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- OCTOBER 18, 1900. THE MARINE RECORD. 2. eee LATITUDE AND LONGITUDE BY THE GREATEST ALTITUDE, AND BY EQUAL ALTITUDES OF A HEAVENLY BODY. (Continued from last issue.) _ The practical application of the preceding method of find- ing latitude and longitude by the greatest altitude and by equal altitudes near the meridian is as follows: Take an altitude of an object within about one hour East of the meridian and note the time by watch; repeat the ob- servation when the object is West of the meridian at the same altitude and also note the time. The difference of the observed time by watch for the two altitudes equals the elapsed time and half of it equals T when the object is the sun. But for any other object the elapsed time has to be converted into moon time, planet time or star time, as the case may be, and half of the converted time equals T. In such a case the rate of speed also has to be determined with regard to the converted time. The latter equals elapsed time plus change of the mean sun’s right ascension during the interval between observations, minus change of the right ascension of the object during the inter- val between observations. Half the sum of the observed times indicates the time by watch when the greatest altitude occurs for which time make out the latitude by ac- count. A. Reckoning for the time of the greatest altitude. a, latitude by equal altitudes. With the latitude by account for the middle of the elapsed time and the declination find p by formula (r). Divide the rate of speed by 60 which equals e. With the true course made good counted from North or South and e find g by formula (4) upper sign for Westerly, lower sign for Easterly courses. Find y by formula (9) and y by formula (11) and both re- sults add to the observed true altitude which gives the greatest altitude reduced to the meridian; with which pro- ceed as usual. Repetition of the reckoning required in regard to p when the latitude found differs much from the latitude y ac- count. 6. Latitude by the greatest altitude. Find y by formula (11) and add it to the greatest true al- titude, the sum is the altitude reduced to the meridian, with which proceed as usual. c. Longitude by equal altitudes and by the greatest altitude. Compute the hour angle s by formula 12; upper sign when the latitude increases, lower sign when the latitude de- creases, and find by it the time aboard ship in the usual manner. The difference between ships’ time and Green- wich time at the moment the greatest altitude occurred or was taken is the longitude in time; as this moment is not ex- actly known when only the greatest altitude is observed, it requires always the observations of two additional equal al- titudes to find from the time noted for them the exact mo_ ment. The hour angle of the greatest altitude is the same as before. B. Reckoning for the time of the meridian passage of the object. a, latitude by equal altitudes. Proceed as under Aa. Find y by formula (9) and subtract from it y by formula (11) to the rest add the observed true altitude, the sum is the real meridian altitude from which the latitude is found in the old way. 6. Latitude by the greatest altitude. Find y by formula (11) and subtract it from the greatest true altitude, the rest is the real meridian altitude from which the latitude is found in the usual way. ¢. Longitude by equal altitudes and by the greatest altitude. | Compute the hour angle s by formula (13); upper. sign when the latitude increases, lower sign when the latitude decreases; and apply it, with sign reversed, to the time of the greatest altitude by watch which gives the time of the object’s transit by watch in case of the sun. But for any other object the product of hour angle and elapsed time, divided by the converted time, is to be applied as before. Find the meridian passage of the object in the usual way and compare the timé with Greenwich time by chronometer at the object’s transit, the differ- ence is the longitude in time. The time of the greatest altitude and of the meridian passage of the object by watch is necessary to fix the moment or place for which latitude and longitude is found for immediate or future reference. The method under B, as regards latitude, is simpler than under A and brings the reckoning right up to the meridian passage of the object; in case of the sun upto apparent. { noon, which is of some advantage. the method under A is preferable. An illustration of the reckoning is given by the following example. Example: In 60° and 62° N. latitude by account, true equal altitudes of the sun were found 17° 45’ 43’, true course in the interval N. 30° E.; rate of speed 75.7 miles per hour; time between observations 1h. 49m. 49.4s. Declination 10° S., find latitude and ship’s time for the middle of the elapsed time. According to the formule mentioned above we have lati- tude by account at the middle of: observations 61° o’ N., which, with the‘declination of 10° 0o/ gives p =60.52; the rate of speed per minute e = 1.2617; e sin 30=0.63085; e cos 30° = 1.0927; T = 54.912 minutes. But in regard to time, 0.63085 Hence by formula (4) ¢ = 1 + —— = 1.08675 T5 cos 61° ey (54.912 1.08675)? ena SS ——— — —_ —_- 58.847 p 60.52 P — (ecosn)? =15.13 1.09272 — 15.077 4 Observed true altitude ¥7°45.72/ Greatest altitude reduced to mer. 19° 2.637 Mer. Zen. Dist. 70°57.37/ N. Declination. 10° 0.c0’ S. Lat. in 60°57.37/ N. Hourangle of greatest altitude = —pecosn 60.52 1.0927 a =— wee = 33.07. m. Kast. 2 2 subtracted from 24h 0,00 Apparent time at ship 23h 26.93 m. By the method in use we have: Half elapsed time oh. 54m. 54.5s. = 13° 43’ 38 cos 9.987414 Decl. 10 0 ocot. 0.753681 cosec 0.760330 Io I7 16cot. 0.741095 sin 9.251862 17° 45’ 43°” sin 9.484389 7I 42 53 cos 9.496581 6r 25 37N. lat. in oh. om. os. apparant time at ship. Comparing the results the latitude by the method in use is 61° 25 62—60° 57.37’ = 28.25/ in error, and the time 33.07 m., equal to an error in longitude of 8° 16’, showing vividly the utter worthlessness of the method in use. The prevailing practice of taking half the elapsed time as hour angle with which to compute the latitude, results in obtaining anything but the correct latitude. The greater error, however, is committed by taking the middle of the observed time for the moment of transit of object, a favor- ite practice with some navigators, and advocated by pseudo teachers, rendering the longitude as much in error as the hour angle of the greatest altitude amounts to, in many in- stances several degrees. The following table shows this error in time minutes. TABLE 2. Showing in time minutes the hour angle of the greatest altitude on account of a change in latitude, and also the re- duction to the meridian in arc minutes when the declination of the object is 23° 30’, and its name different from that of the latitude. ous Bales to Huge Reduction in arc minutes. Lati- Change in latitude per Change in latitude per Lati- hour, miles, hour, miles. tude. tude. De- 10 20 30 40 40 30 20 Io De- gress grees Io E,56,|\3: 13.) 4207) q0.23,| 2:08:| 1.17.1 0,5241/0,135|...10 20 2.03 | 407] 6.10} 8.14] 2.71 | 1.53 | 0.68]0.17| 20 30 2.58 | 5.15'| 7-73 |10.31 | 3.44 | 1.93 | 0.86] 0.22] 30 40 | 3 24| 6.49; 9.73 |13.98 | 4.33} 2.43; 1.08|027]| 4o 50 | 4.14} 8.28 |12.43 |16.57 | 5.52 |.3.11 | 1.38] 0.35] 50 60 | 5.52 |I1.c4 |16.55 |22.07 | 7.36] 4.14] 1.84] 0.46] 60 70 «| 8.10 |16 21 |24.31 |32.42 |10.81 | 6.08 | 2.70 | 0.68} 70 80 |15.55 |3l-10 146.65 |62.20 |20.73 |11.66 | 5.18 1.30 | 80 According to the preceding table a vessel in 60 degrees N. latitude changing the latter at the rate of 20 miles an hour, the declination being 23° 30’ S., will find the hour angle of the greatest altitude 11.04 minutes — 2.76 degrees and the reduction to the meridian 1.84 minutes. Neglecting these quantities, the latitude will be nearly two minutes in error and tke longitude 2° 46’. In general the error in longitude increases as the speed, and in latitude as the square of speed. When the declination also changes during observation, errors on account of neglecting corrections are sometimes considerably increased. A change of the declination acts either in conjunction with or in opposition to the change in latitude. A change of the declination in an opposite direc- tion to the change in latitude acts in conjunction with it, and a change in the same direction acts in opposition to it. In the former case the sum of both changes has to be taken into account; in the latter case their difference. : As the change in the declination of the moon is some- times 17 minutes per hour, when acting in conjunc- tion with a change in latitude of 10 miles per hour, acts as if the change in latitude were 27 miles; a change in latitude _ of 20 miles under the same coudition: would act like a. change of 37 miles, etc. Taking 10 degrees as a mean value of the declination and its change 17 minutes per hour, the following table shows” the hour angle of the greatest altitude and the reduction to the meridian. TABLE 3. ; Showing in time minutes the hour angle of the préniont : altitude on account of a change in latitude, and also the re- duction to the meridian in arc minutes, when the declina_ tion of the object is Io degrees; its name different from that of the latitude, and the change of the declination 17 minutes per hour. i FLUE eneieg ane Reduction in arc minutes. | ° Lati- ae ho te es ceca ca tude.| Change in latitude per Change in ‘atitude per | tude. hour, miles. ; hour, miles. De- De- grees grees Io 20 30 | 40 40 30 20 10 IO | 4.20| 5.76| 7.32 | 8.87] 2.43 | 1.65 | 103/0.55| Ie 20 | 5.49 |. 7.53 | 9.56 |11.59| 3 73 | 2.53 | 1.57|0.84| 20 30 | 6.96] 9 54 |12.11 |14.69 | 5.20] 3.53 | 2.19] 1.17] 30 40 | 8.76 )12.00 |15.25 |18.49 | 7.00} 4.76 | 2.95, 1.57 | 40 50 |1£.18 |£5.33 |19.47 |23.61 | 9.43 | 6.41 | 3.97| 2.12] 50 60 |14 90 |20.42 |25.94 |31.45 |13.16 | 8.95 | 5.54| 2.95 | 60 70 |21.88 |29 98 |38.09 |46.19 |20.16 |13.71 | 8.49] 4.52 | 70° ~ 80 |41.98 57.53 |73-08 |88.63 |40.32.|27.41 |16.99| 905.| 80 According to the preceding table, in 60° N. latitude, the latter increasing at the rate of 20 miles an hour, the declina- tion being 10° S. and increasing at the rate of 17’ per hour, a vessel will find the hour angle of the greatest altitude 20.42 minutes equal 5.11 degrees, and the reduction to the meridian 5.54 minutes, By neglecting these corrections as is always the case, latitude will be about 5 minutes in error and longitude 5 degrees; sufficient cause to bring any ves- sel on the strand. JOHN MauRICce. Civil Engineer and Nautical Expert. Chicago, Sept. 1900. oo oo 2 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. Butlalo so uence 3,744,000] 374,000] — 280,000 4,000] 443,000 Chicagorsie.. 0208. 13,372.000] 2,680,000] 3,971,000 515,000 II,coo Detroit isccsriiasnise 396,000 40.000 151,000 84,000 3,000 Duluth. we .++» | 6,714,000 86,000 25,000 54,000 479,000 Fort William, Ont.. "980! OOO) es Seine aiai|io- cease eaten | ee LT Oe ae Milwaukee......... 712,00C] 160,000} 298,000 1,0co 47,000 Port Arthur, Ont QASQOO |e sii eee ek [lees see en] ei eer ToledOses iieinns he {,286,000 319,000 1,455 ,000 24,000 2,000 TROLONEO cesta. ts atts 44,000]. . TS:000l ss acens 115,000 On Canalstiisyacascs 398,000 482,000 112,000 35 000 60,000 Ons akesicn sss sunes 1,074,000] 3,266,000 281.000 93,000 738,000 Ons Miss: RAVER iio ove a alee hor cae? Ab ry (Meanie Grand Total..... 56,978,000] 9,829,000] 12,235 000 986,000] 2 348,000 Corresponding Date, PBOO a ciatats een Veci 47,314,000] 15,065,000] 7,069,000 819,000} 2,102,000 INCKease seine cee 1,577,000] 1,942,c00 216,000 51,000 422,000 | OY Yes aft: 1) Wea eS ra Bear ater nea Ieee UA IGEN [resp uses sel erature ral koarasy ke 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. oo or oo ACCORDING to the Bureau of Statistics the iron and steel trade with foreign countries covering the last twenty years, our position has been reversed. Within the last five years we have actually changed from an importing to an exporting nation. In 1880 we imported five times as much in value as we exported, of iron and steel products. Now we export six times the value of our iron and steelimports. These exports in 1900 aggregated $121,858, 341, thus ranking next to bread- stuffs, cotton and provisions, the three higher in value. There are in the iron and steel exports twenty-one classes, valued at from $1,000,000 to $9,000,000 each.