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MAvy 17, Ig00. THE MARINE RECORD. Dna eeeeewwan a" LONGITUDE BY THE RIGHT ASCENSION OF THE MOON. For more than a century scientific people have entertained and fostered the belief that the angular distance of the moon from some other heavenly body in the Zodiac would furnish the means for finding the longitude at sea. Vast and costly computations have been made for the Nautical Alman- ac every year, forecasting the distances of the moon from about a dozen different objects, for every three hours in the day the whole year round; and all to no purpose, because lunar distances can not be observed with sufficient accuracy at sea. ; In spite of this fact, lunar observations have been made and are still a prominent feature in the examinations of mas-_ ters and mates of ocean-going vessels, because teachers and professors are still of opinion, that ‘‘when these observations are regularly practiced—but in no other case—they furnish . a tolerably accurate method of checking the error of the chronometer at sea;’’ as if regular practice could overcome the inherent defects of the method and the rolling and pitch- ing of a vessel, rendering such observations actually an im- possibility at sea. It is a well established fact that even on shore with a firm foothold, the best obsevers with the sextant, are not able to measure moon distances nearer than one minute correct, causing an error of two minutes in Greenwich time, equal to an error of one half degree in longitude. The fault is notso much in the observers and the instru- ment, asin the method employed. It is'a mistaken idea to find by direct measurement the distances, because their in- crement is so exceedingly small that it makes very little im- pression upon time and can hardly be noticed in the instru- ment. Measurements of that kind require certain methods or devices magnifying the increment, so that a large error in the observations will cause but a small error in the quanti- ties sought. On this principle my new method of finding the longitude by the right ascension of the moon is based. An altitude of the moon in combination with an altitude of some star fur- nishes for the two objects the hour angles, the sum or differ- ence of which equals the difference of the right ascensions of the two objects; and as the right ascension of a star is always exactly known, the right ascension of the moon is easily found, and consequently the corresponding, Green- wich time also. The Nautical Almanac contains the right ascension of the moon for every hour in the day, while lunar distances are given only for every three hours; by the way a great advantage of the former over the latter concerning in- terpolation to find Greenwich time. In the solution of the problem the errors which may affect the reckoning have to be considered; namely, Ist, an error in the approximate mean time at ship, or in the longitude by account, causing 2, an errorin the approximate Greenwich time, attended-by 3, an error in the declination of the moon, and 4, an error in the latitude. The error sub 4 is avoided by taking the altitude of an additional star, and from the two stars compute the latitude by the method explained in the issue of the MARINE RECORD of April I9 last. The error sub 3, causing an error in the hour angle of the moon is as- certained by the formula ‘tanb tanc dt= dc sint tant J é in which b represent the latitude, c the declination of the moon, t the hour angle, dt the change in the hour angle consequent upon a change in the declination of dec. Under this arrangement it will be seen farther on, that the errors sub 1 and 2, are of no consequence. The following example fully illustrates the reckoning. For want of space only the results of the reckoning for latitude are given, differing a little from those published in the above mentioned issue of the RECORD, on account of a small error in the first logarithm of the previous reckoning. Example: March 11, in 78° o’ N. lat. and 40° 5/ H. long., by account, simultaneous altitudes of the moon and two stars B and C were taken, from which the following true altitudes were obtained. Watch showing 3h 4om, B being nearest to the meridian. *B’s true alt. 24° 58’ W. *C’strue alt. 27° 41’ W. Moon’s true alt. 15° 50’ E. find the exact latitude and longitude. By Nautical Almanac, *B’s R. A. 12h 33’ 12.86%. *C’ R.A. 8h 33” 12.86”. Decl. 15° 20’ N. Decl. 25° 30’ N. With these data and the preceding“altitudes are found: By first approx, By second approx. Hour angle of C 76° 36’ 14” G5 8 AAC Lat. 79 50 14 79 59 33 110.23 Cor. of assumed lat—= I10.23—9.32 assumed lat. =120.4I== 2° of 25” 78 0° O Ni : exact lat. 80 0 25 N. With the exact latitude the reckoning for the moon’s R. A. is as follows: dd... >) mi, Watch March Io 15 40 Long. in time 2 40 Approx. G. time March 10 13 0 for which the following data for the moon are found in the Naut. Almanac, hsm) 8; SO March 10, 12h R. A, 19 32 20.13 Decl. 15 59 30.0N. S eo Tan 19 34 22.75 16 14 37.4 N. diff. 2° 2:62 15 7.4 To find the hour angles: Ist for the *C ° / “ Comp.alt. 62 19 o “Tat. 9 59 35 cosec. 0.760629 Pol D. 64 30 oO cosec. 0.044512 5190 48.1.35 68 24 18 sin. 9.968394 Minus Comp. alt. 6 5 18 sin. 9.025558 19.799093 cos. 9.899547 half hour angle 37° 20/ 11” hour angle 74 58 22 W. 2d for the Moon ° 7 uv Comp.alt. 74 Io o “lat. 9 59 35 cCosec. 0.760629 P.D. 73 45 23 cosec. 0.017692 157 54 58 78 57 29 sin. 9 991885 A i AFn LO sin. 8.921831 19.692037 cos. 9.846019 half hour angle 45° 27 713” hour angle 90 54 26 KE. ° / “ Moon’s hour angle 90 54 26 E. OA ie ee 74-58 22 W. ——— h. m. s. diff. of R. A. 165 52 48 = IL 3 3120 *C.R. A. 18: 33.12: 86 Moon’sR. A. 19 36 44.06 Now the axuiliary formula as to the ratio of increase or decrease of the moon’s hour angle on account of an error in the declination has to be consulted, and the following reck- oning to be made: Of. Corey pert (/ lat. 80 0 25 tan. 0.753989 Decl. 16 14 37 tan. 9.464419 H. A. 99 54 26 sin. 9.999945 90 54 26 tan. 1.800378n 0.754044 7.664041n number 5.67603 —0.00461 +0.00461 dete. : —— = 5.68064 de dc I or—— = —— dt 5 68064 This quotient tells, that when the declination of the moon increases, its hour angle increases also, and consequently the greater will be the difference in the computed R. A. and that at Greenwich, whereas a decrease of the assumed declina- tion will rapidly be followed by a decrease of the R. A. and at a certain point both declination and right ascension will agree for Greenwich time. The moon’s true place or orbit is given by the right ascen- sions and declinations in the almanac, the former being the abscissas, the latter the ordinates for 12 hours and 13 hours Greenwich time. These ordinates and the true orbit are in- tersected by the assumed orbit furnishing two triangles from which by simple proportion Greenwich time isfound. A first point of the assumed orbit is furnished by the com- puted moon’s right ascension (19h. 36m, 44.098) as abscissa of the assumed ordinate (Decl.=16° 14’.37”); and ae in- c As the quotient —— is dt cline is given by the above quotient. positive, that is, agreeing with the increase of abscissas and ordinates, the incline of the assumed orbit must be in the direction of the true orbit, and the point where both orbits intersect one another, will be the point at which R. A. and decl. do agree for Greenwich time. This part of the compu- tation is readily made by using proportional logarithms, Auxiliary ordinates of the assumed orbit: 19h. 36m. 44.068.—Igh. 32m. 20-1 38,== 4m. 23.938=1° 5’ 597 . Ly. 4358 log 5.68c6 0.7544 —0° II’ 37.0” 1.1902 assumed 16 I4 37.0 firstaux. ord. 16 3 0.0 2m. 21.318.=35/ 19.65” P.L. 7072 « log 5.6806 0.7544 — 0° & 13.17 assumed 16 14 37.0 e second aux. ord. 16 8 23.9 The first and second auxiliary ordinates pertain to the as- sumed orbit at 12 hour and 13 hour Greenwich mean time, The difference between them and the ordinates of the true orbit at 12 hour and 13 hour are 3’ 30.0” and 6/ 13.5” respec- tively, furnishing the base lines of the two triangles’ men- tioned above. Greenwich mean time at the moment of observation: 6/ 13.5”+3% 30.07=9/ 43.5” : 3’ 30.0%—=60m : x 60m. P. L, 4771 BE 30:07 us 1.7112 2.1883, 9 43.57 P. L. 1.2674 oh. 21m. 36s. .9209 £2) Ome O Greenwich mean time 12h. 21m. 36s. To find ship’s mean time we have : *C’s hour angle 74° 58’ 14”=4h. 59m. 538. W. *R. A, 3313 Merid. R.A. 13 33 6 Mean sun’s R.A. March Io, noon 23h. 16m. 31.gos. Cor. for 12h. 21.6m. 2 1.83 ee oe ee ed Mean time at ship 7 ta 32 M ‘* -Greew. T2662 3.36 Long in time A522 SOU, == onus TAG Oo” K. It is worthy of note, that the latitude by account differs from the true value 2° 0’ 25”, the longitude 11° 51/ 0”, the approx. Greenwich time 0 h. 38 m. 24 s., and thatin spite of all these drawbacks the preceding method furnishes exact results. Proof of the correctness of reckoning and observa- tions is obtained by computing the meridian R. A. from the altitude of the moon, using the exact Greenwich time for the elements of the moon. The vain attempt of observing lunar distances at sea, to satisfy academical pretensions, admits of no comparison with taking simultaneously the altitudes of three heavenly bodies, a task within the reach of any two observers. And as the greater part of the reckoning for three altitudes is along well known lires, mistakes are reduced to a minimum. The only difficuly for a novice may be the construction of the diagram of the orbits necessary to facilitate computation and guard against errors, but this difficulty will soon be over- come by always bearing in mind that the abscissas have two functions, namely to represent the right ascension as well as the Greenwich time. The best results for longitude are obtained when the moon and one of the stars are at the premier vertical. Chicago, May, 1900. JOHN MAvRICE#, Civil Engineer and Nautical Expert. Seen nt MARINE PATENTS. Patents issued May 9, 1900. Reported specially for the MARINE RECORD, We furnish complete copies of patents at the rate of Io cents each. 648,911. Sailing craft. Douglas Beardsley, Auburn,N.Y. 648,923. Sea valve for vessels. Frank Charette, Toledo, O. 649,046. Conning tower for warships. B. A. Fiske, U. S. Navy, assignor to the Western Electric Co., Chicago. 649,065. Propeller for ships. D.G. Martens, Christiana, Norway. 649,084. Motor driven by water currents. Vienna, Austria-Hungary. 649,248. Propeller. C. D. Keller, Toledo, O. 649,250. Marine electric light fixture. G. L. Martin, New York, N. Y. 649,328. Light-buoy. G. W. Lyth, Stockholm, and C. H. Ramsten, Malmo, Sweden. S. N. Stewart,