90 



NA TURE 



[November 25, 1897 



tage is obviously one that is deferred to the later stages of the 

 work, the only instances in the part of the work hitherto pub- 

 lished being that the calculations of sections (v.) and (viii.) of 

 chapter iv, are to some extent facilitated by the previous calcu- 

 lation of section (ii.) of the same chapter. 



The ordinary method of approximation in the simultaneous 

 equations proceeds by determining approximate values of the 

 unknown quantities in order of magnitude, at first neglecting the 

 smaller of these quantities in the equations of principal im- 

 portance for determining the larger ones. It happens, from a 

 well-known cause, that sometimes the coefficients of certain un- 

 knowns are small even in the equation* of principal importance 

 in determining them. Prof. Brown has, in these cases, found 

 it best to defer their determination until he has found all the 

 other quantities in terms of them. 



After considerable experience of both sets of differential equa- 

 tions. Prof. Brown has come to the conclusion that the first set 

 on the whole is the best adapted to the numerical work. An 

 important exception, however, arises. The two coefficients of 

 a term of long period are principally determined by two equa- 

 tions very nearly deducible, the one from the other, the deter- 

 minant of the coefficient varying inversely as the square of the 

 period. The difficulty is considerably lessened by using one 

 equation derived from the homogeneous set. 



The following table will give some idea of the extent of the 

 calculations already performed. The terms have been calculated 



It will be seen that the terms calculated include all that ar 

 algebraically of the second order. The ratio of the parallaxe' 

 is here considered as being of the first order. The terms de' 

 pending on the square of this ratio, it will be noticed, are in 

 sensible to observation. This is fortunate, as the terms cannot 

 be corrected for the neglected mass of the moon. 



We think that the results selected for publication are a little 

 too meagre. They consist of the actual solution itself, and one 

 other set of terms whose calculation divides the labour of each 

 section into two fairly equal halves. We hope that an appendix 

 will be finally published in which the value of every auxiliary 

 quantity will be given. Such an appendix might be of great 

 use in other investigations. It would also be of immense value 

 should there ever be a suspicion of error in Dr. Brown's own 

 calculations, for it would then be far easier to establish the fact 

 of such an error, should one ever creep in, and it would entail 

 less labour to carry through the correction. 



* Calculated by Dr. Hill. 



in twenty- one groups, the order of calculation being indicated 

 by the number in the first coluinn. The second column gives 

 the multiple of the eccentricities, inclination, and ratio of 

 parallaxes that is common to each coefficient of the group. The 

 third column gives the fundamental argument from which all the 

 other arguments are derived by the addition or subtraction of 

 multiples of twice the elongation, Delaunay's notation being used, 

 The fourth column gives the number of terms calculated. The 

 fifth column gives the approximate value in arc of the largest co- 

 efficient, and the sixth column the value of the largest co- 

 efficient indicating a disturbance from elliptic motion. The last 

 column gives the value in arc of the last significant figure, and 

 where, as often happens, the coefficients of a group have been 

 calculated to a different number of decimal places, then the 

 number given in this column corresponds to the coefficient 

 calculated with least accuracy. 



Dr. Brown gives as the approximate values of the constants 

 in the third column of the above table 



NO. 



I e' = 0*017 k 

 1465, VOL. 57] 



0-045 



o = 0*0026 



MARINE BIOLOGY AT THE BERMUDAS. 



A N expedition of the biological department of New York 

 -^*- University went to the Bermudas a few months ago to 

 study the marine fauna, and to investigate the conditions offered 

 for the establishment of a permanent biological station there. 

 The party has now returned, and an account of the observations 

 made is contributed by Prof. C. L. Bristol to Science, from 

 which source the following particulars have been derived : — 



The most attention was given to a search for the various forms 

 and a careful survey of the general conditions subtending their 

 abundance and collection, so that, taken as a whole, the work 

 might prove a reconnaissance and furnish knowledge for future 

 investigations. In this the expedition was fairly successful and 

 would have been much more so but for a long spell of south- 

 west wind which prevented off-shore work, excepting for a few 

 days. Our work was confined mainly to the lee shores, and 

 here we were greatly rewarded. Of corals the genera Diploria, 

 Meandrtna, Astrea, Siderastrea, Pontes, hophyllia, Oculina 

 and Alycediuin were found ; of Gorgonians, Rhipidogorgia and 

 Gorgonia. The Actinaria are very abundant and our collections 

 are numerous. We found but few hydroids and a millespore 

 coral. The Medusoe and Hydro-Medusse are very abundant in 

 the still waters of Harrington Sound. The Echinoderms are 

 exceedingly interesting and abundant. The Holothuria are 

 represented by the genera Holothuria, Semperia, Stichopits, the 

 last being very abundant. The Asteroidea are few, and are 

 represented by one species of Asterias and one of a new genus 

 not yet determined ; the Ophiuroidea by several genera. The 

 Echinoidea are represented by Cidaris, Diadema, Hipponce, 

 Echinometra, Toxopneustes, Mellita and one new genus. The 

 Crustacea are numerous and exceedingly interesting. Our col- 

 lections will be studied by Dr. Rankin, who will report on them 

 later. 



The MoUusca of the archipelago number, according to 

 Heilprin, about 170 marine forms and thirty terrestrial. Among 

 the cephalopoda are Octopus and Argonatita. The naked 

 Aplysia is fairly abundant, and numerous other naked molluscs 

 are found in Harrington Sound. 



The Annelids are not as numerous in the places we searched 

 as we expected, but those we found are new to us and the 

 genera are not yet determined. The sponges are very numerous 

 in genera and plenty in individuals. The Tunicates are ex- 

 ceedingly numerous and offer a rich field for investigations, 

 Amphioxus is reported, but we had no opportunity to search for 

 it. The abundance and beauty of the Bermuda fishes is 

 notorious. Dr. Bean is making a study of them, carrying on 

 the work started by his colleague the late Dr. G. Brown Goode. 

 Incidental to the main work of the expedition we undertook to 

 furnish the Aquarium in New York with live specimens of some 

 of these fishes, and thousands of visitors to that institution 

 testify to their beauty and gracefulness. This part of the work 

 was by no means the least interesting. We installed four large 

 tanks and a pumping engine on White's Island, in the harbour 

 of Hamilton, and acclimatised the fish before transferring them 

 to the steamship On board the boat the fish were supplied 

 with running water, thanks to the kindness of the Quebec 

 Steamship Company, and no small part of our success was due 

 to the generous and skilful aid given us by the Chief Engineer, 

 Mr. Ritchie. Under these favourable conditions our loss was 

 slight, and another season will be much less. It is interesting to 

 note that our efforts to bring invertebrates alive failed in every 



