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394 
making that place their feeding-ground, because of the facility 
afforded them to secure these egg-cases by the abundance of the 
Hyalonemas there. 
The Co-efficient of Safety in Navigation : an attempt to ascertain 
within what Limits a Ship can be located at Sea by Astronomical 
Observations. By Prof. Wm. A. Rogers.—This was an attempt 
to ascertain mathematically the average number of miles that a 
ship may be out of her reckoning, It was a paper of length, 
indicating long and careful research. It stated that in the case 
of British vessels there is a continual increase in the proportion 
of wrecks, as shown in the following :— 
British vessels. Wrecks. 
Inc. 1858 over 1848,.+.4 38 per cent. Inc, 1862 over 1852..... 59 per cent. 
Inc. 1868 over 1858...... 44 per cent. Inc. 1867 over 1857... 57 per cent. 
For 1869 we have a decrease in the number of vessels of 4 per 
cent., and an increase in the number of wrecks of 21 per cent. 
The confidence in reckoning by insfruments had increased the 
danger. He considered separately (1) wrecks by causes beyond 
control; (2) wrecks to obtain insurance ; (3) wrecks by devi- 
ation of compass; (4) wrecks by errors of observation. He 
concluded that 70 per cent. of wrecks were from preventible 
causes. There are 3°3 times as many insured vessels wrecked as 
uninsured. The ratio of errors in chronometers wasillustrated 
in an elaborate series of tables showing that the navigator must 
expect from this source an error of 3°6 miles, must be on the 
look-out for one of 11°5, and must not be surprised at one of 21 
miles, all on the supposition that he has an average chronometer. 
One serious source of error is varying temperature during a 
voyage. The conclusion was that the navigator who assumes 
that he can get the place of his ship certainly within five miles, 
or probably within fifteen, exhibits an over-confidence which 
may lead to his ruin. 
There were other papers of interest, by Prof. Elliott, on Inter- 
national Coinage ; by Prof. Wheildon, on the Arctic Regions ; 
by Gen. Barnard, on the Relation of Internal Fluidity to the 
Precession of the Equinoxes ; by Prof. Hilgard, on Transatlantic 
Longitudes, and on Meridional Ares; by Col. Whittlesy, on 
Rivers in the Mississippi Valley ; by Prof. Hunt, on Breaks in 
the American Palzozoic Series; by A. E, Dolbear, on a new 
method of measuring the velocity of light. 
Mk. HARTNUP ON DETERMINING THE 
RATES OF CHRONOMETERS* 
‘THE difficulty in predicting the rate of a chronometer for a 
voyage arises from the imperfect state of the instrument ; 
and by a well-arranged and carefully conducted test, these im- 
perfections may be so exhibited as to enable the mariner to avoid 
the danger which must frequently follow from the neglect of such 
precautions. The Greenwich mean time is now so easily obtained 
in most seaports, that there can be no difficulty in ascertaining 
the daily gain or loss of a chronometer, if the rate so found could 
be depended on. The communication of time to the port of 
Liverpool, by the firing of the gun which is placed on the Mor- 
peth Dock Pier Head, has been so successful that the difference 
between the flash of the gun and 1 P.M. Greenwich mean time 
has not, on any occasion during the past year, been such as could 
lead to an error in a ship’s longitude to the extent of the width 
of the Mersey opposite the point on which the gun is placed ; and 
by observing the flash of the gun on two occasions at an interval 
of a few days, the rate of a chronometer may be obtained with 
sufficient accuracy for most practical purposes. The rate so ob- 
tained might, however, differ very much from the rate at sea, if 
the temperature in which the rate was obtained in port differed 
much from that to which the instrument was exposed on the 
voyage. 
Imperfect thermal adjustment is a defect so well known, that 
during the past thirty years the attempts made to improve the 
quality of marine timekeepers have been mainly confined to the 
compensation balance. The ordinary balance does not perfectly 
compensate for the change in the elasticity of the balance-spring, 
caused by change of temperature, and various forms have been 
given to balances with the view of attaining greater perfection. 
Balances have, without doubt, been made to compensate for 
change of elasticity in the spring throughout long ranges of tem- 
perature, but there is evidently some objection to their general 
adoption for the merchant navy. It is possible that the thinness 
of the laminz, and peculiarity in the construction of balances 
* Extracted from the Report of the Astronomer to the Marine Committee, 
Mersey Docks and Harbour Board, for the year 1872. 
Bly ei. 
. ‘ATURE 
which are made with the view of removing the defect above 
named, may render them less permanent in their action, and 
more liable to injury in the hands of a less skilful mechanic than 
the original maker; but however this may be, the ordi : 
balance seems to be almost universally used in the merchant 
navy. This having been found to be the case, about four years 
ago arrangements were made at the New Observatory for the 
trial of chronometers in three definite temperatures with the view 
of showing the amount of change iff their rates due to error of 
thermal adjustment, and more than one thousand marine time- 
keepers have now been tested in 55°, 70°, and 85° of Fahrenheit. — 
From a careful examination of the records of these tests there 
appears to be a definite temperature peculiar to each chrono- 
meter in which the instrument goes faster than in any other tem- 
perature, and as the number of degrees above or below this 
temperature of maximum gaining rate increases the chronometer 
loses in a rapidly increasing ratio. If we assume this law of 
variation to be that the change of rate is directly as the square 
of the number of degrees from the maximum gaining rate, the 
rates calculated on that assumption are found sensibly to agree 
with those obtained from observation ; therefore, if we have the - 
rate from observation for each of three definite temperatures, as — 
given in my last two Reports, we can find, by computation, the 
correction for error of thermal adjustment due to any other tem- 
perature. In order to do this it is necessary to find— 
. . the temperature in which the chronometer has its — 
maximum gaining rate, 
the rate at the temperature T, and 
the factor, or constant number, which multiplied by 
the square of any given number of degrees from T 
shows the amount of loss for that numbe- of degrees. 
The following example shows the method of calculating C, ~ 
T, and R from the observed rates in 55°, 70°, and 85° :— 
Res 
Cm 
Chronometer, No. 727. 
s 
Rate im 55° = — 12292. 07 
rar = =O eae 
3 FO) => STIRS et ‘ 
x oS op ae emer 
4 85 [= Sega 
d—d' = = 2°29 
£ ad +d'= + o'21 
2(2_ = 1d) eee 
Cc os. Bes 0'00509 
d+d' + 0°21 , 
Sain C x 60 — 0°3054 ic 
T = 70 — 0°69 = 69°31 
d+ d _ 
60 
From the preceding Examples 
_ Mean Daily Rate 
in 55° in 70° in 85° 
R =r ~(T —[70) — 1°88 + 0°69 x 010035 = — 1878 
G: yb R. 
s s s ] 
No. 727... —2°92—1'88 —3'13...—0'00509,..69°31...— 1°88 
Let N = any number. of degrees from T, then the Rate at 
T+ N=R+ Cx N23 
Required the Rate of No. 727 at 40° 
Here N = 29°31 and N? = 859'08 ‘ 
Hheretore the Rateat 40° = — 1°88 + (—0’00509 x 859°08) 
25. 
The values of C and T remain the same for long periods ; asa 
rule, they do not sensibly change so long as the adjustments are 
not altered, and the instrument remains in good condition ; but 
Ris more changeable, and should be redetermined on all fayour- 
able occasions, To find the change in R the rate must be first 
carefully found in some definite temperature. Suppose, for ex- 
ample, that at some subsequent time the rate of No. 727 was 
found, to be — 2°13, instead of —3'13, in 85°, then the rate at — 
T would be — o'$8 instead of — 1'88 ; but it might not be con- 
venient to obtain the rate in either of the temperatures in which 
the rates are given in the test, and then it may be found as fol- 
lows :—Suppose the rate has been found to be — 1°55 in 81°5, then 
the rate must be computed for $1°5, on the assumption that R 
has not changed, and the difference between the rate observed 
and the rate computed will be the correction to be applied to R. 
The computation is as follows :—81°5 —69°3 or N = 12:2 
and 12'2? = 148'84, 
