742
ASTRONOMY
astronomical observation, and the recently - discovered variation of latitude lias introduced a new element of uncertainty into the determination. In consequence of it, the values formerly found were systematically too small by an amount which even now it is difficult to estimate with precision. Struve’s classic number, universally accepted during the second half of the 19th century, was 20-445". Serious doubt was first cast upon its accuracy by the observations of ISTyren with the same instrument during the years 1880-82, but on a much larger number of stars. His result, from his observations alone, was 20-52"; and taking into account the other Pulkowa results, he concluded the most probable value to be 20-492". In 1895 Chandler, from a general discussion of all the observations, derived the value of 20-50". Since then, two elaborate series of observations made with the zenith telescope for the purpose of determining the variation of latitude and the constant of aberration have been carried on by Professor Doolittle at the Flower Observatory near Philadelphia, and Professor Rees and his assistants at the observatory of Columbia College, New York. Each of these works is self-consistent and seemingly trustworthy, but there is a difference between the two which it is difficult to account for. Rees’s result is 20-47"; Doolittle’s, 20-56". This last value agrees very closely with a determination made by Gill at the Cape of Good Hope, and most other recent determinations give values exceeding 20-50". On the whole it is probable that the value exceeds 20’50"; and so far as the results of direct observation are concerned may, for the present, be fixed at 20"53" The corresponding value of the solar parallax is 8"77 7". In addition to the doubt thrown on this result by the discrepancy between various determinations of the constant of aberration, it is sometimes doubted whether the latter constant necessarily expresses with entire precision the ratio of the velocity of the earth to the velocity of light. While the theory that it does seems highly probable, it cannot be regarded as fully established. III. The combined mass of the earth and moon admits of being determined by its effect in changing the position of the plane of the orbit of Venus. The motion ^the earth ^ie node of this plane is found with great exactness from observations of the transits of Venus. So exact is the latter determination that, were there no weak point in the subsequent parts of the process, this method would give far the most certain result for the solar parallax. Its weak point is that the apparent motion of the node depends partly upon the motion of the ecliptic, which cannot be determined with equal precision. Notwithstanding this drawback the elements of admissible error seem smaller by this method than by any other. The derivation of the distance of the sun by it is of such interest from its simplicity that we shall show the computation. From the observed motion of the node of Venns, as shown by the four transits of 1761, 1769, 1874, and 1882, is found Mass of (earth + moon) = Vassofsun^ 332600 We have already found in gravitational units of mass, based on the metre and second as units of length and time, Log. earth’s mass = 14-60052 ,, moon’s ,, =12-6895. The sum of the corresponding numbers multiplied by 332600 gives Log. sun’s mass = 20-12773. Putting a for the mean distance of the earth from the sun, and n for its mean motion in one second, we use the fundamental equation aV2=M0 + M', M0 being the sun’s mass, and M' the combined masses of the earth
and moon, which are, however, too small to affect the result. For the mean motion of the earth in one second in circular measure, we have 27T W= 31558ir9’log-n = 7‘29907 the denominator of the fraction being the number of seconds in the sidereal year. Then, from the formula „3 = Mo = [20-12773] - 15-59814 we find Log. rr in metres = 11-"17653 Log. equat. rad. ® 6 80470 Sine ®’s eq. hor. par. 5-62817 Sun’s eq. hor. par. 8-762". The writer regards this as at present the most trustworthy of all the methods of determining the distance of the sun. IV. The determination of the solar parallax through the parallactic inequality of the moon’s motion also involves two elements—one of observation, the other of purely ot mathematical theory. The inequality in question has its greatest negative value near the time of the moon’s first quarter, and the greatest positive value near the third quarter. Meridian observations of the moon have been heretofore made by observing the transit of its illuminated limb. At first quarter its first limb is illuminated; at third quarter, its second limb. In each case the results of the observations may be systematically in error, not only from the uncertain diameter of the moon, but in a still greater degree from the varying effect of irradiation and the personal equations of the observers. The theoretical element is the ratio of the parallactic inequality to the solar parallax. The determination of this ratio is one of the most difficult problems in the lunar theory. Using Hansen’s determination, the values of the solar parallax derived from three independent series of observations of the moon are:—8-802" (from Greenwich and Washington meridian observations) ; 8'789" (Battermann, from occultations of stars by the moon); 8-767" (Franz, from observations of a lunar crater). Giving these three results the respective weights 5, 2, and 1, the result is 8'794". But the most recent and as yet unfinished researches of E. W. Brown and G. W. Hill throw doubt on the precision of Hansen’s theoretical ratio. If the latter is corrected by the work of these investigators, the value of the solar parallax derived by this method is reduced to about 8-773". V. The fifth method is, as we have said, the most uncertain of all; it will therefore suffice to quote Motion of the result, which is earth. 7r = 8-818". The following may be taken as the most probable values of the solar parallax, as derived independently by the five methods we have described :— From measures of parallax . 8-802" ,, velocity of light . . 8-777" ,, mass of the earth . . 8-762" ,, par. ineq. of moon . 8‘773" ,, lunar equation . . 8'818" The question of the possible or probable error of these results is one on which there is a marked divergence of opinion among investigators. Probably no general agreement could now be reached on a statement more definite than this; the last result may be left out of consideration, and the value of the solar parallax is probably contained between the limits 8"77" and 8*80". The value 8"80" was chosen at the Paris conference of 1896, and is now generally adopted in astronomical ephemerides. The most likely distance of the sun may be stated in round numbers as 93,000,000 miles. It is possible that observations of Eros, the remarkable asteroid of which we have already
