AU IL 3 1761 04375 3102 U.S. Coast and Geodetic Survey Description. of the , U.S..Coast and Geodetic Survey tide-predicting machine 8 eve ci Serial No. 16 DEPARTMENT OF COMMERCE U.S. COAST AND GEODETIC SURVEY E, LESTER JONES, Superintendent DESCRIPTION OF THE U. $8. COAST AND GEODETIC SURVEY TIDE-PREDICTING MACHINE No. 2 SPECIAL PUBLICATION No. 32 WASHINGTON GOVERNMENT PRINTING OFFICE 1915 cy ee: ee 2, "ret }a) el oe a <9 ven # 4 Fay ee = >< a 4a) - i : A - a an Herne! ge tame oe ope saa ea ek: = ines as tL 2 fod . 4 ee ae ee ret : ; ee J * d 3 - ret: ‘ t ae t : ! | ; é t | | “ i ty ’ ? ; ? : 3 M1 4 : _ , , whe com emis km | hla mR AD Mic) Carson, AA etn PON CONTENTS. Cee PRIMER. geet Ga Soy Gk Chia} 2A pKinle'> Bhs salad ce std CSP ee eee Previous tide-predicting machines. ..........-..2-22.2- 40000. eeeeebeeeeeeeees MRM OE AIOE L a cron fc ia. 2 lq asic ane nena de GU oe hse > pe NTS Te Pe ME ESS) Er Cay ogee eee ae ee ae ee Se NreL eR PE bate ao g eerie as eqns Sok oa cbkiam beak canes des ERE IAIRLAG TOGIOLOE: IO le 5 a Foie 5 oltre dS sigs bono 5's '0% Ge ie thea tase ds Ree ROG DIGUIOLOE ING, Ges ndes gost tae bikes dinate Oo ebcl-hisds aidbs taidee a8 The Ferrel or United States Coast and Geodetic Survey tide-predicting SARIS oR etic 0 eh aia oy Mig oO SARK eh Wiaw SKATES olaboA gO De oo United States Coast and Geodetic Survey pene eiee machine No. 2...... Description of the machine................. Sen ET RUBE Cy cue 5 TUNA AOU NN MEIN os ec 2 RS bd eis A Se hy open SUS ER DHS) 0b SDONING BUG BYE. < 1 obk net has ee hea Foe star wads Vane. 28 CMT ANDI cli ea a gilts @ tren alas wal pi gOe td > BORN od Em 0:8 SPINNER TNR eal A ne ge Ries 4 sik nigie ee oa 2S 256M aale sb aaies DIGPEIRUGY Wi DORISD OH coca 2 aipe geese aos See sen.eYoees ste se BOOREOE COMMODOIND Ila. + ck tuts eh ees cs so. ee a geass OE RE ans ET oy NE ee aa Se a EEE OR Releasable gears. ........-.-----..--- + pS ic ae eae ee ee dye te RMnINPeROsTE MT COMODO 5.2. ois sos ais oo his evans ncstcetedeccseee RUMPIIMIAE TIOU OF DUIOV Es orcas cy eens e tn sinet as ckeee wns CRONIN TC TRMRME Sate Sonn Se pre ne Oe ews ss Ube whe a heh eS e UMM INVES COs cele ig es oe eae vo Vine w ees eS a Wein ! PRE RMN as re Se as aus ve bead soko spe Serae Pace 43> Arrangement of components in front frame...........-....-.-.------ BS SN Sees, ES ccs Soa te ae NS nN Nee eg ee er , os Bia a 2 cog Alle 6 Sapam 2 ENTS Alaa erie ene as eee RIGICUS MCA ac she. nt. cc as tents n bes we cueue coe Eee es oats ca eect EWE SOOM TROCRONIMN ja esos ects dog aldie cain peidtin aciaje Ay oo sine LG 1 So aeaer R y ge b SUMIME SF oe' eon Vows 2ap tent SRG rot ss arene. asl alls eae kins «hs ASU Re CV a, sigs wt Ae doe es 4's UNE Oe MOO COIN Soe cwee sb Che ys with amplitudes for tides of the larger ranges. Also, in predicting the more complicated tides, the device for poimting out upon the dial the times of the maxima and minima failed mechanically in certain positions and required the operator’s attention and assistance. Besides, almost constant use during 12 years had developed consider- able wear, and it was necessary to make frequent repairs. For these reasons it was deemed advisable to replace it by a new machine. Sir William Thomson, engaged for a number of years with the problem’ of mechanically analyzing observed tide curves, saw in the reversal of this process and the production of a tide curve from its component elements the complete solution of the problem of predict- ing tides. It would seem that for this reason the British machines, . including those made for the French and Brazilian Governments and the Roberts 33-component machine, are merely ‘“‘tide curve pre- dictors.”’ Prof. Ferrel conceived the idea of making the machine also bridge over the-gap which lies between the predicted tide curve and the numerical data required for the tide table, by introducing an additional mechanism for summing the sine terms of the derived series, a system of time dials and a height scale, thus producing what may justly be called the first real tide predictor. This machine fell short of filling all requirements, because it gave the times of the maxima and minima only and, as stated before, required resetting and a separate operation for v heights of the com- plicated tides. UNITED STATES COAST AND GEODETIC SURVEY TIDE-PREDICTING ' MACHINE NO. 2. A study of these two types could not fail to reveal that slight changes and simplification of the principles underlying them could be made the basis of a new machine, capable of satisfying all demands. The conversion of the motion of the curve-tracing pen in the Thomson type into that of a pointer indicating numerically the 14 UNITED STATES COAST AND GEODETIC SURVEY. heights at any time, thus avoiding the long process of measuring a curve, suggests itself at the first study of the subject. Time dials with their pointers in fixed relations to the driving shafts of the components were already used in the Ferrel machine. A simpler and more direct use of the means already employed in the Ferrel machine for pointing out the maxima and minima of the height function was found in the coincidence of a marked link in the moving chain which sums the first derivative of the height series, with a fixed index in view of the operator. At the instant when this marked link is at, the index the sum of all the derivative heights is zero and, consequently, the height either a maximum or a minimum. When the marked link approaches the index from the right it is a high water and when it approaches it from the left it is a low water. In order to have at the office a record of the predictions copied from the face of the Ferrel machine directly upon the forms to be sent to the printer, careful copies were made of them by hand for some years, after which blue prints or photostat copies of the original tabulations were used. ‘Tide curves, as produced by the British machines, serving as such records, suggested the idea of saving the time and expense of making copies by having the free end of the height summing chain, in addition to pointing out the heights on the dial, also move a pen upon a moving strip of paper and produce a tide-curve record automatically» The marking of the latter into time spaces is a process employed for many years in various ways in the chronograph, meteorological recording instruments, ete., and was accomplished in the British tide predictor No. 3 by means of the momentary lateral displacement of the curve tracing pen. Before making the first plans the subject of mechanical summation was exhaustively studied with the hope of improving upon the chain and pulley, but all the methods suggesting themselves, when devel- oped in detail, led back to that, the simplest and most efficient form of summing harmonic series. A number of practical tests were also made for the purpose of studying the relative merits of bevel and spur gears. The former style of gear wheels having been replaced in the third British machine by the latter to obtain greater rigidity, ~ and the Ferrel machine showing some flexure when set up with large amplitudes, made caution as to this point necessary; espe- cially as the machine was to provide for so large a number of com- ponents. Besides, the shape and dimensions of the machine as a whole depended largely upon the decision as to this point. Having decided in favor of the use of bevel gears and upon the dimensions of the detail parts necessary to insure rigidity, and a half-inch unit for the height amplitudes having been generally accepted as most suitable, a drawing was prepared, upon the scale of 1:10, which was submitted to and accepted by the instrument board sometime in 1895, and the work of construction was begun in 1896. Special Publication No. 32. Plate 5, FERREL TIDE-PREDICTING MACHINE, OR UNITED STATES COAST AND GEODETIC SURVEY TIDE-PREDICTING MACHINE NO. 1. TIDE-PREDICTING MACHINE NO. 2. 15 Owing to various causes it was not until February, 1910, that the machine was completed, excepting as to polishing, plating, and lacquering. It was immediately put into use for predicting the more complicated tides for the 1912 and 1913 tide tables, thus afford- ing opportunity for dismounting, finishing, and reassembling in time for predicting the 1914 tide tables. DESCRIPTION OF THE MACHINE. The names or symbols of the components represented in this machine are given in Tables B and C. As regards the general form of the machine, the reader is referred to plates 6 and 7. The first presents a full view of the right side, showing a desk supporting the dial case ; behind it, regarding the» desk end as the front of the machine, a tall frame mounted on a depression in the base, called the front component frame; and behind this another long and lower one, called the rear component frame. Plate 7 shows the front of the dial case with the dials, pointers, curve sheet, pens, etc., and, looking toward the rear, the left side of the component frames. This side carries the mechanism for summing the cosine or height series; its parts will hereafter be referred to as the height cranks, height pulleys, height chain, ete. Upon the other - or right side are disposed the cranks, pulleys, chain, etc., for summing the sine terms of the derived or time series, hereafter designated as time cranks, pulleys, chain, ete. . A fair idea of the size of the machine as a whole is obtained from the following dimensions: Horizontal distance from front edge of desk to rear edge of rear base plate, 129} inches; vertical distance from floor to top of front component frame, 744 inches; extreme width—i. e., width of base plates—24 inches. ” The dial case is mounted upon an iron base 24 feet high to permit of the use of a wooden covering (the latter was not in place when the photographs were taken) for the desk top. This case is made up of two hard-rolled brass plates ve inch thick, 19 inches wide, and 244 inches high, secured to each other by six brass posts 44 inch diameter. The shafts of the hour and minute and the day and month dials have their bearings in these plates (plate 9). The vertical shaft, 2 inch diameter, runs in brackets secured to the rear plate, the intermediate shafts being mounted in the same manner. The front component frame is made up’ of two hard-rolled brass plates 34 inch thick, 24 inches wide, and 564 inches high, secured to each other, 7 inches apart, by ten ?-inch brass posts. Each of the sides of the rear component frame, of the same thick- ness and material as those of the front frame, is composed of two pieces joined horizontally at the medial line. The sides thus formed held together 7 inches apart by fifteen #-inch posts, are 404 inches 16 UNITED STATES COAST AND GEODETIC SURVEY. high at their ends and 56} inches long, The top of the base plate supporting them is 25} inches above the floor. The two component frames are secured to their base plates with a space of 7 inches between them, thus permitting access to the gear wheels on the ver- tical shafts, and are secured to each other by two cross braces, one at the top and one slightly above the middle of the rear frame, the lower one serving to support a stud gear for transmitting motion from the vertical shaft of the front to that of the rear frame. Distribution of motion.—The general plan of distribution of motion to the various parts of the machine is as follows: By means of the operating crank at the left side of the desk, through a system of spur and bevel gears (plate 8), motion is imparted to the inclined driving shaft (plates 8 and 6), at the rate of one turn of the latter to three turns of the crank. From the inclined shaft, under the desk, through a system of bevel gears with effective ratio of 1:1, motion is conveyed to the vertical driving shaft within the dial case operating the time dials and the paper-winding mechanism of the curve-tracing appa- ratus (plates 3 and 4). The upper end of the inclined shaft drives by means of bevel gears, also of ratio 1:1, the vertical driving shaft of the front component frame (plate 10). The latter, through spur and stud gears of ratio 1:1, moves the forward, vertical driving shaft of the rear component: frame (plate 11), which in turn, through a strong horizontal shaft and 1:1 bevel gears, moves the rear vertical driving shaft of the same component frame. .Thus, all the vertical driving shafts rotate at the same rate of speed. The one within the dial case conveys motion by means of two pairs of bevel wheels 1:2 and 1:1 to the pointer of the 24-hour dial at the left of the center of the dial face (plates 7 and 9), so that two revolutions of this vertical shaft and the three mounted within the component frames correspond to one revolution of the hour pointer or one mean solar day. The pointer of the minute dial, to the right of the former, is driven by two pairs of bevel gears, 3:1 and 4:1. Dial for months and days.—The dial for indicating the days and months, visible through a curved opening above the hour and minute dials and read by an index just below the opening, is fixed upon a shaft which carries a worm wheel with 366 teeth; the worm screw engag- ing with this wheel is driven by the vertical shaft through a pair of bevel gears 1:2. The worm wheel with 366 teeth provides, of course, for the 29th of February, which also has its place on the day Hiak The index or pointer just below the curved opening (plate 7), which curves into the latter and close to the face of the dial, is secured to a short shaft, which carries at its inner end a lever arm with a pin reaching under the lower edge of the day dial, toward which it is pressed by a light spring. A portion of the edge of the dial equal to the angular distance from January 1 to February 28 is of a slightly Plate 6 ication No. 32. ial Publ Spec ON ANIHOVW ONILOIGSYd-AGIL AZAYNS DOILAGOASD GNV LSVOO SSALVLS G3ALINN i i (a re me eet es coe + a DAUR et Nei 9 ST ES ~ Ne § Smt TIDE-PREDICTING MACHINE NO, 2. oar larger radius, so that the pin pressing against it rises and throws the day pointer to the right one day when this portion has passed by or, in other words, the pointer ‘‘jumps’”’ one day. This condition is indicated by a smaller pointer, upon the same center as the former, pointing to the right of a plate carrying the legend ‘‘Common year.” When this small pointer is thrown over to the left or toward the words ‘‘Leap year,” the day pointer is locked and can not “jump” the 29th of February. (The plates with the legends referred to were not in place when the photograph was taken.) The day dial can be released by loosening the milled head nut immediately above the large dial ring, and quickly moved and clamped to any desired position. Connecting shafts—From the vertical driving shafts within the — component frames motion is imparted to the component. shafts which run in bearings in the plates forming the frames by means of horizontal intermediate shafts (best seen in plate 12), and two pairs of gear wheels each, excepting in the case of the components Ssa, Mm, Sa, Msf, and Mf, which move at speeds so slow as to require resort to the use of one pair of gears and a worm screw and wheel. The rear vertical shaft in the rear frame drives 15 and the forward vertical shaft 16 of the 31 components placed in the rear frame. . The vertical shaft in the front component frame gives motion to 9 component shafts, 3 of which are duplicates introduced for reasons to be stated further on, which represent the remaining 6 components of the 37 provided for. The gears in these trains of motion are set in such relation to each other that all the vertical shafts move clockwise when viewing the machine from above and all the component shafts clockwise when viewing the machine from the time side. Dimensions of parts.—The exact dimensions of the parts trans- mitting motion from the crank shaft to the various parts of the machine, as traced out in the foregoing are not of general interest, but are here given for the sake of completeness. Diametral pitch is used in designating the sizes of gear teeth, the number of the pitch being the number of teeth per inch diameter. Driving crank with throw of 6 inches (plate 8) on crank shaft te-inch diameter. On inner end of crank shaft, spur gear 40 teeth, 24-pitch, #-inch face, to spur-stud gear, 120 teeth, 4-inch face, te spur gear 120 teeth, on cross shaft 4-inch diameter. On same shaft, bevel gear, 72 teeth, 24-pitch, 32-Inch face, to bevel gear, 72 teeth, on lower end of inclined shaft, 4-inch diameter. On same shaft, under desk top, bevel gear, 75 teeth, 30-pitch, 34-inch face, to bevel gear, 75 teeth, on lower end of short vertical shaft through desk top, 3g-inch diameter. On same shaft, upper end, inside of dial case (plate 9), bevel gear, 75 teeth, 30-pitch, 34-inch face, to bevel gear, 4503°—15——8 - 1 UNITED STATES COAST AND GEODETIC SURVEY. 75 teeth, on inner end of short horizontal shaft, 34-inch diameter. On same shaft, outer end, bevel gear, 75 teeth, 30-pitch, 0.27-inch face, to bevel gear, 75 teeth on lower end of vertical shaft within dial case, 34-inch diameter. On vertical shaft, next above preceding, releasable bevel gear, 60 teeth, 48 pitch, 0.17 inch face, to bevel gear, 120 teeth, on outer end of intermediate shaft, 0.15 inch diameter. On same shaft, inner end, bevel gear, 84 teeth, 48 pitch, 0.17 inch face, to bevel o— 84 teeth on hour pointer cheat, 0.15 inch diameter. On vertical shaft, next above preceding, releasable béual gear, 180 teeth, 48 pitch, 0.17 inch face, to bevel gear, 60 teeth, on outer end of inclined intermediate shaft, 0.15 inch diameter. On same shaft, inner end, bevel gear 240 teeth, 48 pitch, 0.17 inch face, to bevel gear, 60 teeth, on minute pointer shaft, 0.15 inch diameter. On vertical shaft, next above preceding, releasable bevel gear, 60 teeth, 48 pitch, 0.17 mch face, to bevel gear, 120 teeth, on outer end of intermediate shaft, 0.15 inch diameter. On same shaft, inner end, worm screw 7; inch diameter, 18 threads per inch, to worm wheel, _ 366 teeth, 6.47 inches diameter, on day dial shaft, 5; inch diameter. Inclined shaft, upper end (plate 10), bevel gear, 72 teeth, 24 pitch, +3 inch face, to bevel gear, 72 teeth, on vertical shaft of front com- ponent frame, 7’; inch diameter. On same shaft, next above pre- ceding, spur gear, 110 teeth, 30 pitch, 2 inch face, to stud gear on cross brace (plates 10 and 11), 110 teeth, to spur gear, 110 teeth, on front vertical shaft of rear component frame, ? inch diameter. On same shaft, next below preceding, bevel gear, 75 teeth, 30 pitch, #5 inch face, to bevel gear, 75 teeth, on front end of long horizontal shaft within rear component frame, } inch diameter. On same shaft, rear end (plate 12), bevel gear, 75 teeth, 30 pitch, 2 inch face, to bevel gear, 75 teeth, on rear r vertical shaft of rear component frame, & inch diameter. From the vertical shaft in the front component frame (plate 10) motion is conveyed by releasable bevel gears to bevel gears on hori- zontal intermediate shafts 3 inch diameter, by bevel gears at their inner ends to bevel gears on component shafts 3, inch diameter, all the bevel gears in the front component frame are of 40 pitch and 0.24 inch face. | From the front vertical shaft in the rear component frame (plate 11) motion is conyeyed by releasable bevel gears to bevel gears on horizontal intermediate shafts, #4; inch diameter, by bevel gears at their inner ends to bevel gears on 16 component shafts. From the rear vertical shaft of the rear component frame (plate 12) motion is conveyed by releasable bevel gears to bevel gears on hori- zontal intermediate shafts, °; inch diameter, by bevel gears at their inner ends to bevel gears on 10 component shafts. The 5 remaining Special Publication No. 32, Plate 7. UNITED STATES COAST AND GEODETIC SURVEY TIDE-PREDICTING MACHINE NO, 2, DIAL END. an We) a ee wy TIDE-PREDICTING MACHINE NO. 2. 19 components driven from this vertical shaft, Ssa and Mm at the top, and Sa, Msf, and Mf at the bottom, receive their motion from releasable bevel gears to bevel gears on horizontal intermediate shafts, +; inch diameter, by worm screws at their inner ends, $ inch diame- ter, 13 threads per inch, to worm wheels, 48 pitch, on shafts carrying spur gears 48 pitch, to intermediate sliding spur gears on stud shaft to spur gears on component shafts. The intermediate sliding gears _ are provided for disconnecting the component shafts from the slow- moving worm-screw gears, thus permitting of more rapid setting of the epochs. All the component shafts in the rear component frame are 7 inch diameter, and all the bevel gears are of 48 pitch and 0.20 inch face. Durability of bearings —The intermediate shafts in both the com-_ ponent frames run in bracket bearings made of hard cast brass, secured to one of the plates of the component frame. They can readily be replaced, one at a time, should looseness due to wear require their renewal, without putting the machine out of use. Should wear become too great in the bearings of the component shafts, however, which are in the place of the frames themselves, considerable time and expense would be required to repair the machine. For this reason the bearings in the plates were bushed or lined with hard cast-iron rings, forced into place and riveted. It is thought that 50 years’ constant use will not cause sufficient wear to require the renewal of the bushings. The vertical shafts also run in bracket bearings made of hard cast brass, the one in the front component frame being supported by seven. (plate-10), that in the front of the rear frame by six (plate 11), and the rear one (plate 12) by five such bearings. One of the bearings near the middle of each vertical shaft is fitted with a clamping device, consisting of a double-armed steel block fitting over the bracket bearing, with a powerful hexagon-headed steel screw. By means of a large milled-head wrench the screw can be tightened and the shaft clamped so firmly as to prevent its moving under the stresses incident to the loosening and tightening of the releasing gears. The number of teeth in each of the gears conveying motion from the vertical shafts to the component shafts depend upon the speeds of the components. Speeds of components.—The speeds of the components are their angular motions expressed in degrees per mean solar hour. They are derived from astronomical data, and were first determined by a com- mittee of the British association, appointed in 1872, ‘‘for the exami- nation of the question of Harmonic Analysis of Tidal Observations,” Sir William Thomson being chairman of the committee. Sir George H.. Darwin, having taken charge of this work some time later, extended and perfected the list of components, which was finally published in 20 UNITED STATES COAST AND GEODETIC SURVEY. the Report of the British Association for the Advancement of Science for 1883, and has since, together with the system of notation adopted by that committee, come into universal use. The gear ratios or the number of teeth of each of the gear wheels conveying motion from the vertical shafts to the respective compo- nent shafts were obtained by converting the decimal expression of the speed ratio given in Darwin’s table to the nearest unit in the seventh place into two vulgar fractions, which, when multiplied by 30, the angular speed of the vertical shafts in degrees per mean solar hour, will most nearly approach the former decimal expression. By refactoring these ratios it was possible to obtain such diameters of the respective gear wheels as permitted of considerable saving of space when locating the components. The number of the teeth of the gear wheels are given in Table ©, in the columns headed I, II, III, and IV. The product of the gear ratios I: IT and III: IV of a component multiplied by 30, the angular speed of the vertical shaft per dial hour, is the hourly speed of that component as produced by the gears. The difference between this and the theoretical speed, both given in the table, multiplied by the number of hours in a year, is shown foe sock component in the column headed ‘‘Errors of gears per dial year.” It will be seen that the errors in the speeds of all the large com- ponents are less than a quarter degree; only a few of the unimportant ones amount to more than half a degree in a year, quantities which are altogether negligible. Gear wheels —In making the designs the durability or the life of the machine was kept in view. ‘This is altogether a question of the wear- ing out of those parts which can not be readily renewed. The most — important of these, besides the bearings of the component shafts before mentioned, are the gear wheels. These were cut with cutters specially made to order for producing teeth of the well-known inyo- lute type, but with an additional bottom clearance of about 15 per cent of the height of the tooth. This permits of adjustment for taking out play due to wear of a greater amount than can occur in many year’s use. Releasable gears —The releasable gears heretofore mentioned are used when setting the machine for a new station, for disengaging or releasing each component from the remainder of the train and setting it to its proper amplitude and epoch, after which it is again secured to the vertical shaft. As the moving or slipping of any one of them would vitiate the result, special care was taken in designing the clamping device, which is shown in the adjoined illustrations. (Plate 13, fig. a.) A collar A, with a thread at its upper end and a flange at the bottom, is fastened to the shaft by means of three coun- terbored steel screws. . The gear wheel, B, fitting closely upon this Special Publication No. 32. Plate 8. MAIN DRIVING GEAR AND AUTOMATIC STOPPING DEVICE. ey x Lemire a ac bee TIDE-PREDICTING MACHINE NO, 2. 21 collar and resting upon the flange, has sunk into its upper surface a recess, 6, which is filled by the flange of the collar (. The latter is free to move vertically, but prevented from turning by a small steel screw reaching into a vertical groove, a, in the collar A. The lower surface of the collar Cis slightly ‘‘dished’’; after being fitted accurately into the recess ), it is split twice, at right angles, nearly to the top. When the milled nut D is screwed down with a small pin wrench the edge of the collar C is pressed against the edge of the recess 6 with such force as to make slipping practically impossible. Arrangement of components.—The arrangement of the components in relation to each other as regards location was considered carefully with the object of reducing flexure and friction to a minimum. As far as economy in space would permit the components with the largest amplitudes and greatest speeds were placed nearest to the free ends of the summing chains and connected most nearly direct with the main driving shaft, while the others were placed farther toward the fixed ends of the chains and away from the source of ° power. The product of the maximum amplitude and the speed of each component was taken as a measure for assigning its place. Viewing the machine from the time side (plate 6), the components are arranged in’ the following order, beginning at the left or front and going toward the right or rear: Upper RANGE. FRONT COMPONENT FRAME, REAR COMPONENT FRAME, Driven by front vertical shaft. M,, MK,, S,, MN, ve, Se, po, 2N. Driven by rear vertical shaft, OO, Xo, S;, M,, J,, Mm, Ssa. Lower RANGE. FRONT COMPONENT FRAME, eyeay ets O acOOri 2 * REAR COMPONENT FRAME, Driven by front vertical shaft. (MS),, Ms, Ky, 2MK, Ly, Ms, 25M, P,. Driven by rear vertical shaft. 2Q, Re, T2, Q1; py, Uf, MS/, Sa. Be UNITED STATES COAST AND GEODETIC SURVEY. The horizontal distance between each two component shafts was, of course, fixed by the diameter of the chain pulleys, which was taken as 2 inches, measured upon the center of the chain. Harmonic motion of pulleys.—The several views of the sides of the machine show plainly that provision was made for simple harmonic motion of all the chain pulleys and in what manner this was done. The frames with rectilinear horizonital slots 0.24 inch wide were cut from sheet steel ;4¢ inch thick, and drilled and filed out to shapes ren- . dering them light, without impairing their rigidity. They move in grooves planed into the inner sides of hard brass angle pieces, which are screwed to the side plates. Component cranks.—The lengths of the component cranks, depend- ing upon the height unit adopted for the machine and the maximum amplitude of each component, were made ample, in order to provide for any extreme case. They are given in the last two columns of Table C. | The component cranks are situated immediately behind these frames, their hubs serving as shoulders of the component shafts to which they are securely pinned. The cranks (see adjoining illustration, plate 13, fig. b) are of hard brass and have L slots, a, milled through them, into which are fitted accurately the heads of the steel crank pins, 6. The latter are bored out and threaded to receive the square-headed clamp screws, c, by means of which the crank pins can be fixed firmly in any position upon the cranks. A thin slightly curved plate of hardened steel, d, between the head of the crank pin and the bottom of the 1 slot, protects the latter from being bruised by the clamp screw and acts as a spring which prevents the crank pin from falling when released. Upon the crank pin, which is 0.19 inch diameter, and finely polished, turns freely a closely fitting rectangular block of hardened steel, e, which fits accurately into and slides along the slot of the steel frame. The milled head wrench for loosening and tight- ening the clamp screw ¢ is at B. Upon the side of each crank at its center is mounted a steel pointer, for setting the epoch of the component upon a silvered degree circle screwed to the side plate. The time crank is set upon the shaft 90° ahead of the height crank, and the circles are numbered and the pointers placed so that the effects upon the height chain vary as the cosines of the angles indicated by the pointer, and those upon the time chain as the sines of the same angles. For greater convenience and to avoid errors in setting, the circles of the upper and lower ranges of components were numbered alike and the pointers set upon the crank so that, facing them, all the height circles have their zeros at the right side, the numbering increasing counter clockwise. When facing the time circles, the numbering increases clockwise from the zeros at the tops of all the circles. Plate 9, Special Publication No. 32. oC ee a a ee ee a Ac EHR, en SE Hee eR SIDE VIEW, ’ DIAL CASE Rk Paeeoes I ‘ te 3 c Sy ea i mK ; ied Ye : ¥ t's ; 2 x20 : we : TIDE-PREDICTING MACHINE NO. 2. 938 The components Sa and Ssa have height cranks only, the sine terms of their first derivatives being too small to be taken into account. Chain pulleys—The chain eer turn on — pins 0.18 inch diameter, screwed into steel plates 7 js inch thick, 43 inch wide, and 112 inch high, which slide in grooves planed sie the inner sides of J-shaped hard brass guides, screwed to the sides of the plates. Incidentally these guides serve to unite securely the two halves of the plates forming the rear component frame. The steel plates car- rying the pulleys, or pulley slides, excepting those of some of the larger components which will be referred to further on, are en enc a directly with the cross-slot frames by means of steel strips 7s inch thick and 0.2 inch wide. One side of each pulley guide is willing to accomodate the silvered amplitude scale and its numbering, which is read by means of an index line cut upon a small strip of German silver screwed upon the pulley slide in a manner to permit of its being adjusted accurately to the zero of the scale when the crank is in a horizontal position or the amplitude is set to zero. Amplitude scales—Only the negative halves of the amplitude scales are ruled upon the pulley guides. To set the amplitude, the component shaft is released, the crank set vertical pointing toward its chain pulley; the crank pin is released with the aid of a milled- head wrench and moved up or down until the index on the pulley slide indicates the desired amplitude upon the scale, when the crank pin is again tightened. The unit of the height scales, 0.5 inch, is subdivided to tenths, which permits of setting amplitudes to wane dredths by estimation. The time-scale unit of each component is the product of the height-scale unit and the ratio of the speed of that component to that of the mean moon, or ¥,, in accordance with the coefficient of the derived series. The maximum amplitudes of the larger components, upon the scale of 0.5 inch per height unit, require cranks so long that the machine as a whole could not have been kept within dimensions suitable for an ordinary-sized room without special provision. The maximum amplitude for M,, for instance, requires cranks of 10 inches on the height and time sides. To accommodate these components in a reasonable space, two component shafts were provided for M,, S,,and ,, and the motions of their respective chain pulleys and those of several other components were doubled by means of racks fastened to the cross-slot frames which gear into the smaller ones of pairs of 1:2 spur gears, the larger ones engaging into racks fastened to the pulley slides. This reduced the largest of the cranks to 2.5 inches. The racks are 0.2 inches wide, of 40 pitch, and are held in close gearing with the spur gears by flanged rollers which are adjustable for taking up any play due to wear. Counterpoise weights were provided for 24 UNITED STATES COAST AND GEODETIC SURVEY. the components in the upper range to relieve them of the undue strain of the weights of the chain pulleys, slides, and racks, the effects of which are doubled by the doubling gears. All these components are mounted in the front component frame. They are arranged as follows: Arrangement of components in front frame. UPPER RANGE. | Leng Components. Cranks. tah Gearing. crank. M ight crank ab Doubling : e Oratiks . 64... -- setasx 2; ou < L. Crccabeiatatn te Silat ae Pgh Se nea ah a Sites - {tine CRON isin ioncnecs opens 2. 50 Doe = Se es orank 55.55350. 55-450 1.23 Do. a let inline ahaa alah ley te Peg ns ag Sey» MDG CTONE sp parcl ess canas ay 1.25 Do. oe GtumBsssiil. 2ed..0 1.50 Do. Nae nee yeeeeeeeceeeceeeeeee cece essen seen eens Time crank. «2. -1s-<52--ce-% 1.50 Do Ky prepa a orahik: «it SUG. ds. 1.38 Dot < SR ee eee ee eee tf Re CREE ws Seer adaedsenaeE 1.45 | Not doubled. M, (leh ora CUMMINS ds Cases Sceeee 2.00 Do. 7 ahah ae ty chaietiak: b Ph eh ie RT: ime crank. .../.-.---- Special Publication No. 32. Plate 11. LS | 4 7 — ¢ ” te ‘ {is -{ is + (eae of i oem 9 FORWARD VERTICAL DRIVING SHAFT, REAR COMPONENT FRAME. TIDE-PREDICTING MACHINE NO. 2. 27 of the horizontal opening in the dial case. Whenever the chain, the machine being set for a station, is in this position, the sum of the harmonic motions of the time pulleys is zerd, and at that instant, as pointed out on the day, hour, and minute dials, the height indicated by the height pointer is a maximum or the height of high water, or a minimum or the height of low water. Paper-feeding mechanism.—The paper-feeding mechanism of the curve-tracing apparatus is arranged in the following manner: Upon a mandrel mounted within the dial case in the upper right-hand corner (plates 9 and 12), which can be quickly removed and replaced, isslipped the blank roll of paper holding on a 1-inch wooden core 380 feet of bond paper, 6 inches wide and 0.0024 inch thick. From the blank roll the paper passes around a 1-inch idler roller mounted in the front plate of the dial case, across the face of the latter for a distance of 13 inches and around the feed roller, which is provided near each end with 12 fine needle points for engaging the paper, into the interior of the dial case (plate 9), where it is taken up by the receiving roller, to which it has been fastened by entering its end into a narrow slit. The feeding roller is set in motion by a spur gear at the top of the vertical shaft which operates the time pointers. This spur gear, 46 teeth, 40 pitch, engages the lower one of two stud gears connected to each other by a ratchet wheel and pawl, the upper one engaging into the spur gear, 46 teeth, at the lower end of the feed roller. The circumference of the feed roller being exactly 6 inches, one revolution of the vertical shaft, which corresponds to 12 dial hours, therefore, feeds 6 inches of paper, or 4 inch per dial hour. The ratchet and pawl in the stud gear are placed so as to leave the paper at rest when for any reason the machine is turned backward. If desired, the paper feed can be thrown out of action altogether by turning a small milled head on the ratchet stud gear. A.sprocket wheel with 16 teeth, held by adjustable friction to the upper end of the feed roller, drives the receiving roller by means of a chain and an 8-tooth sprocket. The ratio of the sprockets is such as to force the receiving roller to wind up the paper delivered by the feed roller with the tension furn- ished by the retarding friction of the driving sprocket on the*feed roller. The paper exposed on the dial face is kept taut by an ad- justable retarding friction under the mandrel holding the blank roll. The device works smoothly and winds up without hitch the whole of a year’s tide curve. To remove the completed roll, the sprocket is lifted off the receiving roller and set upon a pin provided for the purpose; pulling out a pin at the back of the dial case permits of the removal of the upper bearing bracket, when the whole can be lifted out and the metal core of the receiving roller removed from the paper roll. 28 UNITED STATES COAST AND GEODETIC SURVEY. For marking upon the sheet the record of the predictions indicated to the operator by the pointers and dials there are provided two pens (plates 7 and 14), one for tracing a base line and marking the hour and day spaces and the times of the high and low waters, and the other for tracing the predicted tide curve. The curve pen uses about half the ink it can hold for a year’s curve, the base-line pen somewhat less. Base-line pen.—The base-line pen (plates 7 and 14) is mounted by means of a metal lock joint, like that of the curve pen, on a swivel arm with a spring for pressing against the paper. The swivel arm is secured to the outer end of a shaft (plate 14), which carries two arma- tures, one for an upper and one for a lower electromagnet. A spring keeps the armatures at equal distances from their respective electro- magnets, the pen tracing a straight line upon the paper moved along under it. The swivel arm holding the pen can be raised or lowered a small amount for exact adjustment of the pen point to mean sea level of the curve. The electromagnets, together with the pen shaft and its armatures, are mounted upon an angle plate held against the inner side of the front plate of the dial case by two screws which, when loosened, permit of adjusting the pen point laterally, so that the curve pen will just clear it m its vertical movement. The unavoidable error in time, due to the fact that both pens can not pass through the same point, amounting to two or three minutes, can at any time be accurately recorded on the sheet by pulling the curve pen, when above the base line, down and across the base line, thus making it trace a vertical line, and then making a vertical line with the base-line pen by pressing against either of the armatures. The distance between these two lines is the measure of the error. The upper electromagnet is in circuit with a battery and a current- making device, which consists of a platinum-tipped contact spring resting upon the edge of a rubber disk, in which are imbedded, accu- rately spaced, 24 narrow strips of platinum. This rubber disk is secured to the shaft of the hour pointer within the dial case (plate 9). An extra strip of platinum is placed close to that representing the twenty-fourth hour, or midnight. The contact spring can be brought to exfct agreement with the hour and minute pointers by means of a fine-threaded screw. As each platmum strip passes under the contact spring the upper electromagnet attracts for a moment the armature, which throws the base-line pen downward for an instant and makes a short mark below the base line for each dial hour, a double mark indi- cating the twenty-fourth hour, or midnight. Another circuit, including the same battery but the lower electro- magnet, is closed when the projecting point of the platinum link in the time chain is in coincidence and contact with the fixed platinum index seen by the operator in the middle of the horizontal opening in Special Publication No. 32. Plate 12. REAR VERTICAL DRIVING SHAFT, REAR COMPONENT FRAME. . : 5 7 ik TIDE-PREDICTING MACHINE NO, 2. 29 the dial case. At such times the base-line pen is thrown upward, making a mark above the base line, which is a record of the time of the high or low water traced by the curve pen. Both this circuit and the one making the hour and day breaks have one battery wire in common, which is led to a small switch at the left side of the desk, just above the crank shaft (plate 8), by means of which the battery can be cut out when the machine is not in operation. Curve pen.—The curve pen is mounted in a swiveling arm on a light carriage which slides along two vertical steel rods. The pen, of the ordinary fountain type, is pressed against the paper by a light coil spring under the outer end of the swivel*arm, but can be kept away from the paper by the turning of a small nut. Being fitted with a metal lock joint it can be quickly removed and replaced in exactly the same position. Motion is imparted to the curve pen by the height chain through the height sum pulley in the following manner. Scale of the tide eurve.—The horizontal shaft running in brackets fastened to the back of the dial case, the lower one seen on plate 4, the rotary motion of which, as before stated, is thirty one-hundredths that of the height sum pulley, carries upon it three sliding change gears of 48 pitch, with 75, 100, and 90 teeth, respectively. Immedi- ately above this shaft is mounted another one with three gears of 75, 50, and 60 teeth, respectively, and, at its outer end, a thread grooved pulley with a circumference of 4 inches, measured on the centers of the chain fastened at its side and wound around it (plate 14). From this pulley the chain passes through the dial case around an idler pulley in its front, up past the curve pen carriage over another idler | pulley to a counterpoise rising and falling within the dial case. A clamp and clamp screw at the pen carriage permits of the latter being secured to the chain at any desired point. . By means of the three different ratios of the change gears a motion of 1 inch of the free end of the chain, or one-twelfth revolution of the height sum pulley, can be converted into pen motions with either of the following values: With gears 75:75, or 1:1, 5 30 |, 75 : With gears 90:60, or 3:2, 5 x ~ x - x 4=0.15 inch. 100 . 1 30 i With gears 100 :50, or 2:1, Tp x 100 x 0 X 4=0.2 inch. When the amplitudes set up in the machine are multiplied by four and the 10-foot scale is used, the tide curve may be traced, within the limits of the height of the sheet, upon scales of 1 to 15, 1 to 20, or 1 to 30 of nature; with amplitudes multiplied by two and the use of the 80 UNITED STATES COAST AND GEODETIC SURVEY. 20-foot scale, 1 to 30, 1 to 40, or 1 to 60, and with amplitudes at their true value and the use of the '40-foot sauie: 1 to 60, 1 to 80, or 1 to 120 of nature. ‘Tide curve.—The tide curve, though traced incidentally to the regular predictions for use as a record, also serves another purpose. The tides at some stations are of the form in which at times the diurnal overcomes the semidiurnal wave, thus producing vanishing or evanescent tides (plate 15, at a), in which frequently a theoretical high or low water is lower or higher than the preceding low or high - water, respectively. In such cases it becomes necessary, in order to avoid cumbering the tide tables with theoretical data, to make such compromises as are most suitable for the practical needs of the mariner. This can be done by an experienced operator by inspec- tion of the curve, of which more than a day is exposed at all times, as the predictions proceed, so that, when the high and low waters of the last day of the year have been written down, the printer’s copy for the station is completed. On plate 15 are shown two facsimile curves on actual scale produced by the machine. One of them shows, at } the manner in which the ~small difference in time between the curve and base line pens is ascertained. Automatic stopping device.—For relieving the operator of the greater part of the strain due to watching the appearance of the platinum zero link in the time chain, and stopping the machine’ at the instant of its coincidence with the index, an automatic stopping device is provided. It consists of an electric circuit which, when closed, causes an electromagnet mounted under the desk top (plate 8) to throw down upon the edge of a ratchet wheel, 5§ inches diameter, 400 teeth, # inch face, secured to the crank shaft, a steel pawl, thereby arresting the motion of the crank and stopping the machine. The cir- cuit is closed by a contact spring which rests upon a hard-rubber cyl- inder (plate 9) on the rear end of the shaft holding the pulley upon which the time chain ends. A small platinum plug in this cylinder comes in contact with the spring, which latter is fitted with a fine motion adjustment, when the zero link of the time chain is im coinci- dence with the index. The lateral screw motion of this shaft prevents the platinum plug from ‘again making contact with the spring when the shaft has made one or more revolutions on either side of the zero position of the chain. The circuit is led through an insulated ring on the hub of the crank and a contact kept closed by a spring. A slight inward pressure against the crank handle overcomes this spring, breaks the circuit, and releases the armature and pawl, thereby permitting the machine to be moved forward to the next stop. By means of a small switch just below the crank the battery can be cut out. Special Publication No. 32. Plate 13. Scale: Full Size Fig. a RELEASING GEARS ON VERTICAL DRIVING SHAFTS. Scale: Full Size Fig. d -COMPONENT CRANKS. TIDE-PREDICTING MACHINE NO. 2. 31 Upon the crank shaft, close to the bearing in the desk frame (plate 3), is secured a small ratchet wheel. A pawl, kept lifted away from this wheel by friction springs when the machine is moved forward in the right direction, is instantly thrown into engagement when the crank is accidentally turned backward. By pushing in one of the small buttons just above the crank the pawl is locked, which permits of moving the machine backward when desired. Pushing in the other button again secures the machine against accidental backward motion. Speed of machine.—The speed with which the machine may be turned, were its object only to produce a tide curve, as is the case with the British machines, varies somewhat with the amplitudes set, a large tide requiring a slower motion of the crank than a small one. The average speed is 20 turns of the crank per minute. A dial day requiring six turns, a year’s curve could be traced in 1 hour and 50 minutes; but the curve is produced incidentally only to the main purpose of the machine, which is to indicate the times and heights of the high and low waters for filling out the blank forms to be sent to the printer. As ascertained from the predictions of all the compli- cated tides for the years 1912 and 1913, made in the year 1910, the time of setting the machine for a station varies, according to the number of components involved, between 2 and 3 hours for one man; that of operating the machine and copying upon the forms the indi- cated times and heights for one year, from 7 to 12 hours. The dif- ference in the time of the latter operation is due to the greater or less frequency of periods of diurnal or evanescent tides, which require more or less judgment on the part of the operator and therefore cause more or less delay. Temperature error.—As regards the question of error due to the effects of changes in temperature, which would appear of moment in view of the great length of chain, it may be said that the results are practically unaffected by thermal expansion or contraction. A rough determination of the effect upon the free end of the chain, which in- volves the thermal coefficients of brass and steel and the doubling effect of the motions of the chain pulleys, shows a shortening by 0.055 inch or 1.4 millimeters for a rise and a lengthening of the same amount for a fall of 25° F. or 14° C. Such changes of temperature can take place only from season to season, during which time the machine has been readjusted a number of times. A possible source of error in the results obtained with the machine, which had, however, been anticipated by the treatment of the chain before described, is that due to wear in its many joints (27.6 feet by 125 links equals 3,447) and consequent lengthening of the whole. For the purpose of testing its constancy in this respect, all the components were carefully set to zero and the position of the mean sea level ° 32 UNITED STATES COAST AND GEODETIC SURVEY. pointer of the height sum pulley and that of the platinum zero link of the time chain in relation to their respective indices noted several times during the prediction of the tides for the 1912 and 1913 tables. No change ingthe lengths of the chains could be noticed. Accuracy of the machine.—At first thought one would probably sup- pose that the best test of the accuracy of a tide-predicting machine would be a comparison of its results with actual observation at the port for which it is set up. Such a comparison is always possible by setting the machine for a preceding period during which automatic tide-gauge readings were made. But the tides of nature are so much affected by meteorological conditions, which can not be predicted, that such a comparison must necessarily be more or less rough. After mature consideration it is found that the best test of the accuracy of a tide-predicting machine as a piece of mechanism is to compare its mechanical solution of the equations put into it with the corresponding results obtained by computation from the same elements. Such a comparison was made, using the regular predictions for _ 1912 and 1913 tide tables, at the station Aden, Arabia, with 34 com- ponents, and at Hongkong, China, with 30 components, hourly heights being read off the dial, by estimation to hundredths of feet, upon a day at the end of the year for which the predictions were being made. The greatest difference between the predicted and computed 24-hourly heights was 0.02 foot in the case of the Aden tide, and 0.06 foot in that of Hongkong. The results of the latter test are shown in Table A. TaBLeE A.—Test for accuracy by comparison of predicted with computed heights—Hourly heights for Hongkong, China, Dec. 31, 1912. Predicted. Comaubed, | +: a Pabeinteds Compete Hour. Com- Hour. Com- puted. puted. = Dial. | Curve. Dial. | Curve. Dial. | Curve. Dial. | Curve. Feet. | Feet. | Feet. | Feet. | Feet. Feet. | Feet. | Feet. | Feet. | Feet. Ore 5). 4,28 4,32 4.32 | —0.04 0,00 Hi 125.2025 1,51 1,54 1.56 | —0.05 | —0.02 1 ER Pees 4.65 4.68 4.68 | —0.03 OOOH TRE ee ae 2.31 2.34 2.37 | —0.06} —0.03 De sauna 4.78} 4.80] 4.80} —0.02 0.00 || 14....... 3.00} 3.06] 3.06] —0.06} ~ 0.00 Diswdroe 4.60 4.61 4.59 | +0.01 | +0.02 || 15....... 3.48 3. 52 2.53 | —0.05 | —0.01 4.5% waist 4.07 4.07 4.05 | +0.02 | +0.02 || 16....... 3.70 3.72 3.73 | —0.03 | —0.01 eae 3627 8.25 3.22 | +0.05 | +0.08 |} 17....22. 3. 64 3. 66 3.66 | —0. 02 0.00 Ohare as 2.32 2.30 2.28 | +0.04 | +0.02 || 18....... 3.38 3.38 8.40 | —0.02 | —0.02 pean ee 1,42 1.40 1.37 | +0.05 | -+0.03 |} 19....... 3.04 3.03 3.07 | —0.03 | —0.04 ae oe 0.70 0.70 0.66 | +0.04 | -+0.04 || 20....... 2.73 2.73 2.75 | —0.02} —0.02 Ds aes 0.31 0.32 0.27 | +0.04} +0.05 |} 21....... 2.50 2.50 2.51 | —0.01 | —0.01 Boxee ce 0.34 0.36 0.33 | +0.01 4-0.03 1] 22. cae 2.46 2.47 2.47 | —0.01 0. 00 2 4 0 hy See 0. 76 0.79 0.81 | —0.05 | —O.02 || 28....... 2.64 2.65 2.67 | —0.03 |} —0.02 Plate 14. tion No. 32. ica Special Publ DIAL CASE AND FRONT COMPONENT FRAME, TIME SIDE. TIDE-PREDICTING MACHINE NO. 2. 38 The curves traced during the predictions of these hourly heights also served as a means of comparison between results as computed and-given by the machine. The facsimile curve on plate 15, marked Hongkong, 1912, contains the day, December 31, for which the hourly heights are given in Table A. In order to ascertain the certainty of action of the machine, pre- dictions were made for a number of days a number of times in suc- cession, the machine being turned back between each set of predic- tions. The agreement between the heights and times of the different sets were within 0.02 foot and 1 minute, respectively. The curves traced in these tests, being on a small scale, revealed no differences when laid upon each other. A practical agreement was also found between the predictions made for the same period by three different observers. 7 Amplitude unit.—A tidal calendar giving the tides for the ports and stations of all countries is, like astronomical publications, of international import. It would seem at first glance that the ampli- tude unit of this machine might preferably have been based upon the meter rather than the foot, but when it is considered that by far the largest number of charts used by the navigators of all nations give the soundings in fathoms or multiples of the foot, the advantage of using the foot is apparent. Should predictions in meters be required, the conversion of the metric into foot amplitudes, which need only be done once for each station, and the addition of three height-dial rings with scales of 3, 6, and 12 meters, would prepare the machine for the prediction of heights in meters. | 84 UNITED STATES COAST AND GEODETIC SURVEY. TaBLe B.—Table of components represented in tide-predicting machines. fete . maxima British | Roberts’s and United oops pene Pstoreaght French | Brazi Roberts’s Ps United Coasts anil On, OF ce, Or | British fimens razilian | universal| States | Geodetic Symbois British British | tide pre. | tide pre- | tide pre- tid Coast anal! & ofecompo- | tide pre- | tide pre- dictor dictor S Pres) Case oe urvey nents, dictor dictor dictor | (16 com- | (12com- | -fictor | Geodetic | tidesro- No.1 No. 2 0.3 | Sonents).| ponents). | 3 com- | Survey | die (10 com- | (24 com- FS ba ort) ponents). Sed Ate Sd ponents). | ponents). No. ponents) (19 com- ponents). Fr ase ee ed cote SES Fees eres: MiP on os te osls ea eee ae a a ame ne ree J 1 Byrsisa cue Ki Ky Ky Ky Ky Kj Ki Ki Wis. 3 5 sdb Ke Ke Ka Ke Ka Kg Ke Ke AG om Resa hee Le Le Le Le Le Le Le Le Jess vaso sccsndlocutedaadskhece tae caneeleveeabnlandldabaats celia einen sae deg de dg Wee ail wre ode Cle 0 hin Chale nine SaCaaa CoMdete dads leaned esumenuh saat ee Urcions = bead Mi My MER widlda Se poks M2 Meg Me Mo Me ” Me Me Me Meco cacandls cae pe cee caliuvie singaalione eke ce solic sways cue cadena a ssinee Mies ES Bk eaten wacele M; jt ane ee, Mg My, My My stegeeeeees M4 My My Magis -cateepesscebieee Ms Me: Mg i) GbE, Ca Me Ms Me Massed Shs bs Ricecenticsscincce ties dav aenebeinl > bee caine oe ee Mgt —a5 lovdcnty sek Mg WEL sv ocaneécSlpudaghsanudiechewten Ghulscasthpkdsel> eucket ceaenii ae ten ME ..4 Wee ctecuncan Mf Wee oe rests oeeteeewee Me IT Fe ct iain coven Sv eneh-s toe hanees ME OT eso aseere MK PS: fee ee aedshheeee 3.) EMR RSG Me pe PCy Ss CREAR ES the oi PRE RE ZED & SMR see 2MK MDG: « caede-cee beens Sadas asewud est Pasbeees > deduced sos kd aia Many: ote sade oak Mm MIN secs ase aleauoceees BENT) PAS UC gs seta Gas heantieee beh cake seats L 8 Sa Baer re MN 5 fA Es (MS) (MS) (MS) RUG Faerun enjoy (MS) (MS). (MS)« SREB SE 5 os Sec CE CEES Saas a ak « Soi lebbe en hE Brees Soa tetcks bites SMSO. SL. Ye BE TRIS) A Sabet RIS a Eb oe Rees £2. Sesh mela de cobs « ehss baer eke DESE suty shu eet MSf UDn wan se cen eenlenencncecee #2 v2 2 2 #2 2 #2 ING: a ck uw cea Ne Ne No Ne Ne No Ne Ne BO 2: 5, SR cc AN ERROR ite OMA Siege Rn cee Te Oe ce aes 2N Vat... eden nes hease v2 yo ye v2 v2 ve v2 Sr o caw acieeeeanabecans O07; O; 0; O; 0}; O71 O; GO io cide Se aliieie’t Fan sak los cecntabentasasemedaeelasweuies ndabeeaeie nae anlar Geeta Se 00 Pic wmane soak Py Py Py Py Pi Pi Pa Py Otte. teceeos Qi Qu Qi Qu Qi Qi Qi Qi BOD Sov i cnc cecladalc cone tulacecadantpefawmal caceebiseusaekil nal iemem un we ellie k paen anne 27. 9682084 125 82 74 121 | 27.9681516 | + .50 0.6 0.6 Ut ae 28. 4397296 65 46 53 79 | 28.4397358 | — .05} 1.50x2 1.502 MU cca sclescwee 27. 8953548 68 58° 46 58 | 27.8953627 | — .07 0.5 0.5 oS are ean 28. 5125830 89 69 70 95 | 28.5125858 | — .02 1.0 1.0 Beyrece aan eee 13. 9430356 92 89 58 129 | 13.9430363 | — .01 | 2.25x2 2. 20 Miia akeceascax 16. 1391016 134 131 71 135 | 16. 1391009 | + .O1 0.4 0.3 Ss 14, 9589314 91 73 50 125 | 14.9589041 | + .24 2.4 1.3 eee het seca cele. 13. 3986609 84 88 51 109 | 13. 3986656 | + .04 1.5 0.7 Be tw SR CER Ors 12. 8542862 127 114 50 130 | 12. 8542510 | + .31 0.3 0.2 hn sun ep wee ees 30. 0410686 85 50 43 73 | 30.0410959 | — . 24 0.2 0.2 ne Gata ai Ghd emily 13. 4715144 69 70 41 90 | 13. 4714286 | + .75 0.4 0. 27 UT's sedis oa 15. 0000000 | 63 75 50 84 | 15. 0000000 . 00 1.0 0.6 BOON a o's evo 30. 0000000 70 70 70 70 | 30. 0000000 .00} 1.23xK2 1,252 BA soci 30. 0000000 70 70 70 70 | 30. 0000000 .00 | 1.23x2] 1.25x2 1 RPE eae 60. 0000000 75 45 60 50 | 60.0000000 . 00 0.5 1.0 eels ain tte le'2 wale ot 90. 0000000 90 48 80 50 | 90.0000000 - 00 0.5 1.5 ORS Se 0. 0410686 51} 149 1 | 125 60 120 | 0.0410738 | — .05 | 2.00X2 |......--06 ae See ae 31. 0158958 69 47 50 71 | 31.0158825 | + .12 0.7 0.7 ik 5 solic i e'cic''o 0. 0821372 51 149 1 125 | 0.0821477 | — .09 SUitseciecaanne asic acd wages ot 29. 9589314 81 50 45 73 | 29.9589041 | + .24 0.5 0.5 : uk | a > % vy 2 an eg at Bie cua = 7 Aes a 1G i Shia is ee 84 . f 4 , : 3 - 7 4 ; \ bes 2 ) \ os | Gv bie VE SS : . " am - : “ys 7 . * - ee ‘ J i? ahd 7 3 pa * ‘ Pare? , - > - ‘ > oF eee 3 as - ; ‘ S de r ne - € “~" ; é> OA ti iy aaa .. 4 . = , = i 1 ho Set - > Peo ee Ente ale eho r es Rte ey Ptah winks ; , ; Lo U.S. Coast and Geodetic Survey Description of the U.S. Coast and Geodetic Survey tide-predicting machine | PLEASE DO NOT REMOVE CARDS OR SLIPS FROM THIS POCKET UNIVERSITY OF TORONTO LIBRARY