September 15. 1898] 



NATURE 



489 



and the length of this pendulum can be altered by raising or 

 lowering a sliding piece. The second pendulum carries a 

 table on which a piece of black paper is slowly drawn by 

 clockwork in a direction perpendicular to the plane of vibration, 

 and the sand escaping from a hole in the cup of the upper 

 I pendulum traces out the vibration curves on the paper, the 

 i thickness of the line of sand being greatest where the motion 

 ' is slowest and vice vena. By an electric arrangement the 

 two pendulums can be started with any required difference of 

 . phase. The use of sand is not very convenient if the draw- 

 ings are to be preserved, but they can be photographed, and 

 the figures given by Prof. Righi show distinctly the variations 

 of thickness of the sand with the speed. Prof. Righi's paper 

 forms the subject of a communication to the Bologna Academy 

 of Sciences. 



Our present knowledge of the theory of errors receives an 

 interesting addition at the hands of M. Charles Lagrange in the 

 form of a contribution to the Bulletin de F Acad^inie royale de 

 Belgique (vol. xxxv. part 6). Without going into details of a 

 purely mathematical nature, certain of M. Lagrange's con- 

 clusions appear sufficiently important to be worth noticing. In 

 taking the arithmetic mean of a number of observations as the 

 most probable value of the observed quantity, common sense 

 suggests that any observations differing very widely from the 

 rest should be left out of count as being purely accidental, and 

 thus likely to vitiate the result. But as it is impossible to draw 

 the line from theoretical considerations between values retained 

 and values omitted, any such omission would necessarily be 

 unjustifiable. This discrepancy between theory and common 

 sen.se is, to a large extent, reconciled by M. Lagrange's " theory 

 of recurring means." According to this theory, the weight to 

 be assigned to any observation is inversely proportional to the 

 square of the error of the observed value relative to the most 

 probable value. Taking, then, the arithmetic mean of a number 

 of observations as a first approximation to the most probable 

 value, the errors relative to this mean determine the weights of 

 the various observations. The weighted mean is then taken as 

 a second approximation to the most probable value. This mean 

 determines a fresh series of weights to be assigned to the 

 observations by which a new weighted mean — the third 

 approximation to the most probable value — is found, and so 

 on to any required degree of approximation. These successive 

 means are called by M. Lagrange "recurring means," and by 

 their use the effects of sporadic errors are, to all practical 

 purposes, eliminated, since the weight assigned to the corre- 

 sponding observations soon becomes relatively small. 



In the latter half of 1895, a new fish hatchery, under the 

 direction of the United States Fish Commission, was established 

 at a small place called Ten Pound Island in Massachusetts Bay, 

 and in the autumn of 1897 there were hatched and " planted" 

 in the waters of the bay over 60,000,000 small cod fry. At the 

 end of the year some 30,000,000 eggs were still in process of 

 hatching. The number of eggs successfully hatched is much 

 greater in the early than in the latter half of the season, when 

 only 54 per cent, of the eggs are successfully hatched in propor- 

 tion to the first half. From ^^ Journal of the Society of Arts, 

 we learn that Sir D. Colnaghi, H.M. Consul at Boston, says 

 that men proficient in stripping a codfish of its spawn are put on 

 board the shore fishing boats which land their catch at Kittery, 

 Maine, in the proportion of one man to each boat. As the fish 

 are taken alive from the water, they are inspected and, if suit- 

 able for the purpose, are stripped of their eggs, which are placed 

 in jars and forwarded to Gloucester, Massachusetts. More or 

 less, the eggs are injured in transit, but it has been, on the whole, 

 advantageous to forward them to Ten Pound Island, where good 

 results in hatching have been obtained. Nature is followed as 

 NO. 1507, VOL. 58] 



far as possible in the hatching process, the eggs being placed in 

 perforated boxes and sea water direct from the ocean being con- 

 tinuously pumped through the boxes, so that the temperature 

 may be as nearly as possible the same as that of the ocean. As 

 soon as the eggs are hatched, the small fish are planted or 

 released in the waters of Massachusetts Bay and have to rely on 

 themselves, the same as the fry spawned in the open ocean. 

 Ipswich Bay, Massachusetts, and the contiguous waters appear ■ 

 to be a favourite spawning ground for codfish, and the artificially- 

 hatched fry, therefore, mingle with the many others of their kind 

 and take the same chances in the struggle for existence. There 

 are, of course, no data on which to base any calculation as to 

 the percentage of artificially-hatched fry which reach maturity, 

 but the officers of the Fish Commission claim that the fish 

 released by them are hardier in proportion, the weaker ones 

 having been sifted and the stronger alone planted. As regards 

 the success of the hatchery, it is proved that since the Fish 

 Commission commenced operations the supply has certainly 

 increased. Some years ago so few codfish were taken by the 

 shore fishermen, that the fishery had become unremunerative, 

 but at the present time fish are fairly abundant, and the fishery 

 gives employment to a good number of men, who themselves 

 admit that the hatchery operations have been successful. After 

 the codfish season is over, the officials turn their attention to 

 lobster hatching, and the same operations are gone through as 

 with the codfish. 



A NUMBER of interesting facts concerning illuminated buoys 

 are brought together in an article in the Times of September 6. 

 From this description it appears that Mr. J. Pintsch was the 

 first to successfully construct a buoy to show a light at night. 

 The light is produced by gas, which is stored in a compressed 

 state in the body of the buoy, and passed up to the burner 

 through a small pipe controlled by an ingenious automatic regu- 

 lator which causes the gas to be emitted at a low and uniform 

 pressure. Stored up in the buoy in a compressed state — the 

 pressure being equivalent to that of about five atmospheres — 

 and passing out very slowly, the gas will last some two or three 

 months burning always by day and by night. Coal gas cannot 

 be used for this purpose because compression robs it of more 

 than half of its illuminating power, while in the case of oil gas 

 the loss is so slight that it is practically immaterial. The light 

 itself is surrounded by a small lenticular arrangement intended 

 to enhance the illuminating power, enclosed in a glass lantern 

 fixed about eight or ten feet above the sea level, and in clear 

 weather is visible five miles. At first it was found desirable to 

 use only a fixed light, but more recent experience has shown 

 that it is possible by suitable mechanism to show a quick flash- 

 ing light and an occulting light, these variations being extended 

 by the use of coloured glass. 



Recognising the great value to navigation of lighted buoys 

 which could be depended upon, the Elder Brethren of the 

 Trinity House (we learn from the article referred to in the 

 foregoing note) have done much to encourage the develop- 

 ment of the system in this country by placing gas-lighted 

 buoys at many important points in the channels at the entrances 

 of the Thames, in the Solent, and elsewhere. These guides to 

 navigation have also been established by the Scottish Lighthouse 

 Board, the local authorities for the Mersey, the Clyde, the Tees, 

 the Ribble, King's Lynn, and sundry other seaports, and now 

 on the coasts of the United Kingdom there are close upon one 

 hundred gas-lighted buoys in position. In the Suez Canal, in 

 Canadian and Australian waters, these buoys are in use. In 

 America, also, a considerable number are employed ; but the 

 United States Lighthouse Board has, also, some electrically- 

 lighted buoys in Gedney's Channel approach to New York. 

 These buoys are connected to each other and with the shore by 



