518 



SCIENCE. 



[Vol. I., No. 18. 



of the sugar when dissolved, saj- we do not 

 know. 



Bej'ond this fault, which is common, the 

 book is of merit as giving many experiments 

 with apparatus of easy make. Tliere is at 



times a lack of exact knowledge displaj-ed, as 

 from one who has studied in the schoolroom 

 and not in the ph3-sical laboratorj-. But with 

 the young learner tlie work will, without 

 doubt, prove fresh and instructive. 



WEEKLY SUMMARY OF THE PRO GUESS OF SCIENCE. 



ASTRONOMY. 



Virtual change of the astronomical unit of 

 time. — Mr. E. J. Stone has recently communicated 

 to the Royal society an important paper on a virtual 

 change of the astronomical unit of time, which has 

 taken place in consequence of the difference between 

 Bessel's expression for the sun's mean longitude and 

 the corresponding formulae of Hansen and Leverrier. 

 The investigation was primarily undertaken for the 

 purpose of finding an explanation of the rapidly in- 

 creasing discordance between the moon's place and 

 that indicated by Hansen's lunar-tables; and, after a 

 careful examination of a number of other hypotheses, 

 Mr. Stone thinks he has found the cause as indicated 

 above. 



For the sun's mean longitude, — 



Bessel gives O = 280°46'36".12 + l,296,027".6182< ■l-0".00012218<!, 

 Hansen " = 28O°46'43".2O + l,296,027".6741il+ 0".00011069ll=, 

 Leverrier " O = 280°46'43".51 + 1,296,027".67S4 1 + 0".00011073 P, 



in which t is reckoned, as supposed, in Julian years 

 from Jan. 1, 1850, Paris mean noon. Now, the old 

 observations which Hansen used In forming his 

 limar-tables, and in determining its constants, were 

 reduced according to Bessel's formula. When we 

 compare tables, tbus formed, with observations in 

 which the date of observation is referred to the sun's 

 place by means of Leverrier's or Hansen's tables of 

 the sun, just such a discordance must arise as if the 

 length of the unit of time had altered ; i.e., as if Bessel's 

 Julian year were different from Leverrier's, which is 

 now used in our ephemerides, having been adopted 

 about 1864. Up to 1863, Hansen's lunar-tables were 

 satisfactory : since then, the error of the moon's longi- 

 tude has increased from -t-0".121 to -l-10".2tt5. 



Mr. Stone thinks this will also clear up some per- 

 plexing discrepancies in results as to the moon's 

 secular acceleration. He points out that Hansen's 

 tables "cannot safely be used in the discussion of 

 ancient eclipses until the eSects of this confusion 

 of units of time have been cleared." [This abstract 

 is made, not from the paper itself, which is not yet 

 printed, but from an account given of it by Mr. Stone 

 to the Royal astronomical society.] — {TUe observ., 

 May.) 0. A. T. [1014 



MATHEMATICS. 



Sub-invariants. — In the two instalments of his 

 memoir which have thus far appeared. Prof. Sylves- 

 ter enters upon a new development in the modern 

 algebra; namely, the theory of semi-invariants re- 

 garded as belonging to a quantic of unlimited order, 

 in which aspect he designates them as sub-invariants. 

 An important distinction between regarding a semi- 

 invariaut as appertaining to a particular limited 

 quantic and regarding it as a sub-invariant, is, that it 

 may, while irreducible in the former character, be re- 

 ducible in the latter. The new problem thus arises 

 of determining tlie absolvitely irreducible sub-invari- 

 ants of any given degree and weight. In section I. a 

 number of general theorems are established concern- 



ing sub-invariants appertaining to a single quantic, 

 and to systems of qnantics, all of unlimited order; 

 and a method is indicated by which the author has 

 succeeded in disproving the proposition that ground- 

 forms and syzygants cannot coexist. Section II. 

 contains tables of ' germs ' for the quintic and sextic, 

 the germ of a sub-invariant being the multiplier 

 of the highest power of its last letter. Section III. 

 is devoted to a systematization of the method of 

 deducing the complete system of ground-forms of a 

 quantic by direct algebraical operation from the sim- 

 plest system of forms in terms of which any other 

 form, multiplied by a power of the quantic, can be 

 rationally and integrally expressed. The method 

 is due to Prof. Cayley, and is easily applied to tbe 

 cubic and the quartic; but, beyond these very simple 

 cases, its application would be practically impossible 

 without the aid of the methods now introduced by 

 Prof. Sylvester. The application to the quintic is 

 given in extenso. Section IV. treats of absolutely 

 irreducible sub-invariants; the generating functions 

 are obtained for absolutely irreducible sub-invariants 

 of the first seven degrees; from the generating func- 

 tion for the seventh degree it is inferred that ground- 

 forms and syzygants must necessarily coexist in the 

 case of qnantics of a sufl5ciently high order, which 

 constitutes the disproof above referred to. This sec- 

 tion is followed by an excursus on rational fractions 

 and partitions. (See 1016.) — [Amei: journ. math., 

 V. 1, 2.) F. F. [1015 



Rational fractions and partitions. — In an ex- 

 cursus on this subject, Prof. Sylvester gives, in an im- 

 proved and more complete form, the theory of simple 

 denumeration first published by hira in 1855. The 

 object of the theory is to find an analytical expression 

 for the general coefficient in the expansion of the 

 generating function; but its cardinal theorem applies 

 to tlie expansion of any rational fraction, and not 

 only of such as arise in the theory of partitions or de- 

 numeration. — [Amer. journ. math. , v. 2. ) f. f. 



[1016 



PHYSICS. 



Radiation and absorption of rock-salt. — Herr 

 C. Baur has made some observations on this sub- 

 ject. His results do not agiee with those of Mel- 

 lon! and Magnus. Melloni considered tliat heat, radi- 

 ated from rock-salt, was not absorbed by plates of 

 I'ock-salt, any more than heat radiated from other 

 substances. Magnus found that rock-salt plates ab- 

 sorbed heat radiated from rock-salt much more than 

 that radiated from other substances. He believed 

 that the radiation from perfectly pure rock-salt would 

 be completely absoi-bed by a plate of the same sub- 

 stance, and that the apparent exceptions to this law 

 were due to impurities in the radiating plate. Herr 

 Baur concludes from his experiments that, 1. Rock- 

 salt absorbs its own radiations better than those from 



