THE TRANSATLANTIC LONGITUDE. 71 



cient muscular force to produce a galvanic circuit. For the sharpest observation 

 a delicate adjustment is requisite; yet this very delicacy of touch, which requires 

 ordinarily no muscular effort, becomes a source of inaccuracy vphen the habitude 

 of observation thus acquired is applied to a coarsely-adjusted key. From this ex- 

 treme case downward, every degree of gradation may exist, and this crude source 

 of discordance between individuals may acquire great importance, under some cir- 

 cumstances, when the same key is employed by different observers ; since the most 

 delicate adjustment tolerable for one person, may and often does require too strong 

 a pressure for another's observations to be at all satisfactory. 



These various considerations are here presented in some detail, inasmuch as 

 they have proved particularly important in this investigation ; in which the ques- 

 tion of personal equation has been the most embarrassing, and in which all the 

 considerations here presented are to be carefully weighed. 



It will readily be seen that the measurements of personal difference by the ordi- 

 nary method, properly and successfully used in connection with tbe determinations 

 of longitude by star-signals, are inapplicable, in great measure, to determinations, 

 like the present one, by comparison of clocks. For the clock-corrections at the two 

 stations, upon the correctness and congruity of which the resultant longitude is 

 dependent, are determined by the combination of transits of high and low, zenithal 

 and equatorial stars. And the personal difference of observers for the aggregate of 

 such observations upon stars not the same, is a quantity entirely different from that 

 which would be deduced from, and applicable to, stars of any one particular class. 

 Indeed, when transits of stars at declinations beyond the limit proper for chrono- 

 graphic determinations are combined with the time-stars in the neighborhood of 

 the zenith or equator, the two values of the personal difference are scarcely com- 

 parable. In a word, the values applicable to the method of star-signals are inap- 

 plicable to the method of clock-comparisons, and their employment may result in 

 not the removal, but the introduction, of error. For time-determinations in general, 

 there are two modes in which the personal equation may be measured or eliminated. 

 One is an interchange of stations by the observers ; the other is the systematic 

 determination of time by the two observers independently, using the same instrument 

 and clock, and a well-determined series of stars carefully reduced to the same 

 equinoctial points. These methods give, not the personal difference strictly speak- 

 ing, but the mean value of the personal differences for such stars as are habitually 

 employed for determining time ; and either of them thoroughly applied would 

 remove all effect of personal equation from the longitude as measured by clock 

 comparisons. The last-named method is, as is well known, exclusively employed 

 at Greenwich, and with excellent results. 



Of course neither of these methods was available for the trans-Atlantic longi- 

 tude. The remoteness of the stations from each other, and their difficulty of access 

 precluded any undertaking of the kind, except at an inadmissible outlay of time 

 and money. It was therefore arranged that a thorough series of comparisons be- 

 tween all the observers should take place at the earliest possible time after their 

 return to the United States, and the corrections to be adopted thus determined. 

 The misapprehension by which the intended elimination of the personal equation 



