British Association. 305 



different amount, the observations would decide whether a level 

 line agrees with low water, mean water, or high water ; and, thus, 

 what is the true level of the sea. 



4. 3Ir. Luhboch then read a paper on the importance of forming 

 new empirical tables for finding the moon's place. Although astro- 

 nomical tables are sufficiently perfect for the general purposes^ of 

 navigation, yet astronomers are not satisfied to rest here ; but desire 

 to reach, by calculation and theory, a higher degree of accuracy, 

 such as that obtained by the best instruments in fixed observatories. 

 The most remarkable works on the theory of the Moon are, on 

 account of their extent, those of M. M. Damoiseau and Plana. 

 Those of M. Damoiseau's calculations are, howfver, in such a shape 

 that it is almost impossible to verify them. M. Plana s work con- 

 stitutes a new era, from the circumstance that the results are de- 

 veloped according to the powers of the eccentricities, inclinations, 



_ &c., as also of the quantity in denoting the ratio of the sun's mean 

 y[ motion to that of the moon ; otherwise the calculations are similar 

 to those of M. Damoiseau and there exists, finally, a great difficulty, 

 from the circumstance that the expressions for the co-efficients do not 

 converge. Mr. Lubbock, from these aud other considerations, 

 suggests the importance of deducing the numerical values empirically 

 from the best observations, and so construct new lunar tables, which 

 may serve to check the results obtained by theory. This resolves 

 itself into a question of expense merely, since there are plenty of 

 persons to be found adequate to the task of computing th^ proposed 

 new tables. 



5. Sir W. Hamilton was then called upon to give an account of 

 the result of Mr. G. B. Jerrard's process for resolving equations of 

 the fifth and sixth degrees. Professor H. reported that he conceived 

 himself to have proved that, in that particular process it had failed ; 

 but it was only a particular case of a far more general method in- 

 vented by Mr. Jerrard, with admirable mathematical skill, which is 

 adequate to effect a very curious and unexpected transformation, or 

 rather, class of transformations, on the general equations of the M'*^ 

 degree, though it fails when that degree is below a certain minor 

 limit ; and that, for this and other reasons, the researches of Mr. 

 Jerrard are highly worthy the attention of all who interest them- 

 selves in the progress of algebra. It had not been found necessary 

 to employ the grant voted in Dublin for an experimental discussion 

 of the question. 



6. Mr. Phillips offered a brief statement of the means taken by 

 the Committee of the Association for the purpose of procuring 

 regular and uniform experiments on subterranean temperature. 

 The errors incidental to observations made in the air or water of 

 mines had induced the Committee to recommend observers to attend 

 simply to the temperature of the rocks themselves ; with this view 

 36 thermometers had been duly compared, and the errors of them 

 ascertained ; many of these had been placed in secret situations, at 

 the lead hills, by Professor Forbes ; at Newcastle, by Mr. Briddle ; 

 at Wearmouth, by Mr. Anderson ; near Manchester and at North- 

 ampton, by Mr. Hodgkinson. Within a few days Professor Phillips 



VOL. IV. X 



