for these three stars 15" to 20". B. 60". to 100" in AR. Struve's catalogue has wrong sign for Dec. of H. 90, and it is missing on his chart."

732, 746. B. 63, 64. Struve supposes B. 72 and 74 identical with 63 and 64. G. P. B. says, “probably explained rightly."

759. B. 67. — H. 114. "B. is right. H. 20" in error." G. P. B.

767. B. 69, 73. "Not in Harvard Zones." G. P. B. I have assumed the identity of 767 and B. 69. B. 71. Not found in Harvard Zones.

2

Struve VB. 77. G. P. B. says, "I doubt the existence of this star independently of t', (H. 114).” 783, 795. B. 81, 84. Struve says, "identical." G. P. B. says, “These are two distinct stars, H. 122 and 125." There is, however, an error of 1' in B.'s position.

797. B. 85. Struve says, “B. 85 does not exist in the heavens." Its position agrees very closely with the Harvard Zones.

801. B. 86.

Struve says, "Probably identical with B. 78." These are distinct stars. G. P. B.

825. B. 88. Struve says, it "does not exist in the heavens." It is H. 131. Error of about 25" in Herschel, of about 55" in B.

864. B. 92. Error of 40" in Herschel, 80" in Bond.

ON THE MAGNITUDES OF THE STARS CONTAINED IN THE PRECEDING CATALOGUE

THE difficulties which attend the proper investigation of this subject are very great; and it was Prof. Bond's desire and intention, which he only gave up very reluctantly, to submit the whole matter to a very thorough discussion. But time and strength failed him to accomplish this object to his own satisfaction; and the preliminary results for magnitude which precede, are those which are given in the papers entrusted to my care. They accompany the stars' positions, as well in the partial catalogues which were subjected to his own revision, as in the copy of the final catalogue which he did not see completed, but which was made according to his own directions.

I have, however, omitted from the printed catalogue the magnitudes of the stars a and d of the trapezium, as they were manifestly given too faint; and, as will be seen by the comparisons which come a few pages later, it would perhaps have been better to do the same with a few others.

I shall begin by giving an account of the method of sequences which Prof. Bond employed, to connect the magnitudes of neighboring stars, and of the method in which I myself reduced these in 1864, under his immediate direction. The sequences are thus arranged in the original manuscripts. The stars' names are written in the order of their magnitude. Upon the same line are given stars which differ but slightly. Upon consecutive lines those which differ more largely.

And in some cases it is stated that the difference between two stars on consecutive lines is larger than usual.

The following method was suggested by myself for the reduction of such observations, and carried out.

The slight difference between two stars on the same line was called 1 grade; the greater difference between two stars on consecutive lines, 2 grades, and where noted as especially large, 3 grades. To the brightest star observed in one group or sequence of stars was assigned the magnitude 0 grades; to the next brightest, the number of grades by which it differed from the previous one, and so on.

For example, I give below the first sequence observed, 1858, Jan. 4th.

I inferred from this, that if g represented the number of grades by which each star differed from K, the value of g for the star F would be 3, as the name F occurs first on the second line, and K is called much brighter. Again, g for D would be 4, for A 5, as these occur in succession on the same line; for H, it would be 7, and so forth, as in the following reduction.

Half grades occur where the difference between two stars is considered doubtful. It now becomes necessary to ascertain what these numbers g represent. In the first place the stars selected as the brightest in each sequence being not identical in different cases, for the magnitudes on any ordinary scale each sequence will be represented for any case by

m=x+yg

Where x is a number varying from one sequence to another, denoting the magnitude of the star for which g=0, or the brightest star in the sequence; while y is the ratio of a grade to a magnitude, which may or may not vary from one sequence to another. I assumed, by Prof. Bond's direction, that y was constant for the whole series of observations, and equal to 0.25; a previous determination of the value of y from the materials contained below, by the method of least squares, having shown that in general the variation of y from 0.25 exceeded but slightly its probable error.

In other words, the assumption was that a variation of 0.m 25 on G. P. Bond's scale was equivalent to the difference between the magnitudes of two stars upon the same line; that the difference between two stars in succeeding lines was equal to 0.TM 50 (or 0.75 in case of very large differences), and these assumptions best harmonized the observations of sequences with those of magnitudes made directly.

This process has in general given results corresponding quite nearly to the magnitudes estimated directly, though there are one or two cases of discrepancy among the brighter stars.

The following tables give the sequences, reduced in the first place to grades, and secondly to magnitudes; g being the grade, m the observed magnitude.

=

All the preceding sequences were reduced by the formula m' — m'° +0.25 g where m' is the value of m' for g=0; and the sum of the deviations m-m is 0, except so far as owing to decimals, beyond the first, of a magnitude. The values of m were always estimated on the same night, for the foregoing sequences.

The sequences which follow differ nowise from those that precede, excepting that the value of m° below were taken from a preliminary catalogue of magnitudes, obtained from the Zones of Section I.; and were not estimated the same night that the values of g were.