As persons, unaccustomed to calculations of this sort, may find some difficulty in comprehending the nature of the table, the two following instances will more clearly explain it.

Thus, on the 24th October, 1776, (first column,) at the Cape of Good Hope (second column,) we found the daily error, in the rate of its going, to be 2",26 (third column.) The longitude of that place, calculated on a supposition that the rate of the time-keeper had continued the same from the time of our leaving Greenwich, that is, had a regular daily error of 1",21, is found to be 18° 26' 30" east (fourth column.) And as its rate at Greenwich is, in this instance, its latest rate, the longitude thus found is the same (fifth column.) The true longitude of the place is 18° 23' 15" (sixth column.) From whence it appears, that in our run from Greenwich to the Cape, the watch would have led us into an error only of 3' 15" (seventh column,) or three miles one quarter; or had varied 13" of time (eighth column,) in four months twenty-three days (ninth column,) the period between our leaving Greenwich and our arrival at the Cape. As the Greenwich is the latest error, the tenth, eleventh, and twelfth columns, will be the same with the seventh and ninth.

But, on the 23d of February, 1777, (first column,) at Queen Charlotte's Sound, New Zealand, (second column,) the daily error of its rate was found to be 2",91, (third column.) The longitude of this place, according to the Greenwich rate, is 175° 25', (fourth column.) But having found at the Cape, that it had altered its rate from a daily error of 1",21, to 2",26, the longitude corrected by this new rate is found to be 174° 44' 23", (fifth column.) The true longitude of the place being 174° 23' 31", (sixth column;) it appears that, in our run from Greenwich to New Zealand, the error would have been only 1° 1' 29", (seventh column,) or sixty-one miles and a half, even if we had not had an opportunity of correcting its daily error; or, in other words, that the watch had varied 4' 5",3, (eighth column,) in nine months four days, (ninth column.) But the longitude, as given by its new rate, leaves an error of only 30' 54", (tenth column,) near thirty-one miles, or, in time, 2' 3",6, (eleventh column,) which has been accumulating during our run from the Cape to New Zealand, or in four months nine days, (twelfth column.) The thirteenth and fourteenth columns require no explanation.

TABLE of the Rate and Error of Mr Kendall's Watch on Board the Resolution.
I. | II. | III. | IV. | V. | VI. |
-------|---------------|--------|-------------------------------|
| | | | | |
| |Error of|Longitude |Longitude|True |
TIME. | PLACE. | Daily |by Green- | by |Longitude.|
| | Rate. |wich Rate.|New Rate.| |
| | | | | |
| | | | | |
-------|---------------|--------|----------|---------|----------|
| | " | ° ' " | ° ' " | ° ' " |
1776. | |--------|----------|---------|----------|
June 11|Greenwich |-1,21 | 0 0 0E | 0 0 0E| 0 0 0E |
Oct. 24|Cape of Good |-2,26 | 18 26 30 | 18 26 30| 18 23 15 |
| Hope | | | | |
1777. | | | | | |
Feb. 22|Queen Char- | | | | |
| lotte's Sound,|-2,91 |175 25 0 |174 54 25|174 23 31 |
| New Zealand | | | | |
May 7|Anamooka |+0,52 |186 13 26 |186 13 15|185 11 18 |
June 7|Anamooka |-0,54 |186 8 28 |186 12 43|185 11 18 |
July 1|Tongataboo |-1,78 |185 48 50 |184 53 0|184 55 18 |
Sept. 1|Otaheite |-1,54 |211 41 26 |210 39 8|210 22 28 |
Oct. 17|Huaheine |-2,30 |210 14 52 |208 50 24|208 52 24 |
Nov. 7|Ulietea |-1,52 |209 42 54 |208 25 22|208 25 22 |
1778. | | | | | |
Apr. 16|Nootka |-7,0 |235 32 45 |233 56 0|233 17 8 |
Oct. 14|Samganoodha |-8,8 |197 44 15 |193 12 35|193 31 20 |
1779. | | | | | |
Feb. 2|Owhyhee |-9,6 |214 7 35 |203 37 22|204 0 0 |
May 1|Saint Peter and| T.K. | | | |
| Saint Paul, | stopt. |173 86 0 |159 20 0|158 43 16 |
| Kamtschatka | | | | |
-----------------------------------------------------------------
| VII. | VIII. | IX. | X. | XI. | XII. |XIII. | XIV.|
|-----------------------------------------------|------|---------|-------|
|Accumulated Error by| |Error by New Rate. | |Thermo- | B |
| Greenwich Rate. |Length| |Length| meter. | a |
|--------------------| of |-------------------| of |---------| r |
| | | Time.| | | Time.| | o |
| In | In | | In | In | |Gr. Least| m |
| Space. | Time. | | Space. | Time. | | Height. | e |
|---------|----------|------|---------|---------|------|---------| t |
| ° ' "|H. ' " |Mo Da | ° ' "| H ' " | Mo Da| | | er. |
|---------|----------|------|---------|---------|------|----|----|-------|
| | | | | | | | | |
|+ 0 3 15|0 0 13,0 | 4 23 |+ 0 3 15|0 0 13,0| 4 23| 84| 63| 30, 0|
| | | | | | | | | |
| | | | | | | | | |
| | | | | | | | | |
| 1 1 29|0 4 5,9 | 9 4 |+ 0 30 54|0 2 3,6| 4 9| 73| 53| 30, 0|
| | | | | | | | | |
| 1 2 8|0 4 8,5 |11 22 |+ 1 1 57|0 4 7,8| 2 18| 83| 74| 30, 1|
| 0 57 10|0 3 48,6 |12 25 |+ 1 1 25|0 4 5,6| 1 3| 79| 73| 30,15|
| 0 53 32|0 3 34,1 |13 21 |- 0 2 18|0 0 9,2| 0 24| 85| 69| 30,15|
| 1 18 58|0 5 15,8 |15 27 |+ 0 16 40|0 1 6,6| 2 6| 90| 70| 30, 1|
| 1 22 28|0 5 29,8 |17 17 |- 0 2 0|0 0 8,0| 1 18| 90| 72| 29, 9|
| 1 17 32|0 5 10,1 |18 10 | 0 0 0|0 0 0,0| 0 21| 92| 70| 29, 7|
| | | | | | | | | |
| 2 15 27|0 9 1,8 |24 2 |+ 0 28 42|0 2 34,8| 5 20| 65| 41| 30, 0|
| 4 12 55|0 16 51,6 |30 15 |- 0 18 45|0 1 15,0| 6 13| 57| 36| 20,15|
| | | | | | | | | |
| 10 7 35|0 40 30,3 |34 14 |- 0 22 38|0 1 30,5| 3 27| 88| 70| 29, 8|
| | | | | | | | | |
| 14 52 44|0 59 30,9 |37 18 |- 0 36 44|0 2 16,9| 3 4| | | |
| | | | | | | | | |
--------------------------------------------------------------------------

From this view of the time-keeper it appears, that for near two years it altered its rate very inconsiderably, and therefore that its error, according to the Greenwich rate, if we had had no opportunities of correcting it, amounted only to 2-1/4°. That afterward, at King George's Sound, or Nootka, it was found to have varied exceedingly; of course, the longitude, by its Greenwich rate, was becoming considerably erroneous. About this time, it should be remarked, the thermometer was varying from 65° to 41°. The greatest alteration we ever observed in the watch was, during the three weeks we were cruising to the N.; in which interval, it gave the longitude of the East Cape with a difference of twenty-eight miles, I have marked the longitude of Saint Peter and Saint Paul, as given by the time-keeper, notwithstanding it stopped a few days before we arrived there; this I was enabled to do, from comparing the longitude it gave the day before it stopped, with that given by Mr Bayley's watch, and allowing for the error of the latter.

The use of so accurate a measure of time is sufficiently evident, from its furnishing in itself the means of approximating to the longitude at sea, as may be seen in the above table. But, besides this, we were enabled, by the same means, to give a degree of accuracy to the lunar observations, which they cannot otherwise pretend to; and, at the same time, by reducing a number of those observations to one time, obtain results approaching still nearer to the truth. In surveying coasts, and ascertaining the true position of capes and head-lands, it reaches the utmost degree of practical exactness. On the other hand, it is to be observed, that lunar observations, in their turn, are absolutely necessary, in order to reap the greatest possible advantages from the time-keeper; since, by ascertaining the true longitude of places, they discover the error of its rate. The original observations that were made in the course of this voyage, have been published by order of the Board of Longitude, and to those I must refer the reader, for his further information on this subject.

N.B. The observatories were placed on the west side of the village of Saint Peter and Saint Paul.

Latitude deduced from meridian zenith
distances of the sun, and of five stars
to the S., and five to the N. of the
zenith 53° 0' 38" N.
Longitude deduced from one hundred
and forty-six sets of lunar observations 158 43 16 E.
Longitudy by time-keeper, according to
its Greenwich rate 173 36 0
Longitude by time-keeper, according to
its rate found at Owhyhee 159 20 0
Variation of the compass, by azimuths
taken with three compasses, made by
Knight, Gregory, and Martin 6 18 40 E.
Dip of the North Pole of the magnetic
needle, being a mean of the observations
taken in June and September 63 5 0

It was high water, on the full and change of the moon, at thirty-six minutes past four, and the greatest rise was five feet eight inches. The tides were very regular every twelve hours. On the coast, near the bay, the flood came from the S., and the time of high water was near two hours sooner than in the harbour of Saint Peter and Saint Paul.

SECTION VI.