8 
On the general Principles 
[to. 
ing in what degree this would be the case, and what would be the amount of the 
possible error. # 
30. The only errors to which the determinations are subject, are, Ul. The uncer- 
tainty in noting the exact instant of the phenomenon ; 2nd. The error which may 
exist in the determination of the time of the places of observation; in other words, 
uncertainty in the error of the clocks. The first may be reduced by nmUi\dying 
observations certainly to one-tenth of a second in time; the latter to about the Mime. 
The first observation would be required once at the extreme, and twice at the in- 
termediate stations. The second would only be required at the exttv:ni- stations. 
Supposing the distance of the stations to be about 25 or .TO miles, we .'houltl have 
on a distance of 60 miles, six observations, in which the error might amount to one 
tenth of a second. On the very unfavorable supposition that five errors lay oneway, 
and the sixth the other, we should have four-tenths of a second in timers, T in 
space ; or about 176 yards, as the error on a difference of longitude amounting to T. 
On a difference of 10° or 12° the errors would balance each other more or less, so 
that the error would not probably exceed half a mile 1 5 . 
31. The second way of transferring time is independent of the displ v of any 
signal or its visibility, and is, consequently, Jess restricted in its application. I fear, 
however, we cannot say that the independence of the results is really, though it is 
apparently preserved. The operation consists in determining the time at one of 
the points to be fixed, and then transporting the chronometer to which the time 
was referred to the other, repeating the operation there. The chronometer being 
now referred to the account of time at each place, is obviously capable of shewing 
us the difference between the two accounts, or the difference of longitude. In this 
operation the chronometer is supposed to go with perfect exactness or regularity, 
for it little matters whether it gains or loses, provided it gains or loses equally in 
equal intervals of time. It is in the nonaccordance of this supposition with fact 
that the objection to the method consists. Were it possible to make such a chro! 
nometer as we have above supposed, the method would be perfect. 
32. That this has not yet been effected, is sufficiently known, notwithstanding 
the munificent rewards that have been either given or promised to the partial or the 
complete solution of the problem, by the several governments of Europe • yet thouirh 
perfection has not been attained, a near approach to it has been made, and it re- 
mains to show bow far the imperfections still adhering to these beautiful efforts 
of human skill, affect the question in the consideration of which we are encased . t i" 
determination of the longitude. ° s ’ 
33. Chronometers have been made which will steadily preserve, for a considerable 
period, as long as they are not exposed to shocks or irregular motion of any kind 
*heir rate, (as it is called ;) that is the daily quantity by which it exceeds or f-.ll 
short of a supposed perfect clock, agreeing with the mean state of the heavens The«» 
are of course not exactly what we want. Our object is to have such a one as will 
bear being transported from place to place, and will not be liable to chance its ran! 
though it occasionally meet with a little rough usage. Such a chronometer iV to be 
had, but they are not very common, or very cheap. It is found, however that the 
best chronometers yet made, though exceedingly satisfactory for a neriorl ’ |1 l ! 
suddenly and unaccountably altered their rate? id it is the j ossib li v of hwT Y 
only objection to their being employed in da^S^^^ST 
good chronometer will go sufficiently regularly as to admit nf n A. I , ,utle. A 
from day to day to will, ‘in one quarter of a “*? ’TP 8 kn0 ' rn 
one point, the error of this chronometer on 3 then .o , de 1 ter "'. i “ 1 >‘ 
distance of 100 or 200 mile,, repeating our detern.inatioCiteerrm'onl? 1 ’^' “ 
the more accurate, a, the rate £ 
34. With regard to the steadiness of the rate tW i, . . 
the comparison of the rates determined at the two’ places l y J ^ dged of fro,n 
WHh regard to any uncertainty in the rate wind, there 
15 As an example is always better . , 
here present the result of the operations ctrriedA I" ! G ’ ^°wever judicious, — I shall 
Mr. Herschei and hi, amoeiatmlLThn^W of JuSST* 1 .* . G /“»wicl, and Paris, by 
o longitude was found to be 9 in. 21, 46 s difibrin ' l Ac? A ,r ’ an< ^ the difference 
trigonometrical determination. This %£&**'«* 
