cifely fimilar. Why it should be falfe in pneumatics remains to be explained; even allowing the mind to be immaterial. That affection of the mind, called remorfe of confcience, feems to present a plaufible objection to this propofition. Selfaccufation feemingly implies, that a man would not act the very fame part over again, if he were placed in the fame circumftances. Mr. Palmer accordingly obferves, that when a man reproaches himself for any thing that he has formerly done, he certainly confiders himself as having had the power of not doing it;' and that were he to be placed in the fame fituation again, he would act differently. Dr. Priestley had before obferved, that, though men may think in this manner, with refpect to what is paft, they deceive themselves, in fuppofing that they could have acted differently; by their not attending to the change of difpofition, and other circumftances, that have taken place fince the former period. He now adds, that having, fince that time, acquired a different difpofition, and different views of things, they unawares carry them back, and confider how they would have acted with their prefent acquired difpofitions. -Their difpofition being really altered by what has occurred to them fince, they would not now act the fame part over again.' On the whole, without difcuffing the merits of the present controversy, which, from the nature of the fubject, and the improbability of any difcoveries being made in it, may, we apprehend, be carried on to the end of the world, without clearing up the difficulties which attend both fides of the argument:-we fhall only further obferve, that if Dr. Priestley's antagonists feem to have any advantage over him, it is in thofe particular articles (fuch as refponfibility, merit, and demerit, &c.) where they may allege, with feeming juftice, that a belief in the doctrine of neceffity must have an effect on the bulk of mankind, not fo favourable to morality and religion, as the popular belief on this head though the moral conduct of the neceffarian philofopher, who comprehends the doctrine in all its parts, may, as Dr. Priestley alleges, be improved by his belief in it. For his own part, however, he confiders it as the clearest of all queftions,' and the truth of it as indubitable as that of any mathematical propofition whatever. I have no feeling,' he adds, either of fear or arrogance, in challenging the whole world in the defence of it. This argument, I compare to fuch ground as one man may defend against an army.' Aware, however, of the unconquerable bias which even philofophical men, of the greatest integrity and abilities, neceffarily acquire towards certain opinions impreffed upon them by the courfe of their ftudies, habits, fituations, and connections in life; he frankly owns, that he does not expect that any thing he has has now advanced, or is capable of advancing, will make the leaft change in Mr. Palmer's view of things. Our present general fyftem of opinions, whether right or wrong, is probably that which we shall carry to our graves.'-Younger perfons, whofe opinions are not yet formed, may nevertheless derive an advantage from these publications, that we cannot derive from them ourselves. Your fuppofed consciousness of liberty,' Dr. Priestley good humouredly adds, and other popular arguments (though, when analised they really make against your hypothefis), will always fecure you nine out of ten of the generality of our readers;' who, he elsewhere obferves, will never get beyond the very threshold of the business.'- . All that I can do, must be to make the most of my tenth man; and, if I poffibly can, fancy his fuffrage equivalent to that of your nine.' draw Whether this fpirited letter of Dr. Prieftley's is the termination of the prefent controverfy, is yet in the womb of fate. At the close of it, he thus expreffes himself, like a true Neceffarian, on the fubject. Now, that I have advanced, I verily believe, all that I can, in fupport of my opinion, I ought to acquiefce in the success of my labours, be it more or lefs.-I do not, however, make any fixed refolutions. If you make a rejoinder, as I think you ought, and will be advised to do, I, true to my principles as a Neceffarian, fhall act as circumstances shall determine me.' B..J. ART. VI. PHILOSOPHICAL TRANSACTIONS of the Royal Society of cluded from laft Month's Review.] METEOROLOGICA L. Article 32. Comparison between Sir George Shuckburgh and Colonel Roy's Rules for the Measurement of Heights with the Barometer. In a Letter to Colonel Roy, F. R. S. from Sir George Shuckburgh, Bart. F. R. S. IR George Shuckburgh, in his curious paper, entitled, "Obfervations made in Savoy, in order to afcertain the Height of Mountains by Means of the Barometer," and printed in the Philofophical Tranfactions for 1777, had investigated rules for correcting certain irregularities of the barometer, arifing from the different degrees of heat and cold in the atmosphere, and the expanfion of the different materials of which the inftruments are made, as alfo fome others of lefs moment. About the fame time, and from fimilar experiments, made in different parts of Great Britain, Col. Roy had deduced rules for correcting the fame things. To inveftigate the differences between the Colonel's D 3 Colonel's rules and his own, though thefe differences are very fmall, is the defign of this paper; in the courfe of which it appears that the two principal caufes of difference arife from the expanfion of quickfilver and the expanfion of air. The difference arifing from the former Sir George fhews can feldom amount to more than about 5 feet in a height of 11,000. In their equations for the expanfion of air, the difference is indeed greater, and be may 4 feet in 1000, if the mean height of the two barometers be 27 inches, and the thermometer fland at 52°. The error increases as the difference between the heights of the two barometers and the height of the thermometer increafes. Sir George fubjoins fome reafons for fufpecting the accuracy of thofe obfervations, which feem to require an equation that depends on the latitude of the place. Article 33 MATHEMATICA L. An Account of the Calculations made from the Survey and Measures taken at Schehallien, in order to afcertain the mean Denfity of the Earth. By Charles Hutton, Efq; F. R. S. The Newtonian philosophy supposes that attraction is exerted not only between the great bodies which compofe the universe, but also between the most minute particles of matter which those bodies confift of: hence it is evident, fuppofing this doctrine to be true, that the plumb-line of a quadrant, or any other aftronomical inftrument, fituated on the fide of a very high hill, or in its neighbourhood, muft be attracted from its proper perpendicular direction by the matter in fuch hill; and of confequence, the meridian altitude of any ftar, obferved with that inftrument, will be different from what it ought otherwise to be: and, moreover, if the meridian altitude of the fame ftar be obferved both on the north and fouth fides of the hill, the attractions in these two cafes being different ways, the difference of the two meridian altitudes, when corrected for the dif ference of the two geographical fituations of the inftrument, will be proportional to the fum of the two attractions. It was on this principle that Dr. Mafkelyne, Aftronomer Royal, about the year 1770 or 1771, propofed to the Royal Society, to determine, by experiment, the truth or falsehood of the Newtonian fytem of gravitation. The thought was not new, as the Doctor himself remarks, in his proposals, but was attempted once before by the mathematicians who went from France, about the year 1736, to measure a degree of the meridian, on or very near to the equator: the manner, however, in which the experiment was then conducted, was by no means fuch as to give fatisfaction to philofophers in general; and if it had, the importance and delicacy of the experiment is fo great as still to merit many repeated trials; for as the Author of the paper now now under confideration juftly obferves, a frequent repetition. of the fame experiment, and a coincidence of the refults, afford that firm dependance on the conclufions, and fatisfaction to the mind, which can fcarcely ever be had from a fingle trial, however carefully it may be executed.' The refult of the experiment, as well as the manner of conducting it, is related at large by the Doctor himself in the Philofophical Tranfactions for 1775, and an account of it was given in our Review for June 1776. From whence it appears that the plumb-line of the inftrument was deflected from its true perpendicular direction, by the attraction of the mountain, by an angle of about 5 fe. conds: the fum of the two deviations being 11". 6; and which eftablishes the truth of the Newtonian philofophy on the folid foundation of experiment. It remained still to determine, from this most curious experiment, the ratio of the mean denfity of the hill to that of the earth, and from hence, and the known matter of which the hill confifts, that of the latter to common water, or any cher known substance. This is the purport of the paper before us, which takes up one hundred pages of the Tranfactions: for as the business was in its nature entirely new, it laid Mr. Hutton under the neceffity of inventing, and, of course, defcribing at length, the several modes of computation which he has made ufe of, and alfo of giving a fynopfis of the measures which were taken of the feveral lines and angles, that any perfon, who thinks proper, may fatisfy himself of the truth of the computations here delivered. It appears that two principal bafes were meafured, befide other fhorter lines, one on the fouth, and the other on the north-west fides of the mountain. From thefe two bafes, and the feveral angles which were also measured, both vertical and horizontal, from their feveral extremities to different parts of the fummit and bafe of the mountain, as well as different points on its furface, the plan of it, as well as the figure of a prodigious multitude of its fections were computed; and from thence alio the figure of the hill was conftructed, on a very large scale, upon paper. Notwithstanding this ftupendous piece of computation was thus effected, one, not lefs arduous, appeared behind, which was to apply the foregoing calculations and conftructions to the determination of the effect of the attraction of the mountain in the direction of the meridian: and here it foon occurred to the ingenious Computer, that the best method would be to divide the plan into a great number of fmall parts, which might be confidered as the bafes of fo many finall columns, or pillars of matter into which the hill and the adjacent ground was divided D 4 by by vertical planes, forming an imaginary groupe of vertical columns, fomething like a fet of bafaltine pillars, or like the cells in a piece of honey-comb; then to compute the attraction of each pillar feparately in the direction of the meridian; and, laftly, to take the fum of all these computed effects for the whole attraction of the matter in the hill. It is obvious that the attraction of any one of these pillars, on a body in a given place, may be easily computed, and that in any direction, because of the fmallness and given pofition of its base: for on account of its fmallness all the matter in the pillar may be fuppofed to be collected into its axis or vertical line, erected on the middle of its bafe, the length of which axis, as the mean altitude of the pillar is to be estimated from the altitude of the points in the plan which fall within and near the base of the pillar then, having given the altitude of this axis, together with the pofition of the bafe, and the matter fuppofed to be contained in the pillar, and collected into the axis, a theorem is eafily derived, by which the effect of its attraction may be computed. But to retain the proper degree of accuracy in this computation, it is evident that the plan muft be divided into a very great number of parts indeed, to have the pillars fufficiently fmall to admit of this mode of computation, not lefs than a thousand for each obfervatory, or two thoufand in the whole, forming the bafes of as many fuch pillars of matter as have been defcribed above; which, if the attractions of every one had been feparately computed, muft evidently have been a work of fuch labour as would have difcouraged every perfon from undertaking it; but which muft nevertheless have been the cafe if our Author had not luckily hit upon a method of dividing his matter into columns, fo as to abridge the computations in a moft remarkable manner; but which, as well on account of the want of proper diagrams, as the great length of the procefs by means of which it is derived, cannot poffibly be pointed out here: fuffice it to fay, that the refult of this long and intricate calculation was, that the effect of the attraction of the matter in the mountain and adjacent hills, at the fouthern obfervatory, was to the effect of the fame attraction at the northern one, as 69967 to 88644, or as 7 to 9 very near. This difference, Mr. Hutton fhews, is to be attributed principally to the effect of the hills which lie on the fouth fide of the mountain Schehallien, and which are not only larger, but also nearer to it than thofe which are on its north fide. Mr. Hutton next proceeds to compare this attraction with that of the whole earth, and finds, taking a mean of all the meafures which have been given for the length of a degree of one of its great circles, that the whole attraction of the earth |
