REMARKS. We shall here explain a matter in which beginners are apt to make mistakes. In subtracting compound quantities, we mentally place them in a different form for the purpose of solution. Thus, in the preceding example, 48 seconds cannot be taken from 0 seconds, 33 minutes from 0 minutes, nor 9 hours from 0 hours. But, by adding 60 seconds to the upper quantity, and their equal, 1 minute, to the lower quantity; also, adding 60 minutes to the upper quantity, and their equal, 1 hour, to the lower; and, finally, adding 24 hours to the upper quantity, and their equal, 1 day, to the lower, the quantities will be placed in proper form for solution. Thus : 234 0h 0m Os Od 9h 33m 48s 1 10 34 48 23d 24h 60m 60s Beginners are recommended to proceed in the above manner, until they are able to borrow and carry, as it is called, without actually setting the figures down. To reduce the Sun's declination to the Greenwich date. 64.-RULE FIRST. (1.) Take out of the Nautical Almanac, page I. or II. of the month, according as it is required in apparent or mean time, the sun's declination for noon of the Greenwich date, and also take out the "Diff. for 1 hour" from page I. Note the declination N. or S., as the case may be. Affix the sign + or, according as the declination is increasing or decreasing. NOTE.-For the examples in this work, take out the declination from Table VIII. or XV. (2.) Multiply the diff. for 1 hour by the hours and minutes of the Greenwich date reduced to decimals. (3.) Reduce the product to minutes and seconds, and apply it to the declination at noon, by adding when the declination is increasing, but subtracting when it is decreasing. NOTE. Divide the minutes of time by 6, and the quotient will be decimals. EXAMPLES. 1. Required the sun's declination at Greenwich date, apparent time, 1866, April 7d. 6h. 49m. 22s. 2. Given Greenwich date, mean time, 1865, March 10d. 14h. 26m. 18s.; required the sun's declination. Correction, 14 6 NOTE. Whenever a decimal is rejected in a final result, if the first decimal figure be 5, or above it, add 1 to the last figure of the result. If the first decimal be below 5, do not add anything to the result. Thus, in the first example, the declination given in the Nautical Almanac is 6° 51' 5"-4; this is put down 6° 51' 5". Again, in the last example the declination is 3° 58′ 35"7; this is put 3° 58′ 36". NOTE.-By inspection of Table VIII., or of the Nautical Almanac for 1860, it appears that the "Diff. for 1 hour" of declination on The diff. given is that at noon; it is not the th of the daily difference of declination. Hence, if the apparent time at Greenwich were February 1d. 20h. 18m. 10s., it would be more correct to take the declination and diff. for 1 hour for the 2nd of the month than for the 1st. Thus, if the hours of A.T.G. be more than 12, proceed according to 65.-RULE SECOND. (1.) Take the hours and minutes of A.T.G. from 24 hours, and the remainder is the time from noon of the next day. Express this remainder in decimals. (2.) Take out the declination and diff. for 1 hour for the next day. Mark the declination as in Art. 64, Rule 1. (3.) Multiply the diff. by the time from noon, and apply the product to the declination, the contrary way to the affixed sign; the result is the reduced declination. EXAMPLE. Given Greenwich date, mean time, 1865, March 10d. 14h. 26m. 18s.; required the sun's declination. 66.-NOTE.-When the Rule, Art. 65, is applicable, it is more correct than the Rule, Art. 64; but one serious objection to it is, that pupils are apt to make mistakes in applying the product the contrary way to the sign; and therefore, as the difference between the methods is very small, we shall adopt the method by Art. 64, in most of the following examples. The difference in the preceding example is only 1". 67.-To find the latitude from the observed meridian altitude of the Sun's lower limb. RULES. 1. Find the Greenwich date at apparent noon of the given day, (Art. 63). 2. Take the sun's declination from page I. of the month in the Nautical Almanac, and reduce it to the Greenwich date, (Art. 64). NOTE. For the examples in this work, take the declination from Table VIII. 3. If the sun bear north of the observer, mark the observed altitude N.; if it bear south, mark the altitude S. Apply the index error to the observed altitude by addition, or subtraction, according as its sign isor. 4. Subtract the dip corresponding to the height of the eye, from Table V., and the remainder is the apparent altitude of the lower limb. 5. Subtract the difference between the refraction (Table IV.) and the sun's parallax (Table VI.); or, subtract the sun's correction (Table VII.) 6. Add the sun's semidiameter to the preceding result, and the sum is the true altitude of the sun's centre. NOTE.-The semidiameter is taken from page II. of the month in the Nautical Almanac; or, for the examples in this work, from Table VIII. 7. Subtract the true altitude from 90°, and the remainder is the true zenith distance, which is to be marked S. if the sun bear N., but N. if the sun bear S. 8. Add the declination and zenith distance together, if they have the same name; but take their difference, if they have different names. The result, in either case, is the latitude, and it is of the same |