SCIENCE. 



discover a method of finding the longitude at sea 'within 

 60 miles, ^15,000 if with 45 miles, and .£20,000 if within 

 30 miles. This offer did much to awaken interest in the 

 subject. Though we have long since passed the lowest 

 limit then mentioned, 30 miles, it is doubtful if any two 

 navigators will agree as to what limit we have actually 

 reached. The general testimony of sea-captains, in 

 answer to my inquiries on this point, is that one mile is 

 the ordinary limit within which the co-ordinates of a 

 ship's place can be determined. A few placed the limit 

 at half a mile. Only one navigator, with an experience 

 of 30 years, placed the limit at 5 miles. 



Two methods were proposed for the solution of the 

 problem. Morin proposed what is now substantially 

 the Lunar Method, and Maskelyne undertook the solution 

 of the problem by observing the astronomical phenomena, 

 such as eclipses of Jupiter's satellites. On the other 

 hand, mechanicians devoted every energy to the me- 

 chanical problem. As the result of these labors, we have 

 two essentially different methods for the determination of 

 Longitude at sea. 



I. By Lunar Distances, Occultations and Eclipses of 

 Jupiter's Satellites, &c. 



II. By Chronometers, assuming a rate at the beginning 

 of the voyage. 



The latter has for a long time been regarded as the 

 more accurate method, but the difficulties to be over- 

 come can be readily imagined, -when we consider that 

 even in the determination of the position of fixed obser- 

 vations, in which appliances of ihe uimost refinement are 

 at hand, the places vary widely from the truth. For ex- 

 ample, we find variations, in the measured difference of 

 longitude between Greenwich and Paris, as great as 5.5 s , 

 or 1% miles, existing previous to the introduction of the 

 telegraphic method of determining, longitudes. The 

 range between the earlier determinations of the difference 

 ot longitude between Greenwich and Brussels is 10 miles. 

 Moon Culminations are more accurate than Lunars, but 

 the same in principle. They are the more accurate when 

 the longitude depends upon observations at each station, 

 since the errors of Tables are thus eliminated. From a 

 careful discussion of a long series of observations made 

 at fixed observatories, with the most perfect instruments, 

 it is found that we must expect from the Lunar Method 

 an absolute error of six miles as the result of any number 

 of observations. This corresponds in a general way with 

 Prof. Peirce's investigation. He found that the ultimate 

 limit, when one limb of the moon was observed, to be 

 0.55'. " Beyond this," he says, " it is impossible to go with 

 the utmost refinement. By heaping error upon error, it 

 may crush the influence of each separate determination ; 

 but it does not diminish the relative height of the whole 

 mass of discrepancy." But the discrepancy between the 

 results for different limbs of the moon often amounts to 

 10' in the mean determination of a year. The assumption 

 that the ultimate limit of accuracy is as great as I s seems 

 to be a very moderate widening of the limits. I find it to 

 be 2.4". 



For fixed observatories, using the moon's tabular place, 

 we must expect an error of 3.1 miles, with a range of 

 12.9 miles. For Lunar Distances with sextant, on land, 

 we must expect an error of 10.2 miles, with a range of 

 24.2 miles. For Lunar observations at sea these quanti- 

 ties should at least be doubled. 



We now come to the subject of chronometers. The 

 sources of errors are : 



(a) Variations of rate arising from the action of mag- 

 netism. Airy's experiments show an extreme variation 

 of 5.8" in the daily rate of a chronometer, due to terres- 

 trial magnetism. 



(b) When chronometers are swung on the same sup- 

 port, it is probable that there is a sympathetic action be- 

 tween them, similar to the results recently found by Mr. 

 Christie with the Transit of Venus Clocks. 



(c) Variation on account of change of barometric 



pressure. This varies between 0.3 s and 0.8 s per day for 

 every inch of change in the barometer. 



(d) Variation between land and sea rates. Almost 

 every chronometer will change its rate, when its circum- 

 stances, either of rest or motion, are changed. The Bos- 

 ton standard clock of Messrs. Bond & Son, almost in- 

 variably has a different rate on Sunday from any other 

 day ot the week. So, also, it has a change of rate when 

 the streets are covered to any considerable depth with 

 snow. 



{e) Variation of rate at sea, on account of change of 

 temperature. Mr. Hartnup, of Liverpool, was the first 

 to give, not only the general rate of a chronometer, but 

 also the rate for different temperatures. 



An elaborate discussion of the errors of chronometers, 

 from data collected at the Greenwich Observatory, from 

 chronometric expeditions and from chronometers used 

 in the Merchant and Naval services, the following result 

 has been reached. 



At the end of 20 days the navigator must expect an 

 average error of 36 miles. He must look out for an error 

 of 36 x 32 or 1 1.5 miles, and the amount of his error may 

 prove to be twice this quantity, or 21 miles, all on the sup- 

 position that he has an average chronometer, and this is 

 independent of the errors of observation, which must 

 still be added. 



We come finally to the consideration of the problem, 

 — How near is it possible to find the place of a ship at 

 sea by astronomical observations, taking into account all 

 the errors to which observations are liable ? 



For the sake of simplicity we shall consider but one 

 method, the method usually followed, viz.: by measure- 

 ment of the altitude of the sun with a sextant, at a given 

 time before it comes to the meridian for longitude, and 

 the measurement of its culmination, for latitude. 



We must first of all ascertain the magnitude of the 

 errors to which observations with the sextant are liable. 

 The following are some of the errors which we must 

 ordinarily expect in observations with this instrument : 



{a). Instrumental errors, such as eccentricity, errors of 

 graduation, index error, &c. Errors of this class often 

 exceed one minute of arc. even in a first-class instrument. 



(b) . Errors in noting time. No observer at sea pretends 

 to note the time closer than one second. If we assume 

 this low limit and multiply the co-efficient 3.5 already 

 found, we have an error of nearly one mile. 



(c) . Errors arising from imperiect sea horizon. 



(d) . Errors arising from the use of approximate data. 



(e) . Errors depending on the la itude of the ship and 

 the time of observation. By combination in the same 

 direction, errors of this class may be very large, and, for 

 the most part, they escape the attention of the navigator. 

 The most favorable time for an observation of the sun 

 for longitude is when-it is exactly east or west. Here an 

 error of one minute of arc in the observed altitude pro- 

 duces an error of the same amount in the resulting time, 

 but if the observation is made 40 minutes from the 

 meridian, an error of one minute in altitude may produce 

 an error of 6 miles in the resulting position. 



{/). Errors arising from the error in the estimated run 

 of tne ship between the morning and the noon observa- 

 tions. 



The data for assigning a limit to the errors of observa- 

 tion with the sextant are as follows : 



1. Observations on Shore. From a discussion of the 

 observations by Williams in 1793, by Paine in 1831, by 

 various observers at Willets Point in 1869, 1871 and 1872, 

 by Hall and Tupman at Malta and Syracuse, and by 

 Newcomb and Harkness at Des Moines, we find that for 

 latitude the average error of observation with the sextant 

 is 8', that the average range between the greatest and the 

 least results of a given series is 36", the latter value having 

 a range between 14" and 59". The coefficient comes 

 out 4.4. For time the average error is 1.1*, the range is 

 4.7", and the coefficient is 4.4. 



