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NOVEMBER 8, Igoo. A repetition of the reckoning is only required for the hour angle Por = 60.52; pp — py = 4.55. a, — a, (60.52 120 4.55 59.53 | Therefore, ——_ =} | See RUS L 59 53 60.52 = } (122.00 — 4.48) = 29:39m FH, 24h 0,00 Apparent time at the middle of observ’ns 23h 30,62m When only the greatest altitude is observed the reduction u niay be,found by formula (5@) in which —— represents the 2 a rate of speed per time minute. The hour angle is approxi- Po [ mately — 22 a, the greatest altitude occurs, cannot be noted by watch, and consequently the exact corresponding Greenwich time by chronometer and the longitude cannot be found. The method of equal altitudes explained above is of great practical value, because results can easily be verified by using the actual hour angles of the observed altitudes for finding latitude. For instance, in the preceding example: ) | , but of little use as the exact time when a; — a, — = 29 38 2 a, +a, and 59:53 2 consequently a, = 88.91 and Aoi=— 30515 AS Peo = 62.86, according to formula (1) 2 30. 15? . thecorrection. oy = — = p 62,86 = 1440 Diperved true altitude 17° 45.72 Alt. reduced tomer, 18° 0.18 Meridian Z. D. = PT 5O.S25N: Declination Io 60,00 S. Lat. at second observ. 61° 59.82 N. minus half the diff. oflat. 1 Lat. at middle of observ’s 60° 59.82 N. which very well agrees with the result obtained above. For verification it is always best to use the observation nearest the meridian, that is, the least hour angle. The errors of tle official method in use are now easily ascertained with the assistance of the formule given above. In finding the reduction of the observed altitude to the meridian, the official method neglects the correction of the elapsed time for difference of longitude, which is equivalent to using a in formula (3) for ay, a representing half the un- corrected elapsed time. In other words, if x denotes the difference between a, and a, a, — x is used instead of a,, x being positive for easterly and negative for westerly courses; therefore the error in the reduction equals: Aoi. (a — ¥)* Po Po 2a,x— x? 0.00 x (2a) — x) Po Po 3.F. HODGE & CO THE MARINE RECORD. This quantity or error, equivalent to an error with oppo- site sign in latitude, increases as the difference in longitude increases and as the latitude decreases; on and near the equator the error reaches infinity. Furthermore, the official method neglects the reduction of the greatest altitude to the meridian, whether the greatest altitude is found directly by observation or indirectly from an altitude near the meridian. This quantity or error in al- s2 titude, according to formula (5), equals —, s representing Po the hour angle of the greatest altitude. Therefore, as the errors in altitude affect the latitude in an opposite way, x (2a, —x)+s? the error total in latitude = — —— Po This quantity is to be added algebraically to the latitude in by the method in use in order to obtain the correct latitude. The official method takes the middle of the elapsed time for the moment of transit of the object, whereas it is the moment when the greatest altitude occurs, and, there- fore, the hour angle of the latter equals the error in longi- tude by the official method in use. According to formula (4) this Po : i | = uw (Px — Pi) a | Error in longitude = 1 _ ao Po To get an idea of the magnitude of all the errors of the method in use, barring errors by observation, the following tables are appended: TABLE I. Showing the error in latitude in arc minutes, on easterly and westerly courses, on account of neglecting the change in longitude when the declination is zero, and half*the cor- rected elapsed time equals one hour. RATE OF SPEED PER HOUR, MILES. un bony i Bk 40 30 20 Io a) HA Kast. [west East. | West'| East. | West] Hast. | West 10 |—58.99|/61.71}—43 /91/46.63|/—28 . 82/31 .54|/—13.73|16.45 20 |—29.91|31.37|—22.25/23.71/—14.59|16.05|— 6.93] 8.39 30 |—20.41/21.49|—15.18]16.26|— 9.94/11.02/— 4.70] 5.78 40 |—15.82|/16.76)/—11.75|12.69/— 7.68} 8.62/— 3.60] 4.54 50 |—13.17|14.11)/— 9.76|10.70|— 6.35] 7.29|\— 2.94] 3.88 60 |—II.55|12 63|/— 8.53] 9.61/— 5.51] 6.59/— 2.48] 3.56 70 |—10.42|11.87|— 7.65) 9.09 — 4.86] 6.30/— 2.07] 3.51 80 |— 9.29/12.03|— 6.63] 9.37\— 3.96] 6.70/— 1.30] 4.04 _To find the error for any other declination, multiply table value by tangent latitude and divide the product by tangent latitude minus or plus tangent declination; minus when latitude and declination are of the same name, otherwise plus. TABLE 2. Showing the error in latitude in arc minutes and the ap- proximate error in longitude in time minutes, on account of neglecting the hour angle of the greatest altitude respec- tively its reduction to the meridian, when the declination is zero. : ERROR IN LATITUDE. ERROR IN LONGITUDE é on EUR eden lee aieer Deane A Rate of Speed per Hour, Rate of Speed per hour,. A : Miles. Miles. g 3 40 | 30 20 10 10 20 30 40 3 i 4 Io |— 0,60|— 0.34|—0.15|/—0.04] 0.45] 0.90] 1.35] 1.80}' ro 20 |— I.24/— 0.70/—0.31/—0.08] 0.93} 1.85] 2.78] 3.71] 20 30 |— 1.96|— 1.10/—0.49\/—0.12] 1.47] 2.94] 4.41] 5 88} 30 40 |— 2.85|— 1.60|—o.71/—0.18} 2.14] 4.27] 6.41| 8.55] 40 50 |— 4.05|— 2.27/—I OI|—0.25] 3.04] 6.07| 9.11|I2.14] 50 60 |— 5.88, — 3.31/—1.47/—0.37] 4.41| 8.82|13.23/17.64| 60 79 |— 9.33|— 5.25|—2.33/—0.58] 7.00/13.99/20.99/27.99| 70 80 |—19.26|—10.83/—4 .82/—1.21/14.44|28 . 88/43. 33157.77). 80 To find the errors in latitude and longitude for any other declination by table 2, multiply'table value by tangent lati- tude minus or plus tangent declination, minus when latitude and declination are of the same name, otherwise plus, and divide the product by tangent latitude. The hour angle is positive when the latitude decreases, and negative (east) when the latitude increases, and the longitude is affected accordingly; an eastern hour angle renders the longitude more westerly, a western hour angle more easterly, than by the method in use. JOHN MavRICcE#, Civil Engineer and Nautical Expert. Chicago, October, 1900. or VISIBLE SUPPLY OF GRAIN. As compiled for THE MARINE RECORD, by George F. Stone. Secretary Chicago Board of Trade. CITIES WHERE WHEAT.| CoRN. Oats. RYE. | BARLEY STORED. Bushels. | Bushels. | Bushels. | Bushels. | Bushels. Buflaloi ec coge kes 5940,000 167,000} 461,000 91,000] 922,000 Chicagoan ices eacios 13,008,000] 1,746,000] 3,470,000 538,000 62,000 Detroit: 2530s 518,000 54,000 163,000 50,000 20,000 Duluthincassonsen.e 6,728,000 65,000 350,000 124,000 902,000 Fort; William; Onti.|77970;000|/snsc nics cle en hao ee eee ae eee Milwaukee.......... 29,000 126,000} 487,000 6,090 50,000 Port Arthur, Ont QZ iOOO | soe esha nik [co sbaias Scns ese Gl eye ean etal ec eee ToledOssnciecusstnaiaces I, 281,000 403,000] 1,473,000 24,000 24,000 SROLONILO! secures cena ete 80,000] 2550 3). « BiOOO| esse hres 172,000 On: Canales so.caes ds. 241,000 267,000 FA. OO! Fac tee hee s 3,000 On Lakegencicnc ces 937,000] 2,362,000 998.000 53,000 261,000 On Miss RIVER So cveliscecels ac apencalicicieneise hme: eoasiala oe eecallis see uae Gn Rese ee Grand Total..... 60,032,000] 7.983.000] 12,986,000] 1,100,090] 3 611,600 Corresponding Date, TEQQc Snccae cis nsession 51,001,000] 12,832,000] 6,963,000 pulaal a 3,358,000 Incteasee. i cncsscvee. 259,000). ieee 450,000 50,000] 544,000 DECREASE foe: eiccctiheiclpaais Sorel 1615000 | es, sanice | Shee oe eee ea ae While the stock of grain at lake ports only is here given, the total shows the figures for the entire country except the Pacific Slope. : or or oo Bids for the five battleships and six armored cruisers will be opened at the Navy Department, Dec. 7. There will be an unusual amount of activity in the bidding this year, as there are several new competitors in the field. On the Paci- fic coast the Union Iron Works will this year have fora competitor the Drisden Steel Co., and in the East there will be three new bidders on the large vessels. The construction of these ships constitutes the largest ship-building pereen ever laid down by the Navy Department. MARINE ENGINES, PROPELLER WHEELS, DECK HOISTERS, MARINE REPAIRS. @ 312 ATWATER STREET, DETROIT, MICH. Chas. E. & W. F. Royal Insurance Building, Chicago, Ill. C. T. BOWRING & CO. London, England. 58 William Street, New York City. g and 6 Billiter Avenue, E. C., . Insurance BROWN & CO., J. G. KEITH & CO., - 202 Main Street, Buffalo, N.Y. A. A. & B. W. PARKER, 15 ’‘Atwater St., W. Detroit, Mich. 138 Rialto Building, Chicago, Ill. LA SALLE & CO., Board of Trade Building, Duluth, Minn. Are prepared to make rates on all classes of [Marine Insurance on the Great Lakes, both CARGOES and HULLS. Peck, Victor Signal, Marine Valve Oil, Eldorado Engine Oil, Renown Engine Oil, Atlantic Red Engine Oil, Mineral Seal Oil, Arctic Cup Greases, are trade mark brands manufactured by the The best goods are most economical. Standard Oil Company and found on sale at. all lake ports. Remember the names.