April 5, 1906] 



NA TURE 



54: 



of the German Empire ; these .ire all identical in form, the 

 plan of which is practically that adopted by the Inter- 

 national Meteorological Congress at Rome in 1879, and 

 leaves nothing to be desired. With the exception of an 

 occasional improvement, such as the reduction of the old 

 anemometrical factor, which assumed that the velocity of 

 the wind was three times as great as the velocity of the 

 cups of the instrument, and the addition of a table show- 

 ing for each station the difference between local time and 

 mid-European time adopted in Germany in April, 1893, 

 there lias been practically no change in the contents of 

 publication for many years. This continuity of form is a 

 greal advantage, and considerably enhances the value of 

 the work. 



We have received from the director of the Vatican 

 Observatory, Sig. P. Angelo Rodriguez, O.S.A., vol. vii. 

 of the Pubblicasioni della Specola Vaticana (Tipografia 

 Yaticana, Rome, 1005). In these pages we first have the 

 individual daily meteorological observations made during 

 the years 1902 to 1904, both years inclusive. These are 

 graphically plotted in three tables which are given at the 

 end of the volume. Sig. Mg. Alfredo Tonetti contributes 

 a valuable study of the cloud observations made during 

 the years 1891-6, and this is followed by two appendices, 

 which include observations of meteors for the years [89: 

 to 1S96, and the mean monthly values of cloudiness for 

 the same period. Among other sections of interest may be 

 mentioned a brief discussion of the exceptional high 

 temperatures recorded in July and August of the year 1904, 

 comparison data being added commencing in 1890. Sun- 

 spot observations are also dealt with, and, in addition to 

 the individual daily observations, a summary for each 

 year, commencing with 1896, is added. Special reference 

 is made to the large spot of February, 1905, and a repro- 

 duction (original size) of the solar disc for February 7 is 

 idded, the original photographic image measuring nearly 

 eleven inches in diameter. 



In the Transactions of the Institution of Engineers and 

 Shipbuilders in Scotland (vol. xlix., part v.), .Mr. W. A. 

 Ker publishes a suggestive paper on some common errors 

 in the use of electric motors for machine driving. In it 

 he gives a list of common machines, with the types of 

 motors which he considers most suitable for them. 



Attention is directed in the Engineering ami Mining 

 Journal (vol. lxxxi.. No. 10) to the very low cost of ore 

 dressing which has been attained at the mill of the Osceola 

 Copper Mine, Lake Superior. The average cost per ton 

 of rock stamped in 1905 was only S'.J., as against qd. in 

 1904. Ihese extraordinary figures were obtained in the 

 treatment of a million tons of rock per annum, all the 

 ore pa ;h the mill having been crushed to go 



through a j-inch to 3/16-inch round hole. 



The locomotive industry is dealt with in an exhaustive 

 paper by Mr. L. Le Chatelier in the Bulletin de la Socitti 

 I' Encouragement (vol. cviii., No. 2). Beginning with 

 Trevithick's locomotive of 1803, he illustrates the leading 

 types, and expresses the opinion that the works of the 

 Hanover Engineering Company represent the most perfect 

 example of the international locomotive industry. The 

 Crewe works, with their 7500 workmen and their annual 

 output of seventy-five locomotives, are referred to by the 

 author in terms of warm admiration. 



" Economic Studies in Italy " form the subject of a 

 letter by Prof. Achille Loria in the Economic Journal for 

 March. A noteworthy feature of Italian economics is the 

 absence of any scientific treatment of socialistic problems. 

 NO. 19OI, VOL. J$] 



Is the Bulletin of the Belgian Royal Academy (1905, 

 xi.), the death is announced of the oldest member, M. 

 Gustave Davalque, who was elected associate in 1854 and 

 member in 185'), and drew up reports on mineralogy for 

 tie- society subsequent to 1872. 



Prof. Lligi Bekzolari contributes in the Rendiconti of 

 the Lombardy Institution an interesting account, extending 

 to more than sixty pages, of the work of the late Prof. 

 Luigi Cremona. A 1 i — t of previous biographical notices is 

 given in a footnote. 



Prof. G. Cesaro, of Liege, describes in the Bulletin of 

 the Belgian Academy, x., a new method of proving geo- 

 metrically the principal formula? of spherical trigonometry, 

 notablv Lhuilier's and Euler's formula;, Napier's and 

 Delambre's analogies, and the expressions for the radii of 

 the circles of a triangle. 



Mr. II. M. Taylor, F.R.S., has published in the 

 Messenger of Mathematics, No. 414, a collection of geo- 

 metrical dissections, in which it is shown how 10 trans- 

 form figures from one shape into another by division 

 into a definite number of parts and re-arrangement of the 

 parts. While these constructions afford a highly interest- 

 ing studv, it may be desirable to point out that if it be 

 required, for example, to convert a rectangle into a square 

 of equal area by this method, the construction presupposes 

 a knowledge of the side of the required square. 



In the Bulletin of the American Mathematical Society 

 for January Prof. Jacques Hadamard gives a review in 

 French of the late Prof. Willard Gibbs's " Elements of 

 Statistical Mechanics," which appeared in 1902. Based as 

 the review is on a detailed study of Gibbs's work and of 

 criticisms thereon, the notice forms in some respects an 

 innovation in reviewing which might with advantage be 

 followed on other occasions in connection with mathe- 

 matical works. It is certain that the book in question 

 contained many features that could only be properly judged 

 after long and minute study. 



In a paper reprinted from the Abhandlungen of the Royal 

 Academy of Saxony, xxix., 4, Dr. Otto Fischer disi usses 

 the dynamics of the motion of a system of bodies jointed 

 together and moving in space. An illustration of such 

 jointed systems is afforded by the limbs of animals. In 

 general, a system of n jointed bodies has 3*1+3 degrees 

 of freedom, but there are many cases in which the number 

 is less, and the author shows how the equations can be 

 simplified by replacing the system by a dynamically equi- 

 valent set of particles or " reduced system." 



Under the title " Abhandlung zur Didaktik und Philo- 

 sophic der Naturwissenschaft," Messrs. Julius Springer, 

 of Berlin, are issuing a series of pamphlets, in the form 

 of monograph supplements to the Zeitschrift fill den 

 physikalischen und chemischen Unterricht. The object of 

 these pamphlets is to give expositions of various points 

 connected with the teaching of the sciences in quest ion. 

 No. 5 of the series is by Prof. Hans Keferstcin, of Ham 

 burg, and contains an exposition of the elementary proper- 

 ties of lenses and optical combinations treated from an 

 experimental point of view. In the introduction the author 

 points out that two of the various branches of physics, 

 mechanics and optics, are made to assume a more mathe- 

 matical aspect than the rest, the former by introducing the 

 concept of particles, which reduces the study to that of 

 certain systems of points, the latter by the concept of 

 leading to the study of certain systems of lines. The 



