August 7, 1890] 



NATURE 



341 



to the most recent literature of this subject, Heliopora was 

 thus transferred with reference to the structure of its corallum 

 only, the living animal having been but imperfectly if at all 

 observed. 



In the course of my professional investigations of the fisheries 

 of Torres Straits I have on several occasions obtained specimens 

 of Heliopora, but had hitherto been unsuccessful in observing 

 the living animal. Last i year I obtained this coral on the 

 Warrior Reef near New Guinea, but while apparently living 

 when collected, and kept for days on board ship with the water 

 -continually changed, the zooids refused to make their appear- 

 ance. Through the courtesy of Captain Dawson, R.N., and 

 the officers of H.M.S. Rambler, I have this season journeyed 

 north in that ship, and was afforded the opportunity of conduct- 

 ing a series of investigations in the neighbourhood of the Adolphus 

 Islands, off Cape York, close to the scene of the recent Qtutta 

 wreck, and with relation to which the Rambler had been told 

 off to make a careful survey. 



At low spring-tide on the reef adjacent to the "Mid-Brother" 

 rock, 1 came across a luxuriant growth of Heliopora, and was 

 fortunate on this occasion to accurately determine the nature 

 of the fabricators of this remarkable coral. The first living 

 manifestations presented, and those visible only with the aid of 

 a pocket lens, were the protrusion of a transparent body and two 

 elongate tentacles from the numerous circular pores with which 

 the corallum is studded. At first sight some near affinity of the 

 animal to the bitentaculate Hydrozoon Lar sabellarum of Gosse 

 was suspected. The movements of the zooids during extension 

 and refraction were, however, more active than those which 

 usually obtain among the Coelenterata, and together with their 

 general aspect and comportment suggested a nearer relation to 

 the Annelida. This last-named section of the Invertebrata was 

 found on a closer examination to represent their actual position 

 in the zoological scale. On splitting one of the smaller flattened 

 branches of the coral perpendicularly and parallel with its wider 

 axis, I found that^the entire coronid system was exposed to view. 

 The little annelid fabricators, having an average length of one- 

 fifteenth of an inch, wriggled into the water in every direction, 

 a large number at the same time remaining passively in the 

 tubular chambers which they originally constructed. 



The most prominent external characters of the annelid of 

 Heliopora cerulea consist of the bitentaculate head and six 

 pairs of lappet-like branchiae, which originate in segmental 

 pairs on the dorsal surface and commence about the sixth 

 segment posteriorly from the head. Fine isolated or paired setae 

 are developed in duplicate on the majority of the residual seg- 

 ments, and two brush-like fasciculi of closely adpressed seta: are 

 conspicuous on the dorsal aspect of the penultimate and anti- 

 penultimate caudal segments. On my return to Brisbane a few 

 weeks hence, I purpose preparing and remitting a more detailed 

 account, with illustrations, of the organization of Heliopora. In 

 the interim it has occurred to me that this brief announcement 

 of its nature may prove of interest to many of your readers, more 

 especially as it may assist in throwing fuller light on the affinities 

 of the many fossil genera that have hitherto been affiliated with 

 this type among the Coelenterata, but which in common with 

 Heliopora should probably find their true position among the 

 more highly organized section of the Tubicolous Annelida. 

 W. Saville-Kent, 

 Commissioner of Fisheries, Queensland. 



Thursday Island, Torres Straits, June i8. 



Chambers's "Hand-book of Astronomy." 

 As the writer of the article on " Spectroscopic Astronomy" 

 in the above work, I should like to be permitted to comment 

 upon two points wherein your reviewer has, though doubtless 

 inadvertently, scarcely done me justice. 



On p. 292 (Nature of July 24) the reviewer says that I have 

 "■' selected CQX\.2\n determinations and arranged them in parallel 

 columns to demonstrate the efficiency of the method adopted." 

 The reference is to the comparison which I gave of the results 

 obtained by Dr. Huggins, Mr. Seabroke, and at Greenwich, for 

 motions of stars in the line of sight. But I made no selection. 

 I took all the stars that had been observed at two or more of 

 these Observatories, and gave the mean of all the observations 

 of each star. I might further add that I think your reviewer is 

 scarcely fair in his description of the discordances of my obser- 

 vations : expressed in wave-length, the average difference from 

 the mean is but a small fraction of a tenth metre. But this is 



NO. 1084, VOL. 42] 



an unimportant matter compared with the suggestion that I 

 have published a "selected " — that is, a "cooked" — comparison. 



Then your reviewer complains that I make no reference to 

 Prof. Vogel's observations of Algol, whilst I give my own " later 

 division " of my observations into groups. I made no reference 

 to Prof. Vogel's observations, because they were not published 

 until some considerable time after the final revise of my article 

 had been passed for press ; whilst, so far from my division of 

 my observations into groups being later than Prof Vogel's 

 work, it was two full years earlier, having been communicated 

 to the Royal Astronomical Society in January, 1888, by the 

 Astronomer-Royal (see The Observatory, vol. xi. p. 109). I 

 also gave my results in one of the Gresham Lectures, Easter, 

 1888. E. W. Maunder. 



Royal Observatory, Greenwich, S.E., August i. 



I REGRET that my words allowed the interpretation which 

 Mr. Maunder points out, for I had no intention of insinuating 

 that the comparisons were "cooked." What I take exception 

 to is that, according to the values given, 7 Cassiopeise has a 

 motion in the line of sight of - 12, although on February 19, 

 1887, Mr. Maunder determined it as - 54*2, and eight minutes 

 afterwards as -h 60*9 ; and again, 3 Pegasi is stated to have a 

 motion in the line of sight of - 8, although in November 1881 two 

 determinations, madewithin ten minutes of each other, differed by 

 nearly 114 miles per second. It would seem, therefore, that in 

 i making a tabular statement, even of the mean of such values 

 found by different observers, the magnitude of the probable, error 

 should be mentioned ; for, as I remarked at the time, "To one 

 unacquainted with instrumental difficulties, the motion of stars 

 in the line of sight would appear to be a quantity that may be 

 determined with some accuracy," whereas this is not the 

 case. I have no intention of questioning Mr. Maunder's skill 

 as an observer, but the fact that the discordances, when ex- 

 pressed in wave-lengths, are very small, only supports my con- 

 tention that, until more perfect instrumental conditions are 

 possible, many of the values are useless, and their determination 

 an affectation of accuracy. 



Mr. Maunder has himself to blame for my want of informa- 

 tion with respect to Algol. He gives no reference to the report 

 of the remarks made by the Astronomer- Royal in January 1888, 

 and his own comments, at the meeting of December 1889, upon 

 Prof. Vogel's work, led me to suppose nothing had been done 

 previously. The Reviewer. 



Gregory's Series. 



Gregory's series, on which are founded nearly all the 

 methods of obtaining the approximate value of ir, is made to 

 depend, in works on trigonometry, on De Moivre's theorem 

 and results flowing from it. 



The following does not require the use o( sf - i, but depends 

 only on two things— that the circular measure of an angle and 

 its tangent are practically equal when the angle is indefinitely 



small, and that tan (A - B) = J^'LA-r_^5^__. 

 I ->■ tan A . un B 

 Let _ 



tan ^: tan {a^ + a^x + a^"- -f &c. ) = Jr ; 

 . '. tan {^0 + a-^ipc -^ h) + a^{x + h)'^ + Sec.) - x + h ; 

 . : tan A . {a^ + za^x + 3^3^^ + &c. -f terms involving /i, say H} 



_ & . 



1 + x(x + h) * 

 . tan h {ai -f 2a^ -f- 3^3^;^ -f &c. + U) 

 h{a^ + 2a^ + 3«s*"* + &c- + H) 



{I + x[x + h)\ . («! + 2a^ + za-iX'^ + &c. -f H)' 

 Let h = o; 



{l+x^). (^1 + 2a^+ 3a3j:-''+~&c7)* 

 Equating coefficients of like powers of x, 



ai = I, aj = o, 03 = - i, &c. ; 

 .'. e = a^ -{- X - ^x^ + &.C., 

 where evidently a^ = o, or a multiple of ir. 

 Taking d = -, 



= I - i + i - I + &c. 



R. Chartres. 



