Dec. 26, 1878] 



NATURE 



169 



do, how nearly theory alone, without any empirical cor- 

 rection, will represent the observations. It is then at 

 once apparent that the residuals cannot be represented 

 by corrections to the epoch of mean longitude, mean 

 motion, and secular acceleration, and any approximation 

 to a mean value of the latter would have different values, 

 according to the mode of using the data. To obtain the 

 best result from the ancient and modern observations 

 combined, it was deemed advisable to assign a minimum 

 probable error of 4' or 5" to each residual for the modern 

 observations. Equations of condition for correction of 

 epoch, mean motion and acceleration are formed, and 

 extend from B.C. 688 to A.D. 1875, or over a period of 

 2,500 years, and the resulting corrections to Hansen's 

 values for 1800, are, for mean longitude, +3" '90, mean 

 motion -19" '03, and for secular acceleration -3''''36; 

 Hansen's adopted value of the latter being 12"- 17, the 

 value which best satisfies the observations discussed by 

 Prof. Newcomb is found to be 8""8. Though he considers 

 this correction to the tabular acceleration to be clearly 

 indicated, the residuals for the modem observations are 

 yet of such magnitude as to be wholly inadmissible, and 

 therefore the theory in its present state will not represent 

 observations with any value of the secular acceleration, 

 and respecting the cause of the magnitude of these 

 remaining differences, he makes two hj'potheses : (i) that 

 they are only apparent deviations caused by inequalities 

 in the earth's axial rotation, (2) that they arise from one 

 or more inequalities of long period in the actual mean 

 motion of the moon . Examining the effect of the first 

 hypothesis, he arrives at the conclusion that if it be 

 correct " the problem of predicting the moon's motion 

 with accuracy through long intervals of time must be 

 regarded as hopeless since it cannot be expected that 

 variations in the earth's axial rotation will conform to any 

 determinable law," and, he adds, " success in tracing the 

 deviations in question to the moon itself and to the 

 theory of gravitation is therefore a consummation to be 

 hoped for." With regard to the second hypothesis, it is 

 seen that the residuals of the equations of condition indi- 

 cate that the modern observations may be nearly repre- 

 sented by a term having a period of between 250 and 300 

 years, and hence Prof. Newcomb inquires how closely an 

 empirical correction to Hansen's first term depending upon 

 the action of Venus, the period of which is 273 years> 

 ■vill accord with the modern observations, and he finds a 

 very satisfactory agreement. An additional diminution 

 of 10" in the secular mean motion of the moon results 

 which at the present epoch involves a further diminution 

 in the secular acceleration of o""5, that the ancient obser- 

 vations may be well represented ; thus the acceleration 

 becomes 8" '3 . 7^. A table is given exhibiting the correc- 

 tions to Hansen's mean longitude from 1620 to 1900 for 

 every tenth year; in 1880 it is - i\"'2, and in 1900 

 - 24"-6. 



This important volume concludes with some remarks 

 upon the bearing of the value of the moon's secular 

 acceleration deduced from the investigations, of which 

 we have endeavoured to give a general outline here. Prof. 

 Newcomb thinks it is apparent that one of two propositions 

 must be accepted : "Either the recently accepted value of 

 the acceleration and the usual interpretation of the ancient 

 solar eclipses are to be radically altered, the eclipse of 



— 556 not having been total at Larissa, and that of — 584 

 not having been total in Asia Minor ; or the mean motion 

 of the moon is, in the course of centuries, subjected to 

 changes so wide that it is not possible to assign a definite 

 value to the secular acceleration." It is certain that 

 there will be a difference of opinion upon his main con- 

 clusions, and for this he expresses himself fully prepared. 

 If a definite theory of the apparent inequalities of long 

 period in the moon's motion cannot be formed, or if the 

 moon's mean motion is subject to such changes from age 

 to age that no invariable and well-defined value of the 

 secular acceleration can be deduced, then he urges it is 

 not certain that the question whether Hansen's tabular 

 mean longitude during centuries preceding the Christian 

 era does or does not require a considerable negative 

 correction can ever be conclusively settled, since no con- 

 clusions can be drawn except from observations made 

 near the period in question, and he advocates the neces- 

 sity of a further investigation into the eclipses and other 

 data on the two hypotheses, first that Hansen is correct 

 during the period named above, and second, that a cor- 

 rection of - 16' is required, and suggests that the question 

 should be examined in this manner by some independent 

 authority. If, on the other hand, it is not possible \o 

 form a perfect theory of all the inequalities in the moon's 

 mean motion independently of observations, he thinks it 

 will be practicable to arrive at a value of the secular 

 acceleration from the modem observations, reliable 

 within o"'5. 



ROSCOE AND SCHORLEMMEKS CHEMISTRY 



A Treatise on Chemistry. By H. E. Roscoe, F.R.S., and 

 C. Schorlemmer, F.RS., Professors of Chemistry in 

 Owens College, Manchester. Vols. i. and ii. (Mac- 

 millan and Co.) 



THIS work is a most valuable contribution to the 

 literature of chemistry. Its aim, as stated in the 

 Preface, is to place before the reader a fairly complete^ 

 and yet a clear and succinct statement of the facts of 

 modern chemistry, whilst at the same time entering so 

 far into a discussion of chemical theory as the size of 

 the work and the present transition state of the science 

 permit, special attention being also paid to the accurate 

 description of the more important processes in technical 

 chemistry, and to the careful representation of the most 

 approved forms of apparatus employed. 



The manner in which this design has been carried out 

 is such as might have been expected from the high repu- 

 tation of the authors. The work commences with a very- 

 interesting historical introduction, in which the progress 

 of chemistry is traced from the early times, in which it 

 was merely an art subservient to alchemy, medicine, and 

 a few branches of manufacture, to the time when, by the 

 gradual accumulation of observations, and the discussion 

 of them by men of philosophic mind, it rose to the rank 

 of a science. A clear and impartial discussion is given 

 of the relative merits of the various workers by whose 

 labours the system of chemical philosophy now accepted 

 was developed, showing how the phlogistic theory of 

 Becher and Stahl first established a common point of 

 view from which all chemical changes could be regarded, 



