either .4 or B may he positi e or negati e. The position of a switch 32&#39; in FIG. 22 determines whether a counter count up 1.4 and H algehraic signs the saute) or down 1.4 and I) algehraic signs different).  
  The pulses in each grouping at E8 go to rate multiplier 38&#39; iii FIG. 15. Tlte pulses in each group E9 go to di ider 37&#39; in FIG. 15. The output of rate multiplier 38 is. therefore. equal to K.-l&#39;I&#39;-&#39;.  
  The constants A and B may he determined empirically hy placing the densitometer prohe 34&#39; in two different lluids of two different known densities each time measuring T. The constants A and B may then he calculated from two simultaneotts equations per patent pl.  
  Something ahout certain structures disclosed herein is discussed in the material immediately following. The importance of some of this discussion may he apparent only from suhsequent explanations.  
  A main storage register D&#39; is illustrated in FIG. 2|. As will he descrihed. a predetermined numher B is entered in storage register D periodically.  
  A logic circuit is pro\ided at 13&#39;. Logic circuit 13&#39; has an input from square law computer 10&#39; through switch 32&#39;.  
  In FIG. 2. the said predetermined numher B is peri odically entered in storage register D. as stated pre iously. The magnitude of the predetermined number B may he selected or changed by operating hinary or hi nary coded decimal (BCD) switches. to he descrihed. which are located in a switch matrix A. The switches in matrix A are either connected from a positive potential \l or ground. The outputs of the switches are sampled and impressed upon storage register D periodically. A gating pulse (E13 in FIG. 21) is impressed upon a gating circuit 8&#39; for this purpose.  
 fill  
  Gating circuit B is connected from matrix A to an OR gate matrix C. The output of OR gate matrix C is then impressed upon storage register D.  
  Once the said predetermined numher B has heen entered into storage register D. logic circuit 13&#39; then controls the register D&#39; to count up or down depending upon whether the signs ol A and B are the same or dil ferent. s\\ itch 32&#39; in FIG. 22 heing placed in the one or the other corresponding positions thereof. respectiiely. on this account. The ouput of logic circuit [3&#39; is. thus. impressed upon storage register B through OR gate matriy I.ogic circuit 13&#39; receives pulses to count from switch 32&#39;. Logic circuit 13&#39; recei es other inputs from storage register D&#39;.  
  From the foregoing. it will he appreciated that matrix with logic circuit 13&#39; and storage register D form either a count tip-count down counter depending upon in which position switch 32 lies. This counter may he entirely con entional. if desired. The counter is indicated at 23&#39;.  
  The output of storage register D&#39; is also sampled peri odically&#39; hy a gating circuit 24 which may he of the same type as gating circuit B. Gating circuit 24&#39; receives pulses front AND gate 39 in FIG. 20 to cause it to sample the output of register D&#39;. The output ofgating circuit 24 is impressed upon a storage register 26&#39;. The output of the storage register 26&#39; is impressed upon indicator 27.  
  If desired. indicator 27 may he a hinary indicator or a BCD indicator.  
  All ofthe structures D&#39;.13&#39;. A. B. C&#39;. 24&#39;. 26&#39; and 27&#39; may he entirely contentional or may or may not he identical to the corresponding structures disclosed iit application A8.  
  .-\lternati\&#39;ely. indicator 27&#39; may simply he a row of lamps each connected from the l output oteach of the flip-flops in storage register 26.  
  Pulses are supplied from AND gate 36 to gating circuit B.  
  The purpose ofthe switch matrix A is to set. periodically. the flip-flops in storage register D to selected states.  
  Switch ntatrix A may ha e one double-pole. douhlethrow switch for each hit or flip-flop in register D. Gating circuit B may ha e an AND gate for the set l and set U inputs to each hit or flip-flop in register D&#39;. The OR gate matrix C may have an OR gate for the set l and set U inputs of each hit in register D&#39;.  
  The same outputs of the bits of register D are connected both to logic circuit 13 and to gating circuit 24&#39;.  
  The square ware at junction 406 in FIG. 20 is illustrated at E1 in FIG. 22.  
  The square ware which appears at the output of inverter 415 in FIG. 20 is illustrated at E2 in FIG. 22.  
  The square wave which appears at junction 407 in FIG. 20 is illustrated at E3 in FIG. 22.  
  The square wa e which appears at the output of in- \LTXLI&#39; 418 in FIG. 20 is illustrated at E4 in FIG. 22.  
  The square wave which appears at the terminal junc tion 398 in FIG. 20 is illustrated at E5 in FIG. 22.  
  The square wave which appears at junction 403 in FIG. 20 is illustrated at E6 in FIG. 22.  
  The output of burst oscillator 30 is illustrated at E7 in FIG. 22.  
  The output of AND gate 400 in FIG. 20 is illustrated at E8 in FIG. 22.  
  The output of AND gate 399 in FIG. 20 is illustrated at E9 in FIG. 22. The output of differentiator 416 in FIG. 20 is illustrated at Ell) in FIG. 22.  
  The output of one-shot 417 shown in FIG. trated at [ill in FIG. 22.  
  The output of AND gate 39&#39; shown in FIG. trated at EIZ in FIG. 22.  
  The output ofAND gate 36&#39; shown in FI(&#39;|. trated at E13 in FIG. 22.  
  The phrase &#34;utilization means. as used herein and in the claims. is herehy defined to include. hut not he limited to. an indicator. a process controller. or otherwise.  
  Although a symhol has heen used consistently in the drawings to represent OR gates. it is to he understood that the symhol includes. hat is not limited to. a wire OR gate. Thus. one or tnore or all of the symhols employed herein to represent an OR gate may or may not he a wire OR gate. as desired.  
  The phase OR gate.&#34; as used herein and in the claims. is herehy defined to include a NOR gate with or without an inverter. as may he necessary or desirahle.  
  All of the said patents PI. P2. P3 and P4 are herehy incorporated herein hy this reference hereto as though fully set forth herein here-at.  
  All of the said applications AI.A1.A3. A4. A5. Ah. A7. AH. A) and A are. hy this reference hereto. herehy incorporated herein as though fully set forth herein here-at.  
  As stated pre\iously. dri\er amplifier 48 shown in l-&#39;l(iv 2 may he conventional or of a type disclosed in upplication A3.  
  In a sense. the amplifier of input circuit 36 shown in FIG. 2 also operates as a limiter.  
  .-\(i(&#39; amplifier 37 shown in FIG. 2 also acts as an analog adder as well as an .-\(i( amplifier.  
  In Fl(i. 1. digital function generator 30. having input lead 35. may ha\e the said input lead 35 connected from loop circuit output lead 33 or from any other appropriate conductor in loop circuit 29. or from junction 77 as shown in Fl(i. 2.  
  Phase lock loops are conventional Most of phase lock loop 43 may he conventional. All of phase lock. loop 47 may he conventional. all ofthe other structures illustrated in FIG. 2 heing conventional. However. not will he taken that phase lock loop 43 receives a pulse input from output lead 75 of clamp 42 when the said output lead 75 thereof is not grounded hy threshold detector 54. ()n the other hand. \(0 2|6 shown in FIG. 4 and 245 shown in FIG. 6 may produce any comhinations of output signals. \IL. saw-tooth waves. sine waves and for square wa es. All of this is prior art. For ease of understanding. the outputs of \&#39;(()s 216 and 245 may he assumed to he sine waves.  
  In FIGS. 4 and 6. phase detectors 212 and 243. respectively. may he con entional phase detectors or four quadrant analog multipliers. Such phase detectors easily produce a phase sensitive output signal. For example, see application A5.  
  Low pass filter 2-H shown in FIG. 7 may also he considered to he an integrator. if desired.  
  All ofthe low pass filters disclosed herein mayor may not include amplifiers. as desired. Amplifiers may he inserted anywhere in all of the circuitry disclosed herein.  
 20 is illus 20 is illus- Zll is illus- The phrase &#34;AND gate.&#34; as used herein and in the claims. is herehy defined to include an NAND gate with or without an inverter.  
  The phrase &#34;NAND gate.&#34; as used herein and in the claims. is herehy defined to include an AND gate with or without an inverter.  
  Inder some circumstances. NAND gates 342 and 343 shown in FIG. [4 may he AND gates. if desired.  
  As indicated hereinhefore. hinary or hinary decimal systems may sometimes he used entirely in part. not at all. as shown or to a greater or less e\tent than that disclosed.  
  In FIG. 20. the input to AND gate 413 from inverter 4l-I suppresses the output of AND gate 4| during reset. In some cases. this circuitry may he omitted.  
  The phrase means to impress a signal.&#34; as used herein and in the claims. is herehy defined to include. hut not he limited to. a conductive lead or otherwise.  
  The phrase means connecting.&#34; as used herein and in the claims. is herehy defined to include. hut not he limited to. a conductive lead. a rate multiplier. an input circuit. an AGC amplifier. or other means. a suh combination. a circuit component. or otherwise.  
  The word continuous.&#34; as used herein and in the claims. is hereby defined to include. hut not he limited to. a register updated periodically.  
  The word &#34;densitometer.&#34; as used herein and in the claims. is herehy defined to include. hut not he limited to. that shown with or without l utilization means. (I) a process controller. (3| a density or specific grav ity indicator. or (-I) otherwise All the zero crossing detectors disclosed herein may he squarers. if desired.  
  The phrase specific granity.&#34; as used herein and in the claims. is herehy defined as the ratio of the density of a sample fluid to the density of a reference fluid. the reference fluid heing water or air or any other fluid.  
  All of the clamps disclosed herein may he omitted and gates used in lieu thereof.  
 What is claimed is:  
  I. A digital \ihration densitometer comprising; a prohe including a housing. a vane. electrical means having an input lead. and a detector having an output lead. said vane heing mounted on said housing. said electrical means heing mounted on said housing and heing responsive to a feedhacksignal impressed upon said input lead thereof to ihrate said vane. said detector heing mounted on said housing in a position to receive vihrations of said vane. said detector producing an output signal on said output lead thereof responsive to receipt of vihrations from said vane. said output signal having an A.(. component of a frequency equal to the vihrational frequency of said vane; first means hav&#39; ing input and output leads. said first means input lead heing connected from said detector output lead to prt duce a periodic signal on said first means output lead of a fundamental frequency equal to said vihrational frequency; second means having input and output leads. said second means input lead heing connected from said first means output lead to said electrical means input lead to impress said feedback signal thereon. said feedback signal providing positive feedhack to cause said prohe and said first and second means to act as a closed loop electromechanical oscil lator. at least one of said first and second means including an amplifier. at least one of said first and second means heing constructed to provide gain for said loop to o\erconie damping of said loop including damping of said \ane to an extent such that said electromechair ical oscillator oscillates continuously and said \ane ibrates continuously; at termainal junction. third means ha\ing input and output leads. said third means input and output leads being connected from said first means output lead to said terminai junction. re pectively. to impress a square ave on said terminal junction hav ing a pulse repetition frequency IPRF! directly proportional to said fundamental frequency and a mark-tospace ratio of unity; first and second .\.-\.\D gates. each of said NAND gates having first and second input leads and an output lead; a burst oscillator liming a constant PRF large in comparison to that of said square \\a\e; an inverter having an input lead connected from said terminal junction. and an output lead connected to said second gate first input lead. said first gate first lead being connected from said terminal junction. said burst oscillator liming an output lead connected to the second lead of each ofsaid first and second gates; a di\ ider liming at least a first input lead. and a plurality of outputs leads. said divider acting as a counter and having a torage register with a constant count entered therein during alternate half periods of said square wave. pul es counted by said di\ ider being supplied oi er said first input lead thereof thereto. said di\ider first input lead being connected from one of said gate output leads. a first rate multiplier having a plurality of setting input leads connected from respccti\e bits in said di \idcr register. said first rate multiplier having a serial pulse input lead connected from the other of said gate output lead and a serial pulse output lead: a manually adjustable switch inatri\ having a plurality of output lead a second rate multiplier liming a plurality of setting input leads connected respectively from said matri\ output leads. a serial pulse input lead connected from said first rate multiplier serial pulse output lead. and an output lead. said second rate multiplier produc ing a number of serial pulses on the output lead thereof during said alternate half periods of said square vvave directly proportional to .41 where .4 is the constant introduced by adjustment of said switch matri\ and &#39;I&#39; is the period of said square \\d\|.. the number of pulses produced serially by said first rate multiplier on the said serial pulse output lead thereof being directly propor tional to T an off-set digital computer having at least a first input lead connected from said second rate multiplier serial pulse output lead. said computer liming a plurality of output leads and being adapted to produce digital output signals on said output leads thereof directly proportional to the quantity where b is a constant. said computer ha\ ing an adjustable switch matrix. the adjustment of which varies B.  
  2. The invention as defined in claim 1. herein utilization means are connected from said computer output leads 3. The imention as defined in claim 2. wherein said computer output signals are binary coded decimal sig nals. said utili/ation means including a decimal indicator. the ratio of I to the vibrational period ofsaid \ane being of a first predetermined magnitude. said burst os cillator PRF being of a second predetermined magni tude. said switch matrices being adjusted to cause said indicator to read directly in eight per unit volume.  
  4. The invention as defined in claim 2. herein said computer output signals are binary coded decimal signals. said utilization means including a decimal indicator. the ratio of &#39;I&#39; to the ibrational period of said \ane being of a first predetermined magnitude. said burst oscillator PRF being of a second predetermined magnitude. said switch matrices being adjusted to cause said indicator to read directly in specific gravity.  
  5. The iniention as defined in claim 1. including fourth means connected from the first input lead of the one gate having the said one output lead thereof to reset said divider to Zero on each leading edge of each pulse of the square wave appearing on the first input lead of said one gate.  
  6. The invention as defined in claim 5. wherein said computer has second and third input leads connected from said third means.  
  7. The invention as defined in claim 6. herein utili- .zation means are connected from said computer output leads.  
  8. The invention as defined in claim 7. wherein said computer output signals are binary coded decimal slgnals. said utilization means including a decimal indicator. the ratio of &#39;I&#39; to the ibrational period of said ane being of a first predetermined magnitude. said burst os cillator PRF being of a second predetermined magni tude. said switch matrices being adjusted to cause said indicator to read directly in weight per unit volume.  
  9. The invention as defined in claim 7. wherein said computer output signals are binary coded decimal sig nals. said utilization means including a decimai indicator. the ratio of &#39;l&#39;to the \ibrational period of said ane being of a first predetermined magnitude. said burst oscillator PRF being of a second predetermined magni&#39; tude said switch matrices being adjusted to cause said indicator to read directly in specific gravity.  
  Hi. The in\ention as defined in claim 5. wherein utilization means are connected from said computer output leads.  
  11. The invention as defined in claim 10. wherein said computer output signals are binary coded decimal signals. said utilization means including a decimal indicator. the ratio of i&#34; to the \ibrational period of said vane being of a first predetermined magnitude. said burst oscillator PRF being of a second predetermined magnitude. said switch matrices being adjusted to cause said indicator to read directly in weight per unit volume.  
  12. The invention as defined in claim 10. wherein said computer output signals are binary coded decimal signals. said utilization means including a decimal indicator. the ratio of &#39;I&#39; to the vibrational period of said \ane being of a first predetermined magnitude. said burst oscillator PRF being of a second predetermined magnitude. said switch matrices being adjusted to cause said indicator to read directly in specific gravity.  
  IS. The invention as defined in claim 1. wherein said computer has second and third input leads connected from said third means.  
  14. The invention as defined in claim 13. wherein uti lization means are connected from said computer output leads.  
  15. The invention as defined in claim l4. wherein said computer output signals are binary coded decimal signals. said utilization means including a decimal indicator. the ratio of &#39;l to the vibrational period of said \ane being of a first predetermined magnitude. said