Natural History Museum Library 000163782 PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON. FOR THE YEAR MDCCCXXV. PART I. LONDON: PRINTED BY W. NICOL, SUCCESSOR TO W. BULMER AND CO. CLEVELAND- ROW, ST. JAMEs’s; AND SOLD BY G. AND W. NICOL, PALL-MALL, PRINTERS TO THE ROYAL SOCIETY. MDCCCXXV. / V r u ADVERTISEMENT. The Committee appointed by the Royal Society to direct the publication of the Philosophical Transactions, take this opportunity to acquaint the Public, that it fully appears, as well from the council-hooks and journals of the Society, as from repeated de- clarations which have been made in several former Transactions , that the printing of them was always, from time to time, the single act of the respective Secretaries, till the Forty-seventh Volume: the Society, as a Body, never interesting themselves any further in their publication, than by occasionally recom- mending the revival of them to some of their Secretaries, when, from the particular circumstances of their affairs, the Transactions had happened for any length of time to he intermitted. And this seems principally to have been done with a view to satisfy the Public, that their usual meetings were then continued, for the improvement of knowledge, and benefit of mankind, the great ends of their first institution by the Royal Charters, and which they have ever since steadily pursued. But the Society being of late years greatly enlarged, and their communications more numerous, it was thought advisable that a Committee of their members should be appointed, to reconsider the papers read before them, and select out of them such as they should judge most proper for publication in the future Transac- tions; which was accordingly done upon the 20th of March, 1752. And the grounds of their choice are, and will continue to C iv 1 be, the importance and singularity of the subjects, or the advan- tageous manner of treating them ; without pretending to answer for the certainty of the facts, or propriety of the reasonings, contained in the several papers so published, which must still rest on the credit or judgment of their respective authors. It is likewise necessary on this occasion to remark, that it is an established rule of the Society, to which they will always adhere, never to give their opinion, as a Body, upon any sub- ject, either of Nature or Art, that comes before them. And therefore the thanks, which are frequently proposed from the Chair, to be given to the authors of such papers as are read at their accustomed meetings, or to the persons through whose hands they received them, are to be considered in no other light than as a matter of civility, in return for the respect shown to the Society by those communications. The like also is to be said with regard to the several projects, inventions, and curiosi- ties of various kinds, which are often exhibited to the Society; the authors whereof, or those who exhibit them, frequently take, the liberty to report, and even to certify in the public news-papers, that they have met with the highest applause and approbation. And therefore it is hoped, that no regard will hereafter be paid to such reports and public notices ; which in some instances have been too lightly credited, to the disho- nour of the Society. CONTENTS. I. On the effects of temperature on the intensity of magnetic forces ; and on the diurnal variation of the terrestrial magnetic inten- sity. By Samuel Hunter Christie, Esq. M. A. of Trinity College , Cambridge , Fellow of the Cambridge Philosophical Society : of the Royal Military Academy. Communicated by the President p. 1 II. The Croonian Lecture. On the existence of Nerves in the Placenta. By Sir Everard Home, Bart. V . P. R. S. 66 III. Observations on the changes the Ovum of the Frog undergoes during the formation of the Tadpole. By Sir Everard Home, Bart. V. P. R. S. Si IV. A general Method of Calculating the Angles made by any Planes of Crystals , and the Laws according to which they are formed. By the Rev. W. Whewell, F. R. S. Fellow oj Trinity College , Cambridge. 87 V. Explanation of an optical deception in the appearance of the spokes of a wheel seen through vertical apertures. By P. M. Roget, M. D. F.R. S. 131 VI. On a new photometer , with its application to determine the relative intensities of artificial light , &c. By William Ritchie, A . M. Rector of the Academy at Tain. Communicated by the President. 141 VII. The description of a floating Collimator. By Captain Henry Kater, F. R. S. 147 CONTENTS. VIII. JV otice on the Iguanodon, a newly discovered fossil reptile , from the sandstone of Tilgate forest , in Sussex. By Gideon Mantell, F. L. S. and M. G. S. Fellow of the College of Surgeons , &c. In a Letter to Davies Gilbert, Esq. M. P. V . P. R. S. &c. &c. &c. Communicated by D. Gilbert, Esq. 17 9 IX. An experimental enquiry into the nature of the radiant heat- ing effects from terrestrial sources. By Baden Powell, M. A. F. R. S. of Oriel College , Oxford. Communicated by J. F. W. Herschel, Esq. Sec. R. S. 187 PHILOSOPHICAL TRANSACTIONS. I. On the effects of temperature on the intensity of magnetic forces ; and on the diurnal variation of the terrestrial magnetic inten- sity. By Samuel Hunter Christie, Esq. M. A. of Trinity College , Cambridge , Fellow of the Cambridge Philosophical Society : of the Royal Military Academy. Communicated by the President Read June 1 7, 1824. In the paper on the diurnal deviations of the horizontal needle when under the influence of magnets, which the President did me the honour to present, I stated that these deviations were partly the effects of changes that took place in the temperature of the magnets ; and that although the conclusions which I drew from the observations respecting the increase and decrease of the terrestrial magnetic forces during the day would not be materially affected, it was my intention to undertake a series of experiments for the pur- pose of determining the precise effects of changes of tempe- rature in the magnets, so as to be able to free the observa- tions entirely from such effects. These experiments were immediately made ; but I was in- duced from some effects which I observed, to carry them to B MDCCCXXV. 2 Mr. Christie on the effects of temperature on a greater extent, in the scale of temperature, than was neces- sary for the object which I had at first in view. In consequence of this, and the length of the calculations into which I have been obliged to enter, the accomplishment of my purpose was delayed for a considerable time, and continued indispo- sition has since prevented me, until now, completing the arrangement of the tables of results. In the present paper, I propose to detail the experiments which I made in order to determine the effect of changes of temperature on the forces of the magnets, to the extent to which I observed their temperature to vary, during my observations on the diurnal changes in the direction of the needle, when under their influence ; to apply the results which I obtained to the correction of the observations them- selves, thereby accounting for the apparent anomalies noticed by Mr. Barlow and myself, in the observations made in doors and in the open air ; and by means of these corrected observations, to point out the diurnal variations in the ter- restrial magnetic intensity. It had been my intention to determine purely from obser- vation the portion of the arc of deviation due to the changes which I noticed in the temperature of the magnets ; but I found that this depended so much on the situation of the point at which the needle was held in equilibrio by the ter- restrial forces and those of the magnets, that it would hardly be possible to determine how much of this portion was due to the extent of the change of temperature, or the degree of temperature where the change took place, and how much to the azimuth of the needle, when affected by this change. I was therefore under the necessity of having recourse to the intensity of magnetic forces , &c\ $ theory, and adopted the simplest, and that which is most generally received, viz. that the forces which two magnets exert upon one another may be referred to two centres or poles in each, near their respective ends ; and that for either pole in one of the magnets, one pole of the other magnet is urged towards it, and the other from it, by forces varying inversely as the squares of their respective distances from that pole. Of the correctness of this theory of the action of one magnet upon another, the conclusions which I have ob- tained have given me no reason to doubt. In the observations on the diurnal changes in the positions of the points of equilibrium at which the pole of the needle was retained by the joint action of two magnets and the ter- restrial magnetism, where I noted the changes that took place in the temperature of the magnets, to which observa- tions I have alluded near the conclusion of my former paper, two magnets, as in several of the preceding observations, were placed, with their axes in the magnetic meridian, on the same horizontal table as the compass, at equal distances from the centre of the needle, one towards the north, the other to- wards the south, the north pole of each magnet being towards the north ; and their distances from the centre were such, that the points of equilibrium were nearly 180°, or south, N. 8o° E. and N. 8o° W. To determine here the changes that would take place in the situation of these points from changes in the force of the magnets, arising from a variation of their tempe- rature, it was first necessary to determine the changes in the forces themselves, arising from certain variations of the tem- perature of the magnets, by observing the corresponding changes in the direction of the needle. 4 Mr. Christie on the effects of temperature on To obtain the equation requisite for this purpose, take the centre of the needle as the origin of the rectangular co-ordi- nates, the axis of the x’s being in the magnetic meridian. Let x and y be the co-ordinates to the south pole of the needle, x being measured towards the north, andy towards the west : also, let r be the distance of either pole of the needle from its centre ; p the distance of the poles of each of the magnets from their respective centres ; and R the distance between the centre of the needle and the centre of either magnet. For the sake of expressing clearly and concisely the distances between the poles of the needle and those of the magnets, we will indicate these points as follow : 5, the south pole of the needle ; that is, the pole which, when the needle is freely suspended, points towards the north; n , the north pole of the needle ; $ , the south pole of the magnet which is to the north of the needle ; that is, its pole nearest to the centre of the needle ; I, , the north pole of the same magnet, or its pole which is furthest from the needle's centre ; 0 , the south pole of the south magnet, or that pole which is furthest from the centre of the needle ; , the north pole of the same magnet, or that pole which is "s’ nearest to the centre of the needle. Now resolve the terrestrial magnetic force acting on the north arm of the needle, in the line of the dip, into two ; one horizontal or in the direction x, and the other vertical : and let the horizontal force be M. Also, let the force with which a pole of the needle is repelled from the pole of the same name of either magnet, or attracted towards that of a con- the intensity of magnetic forces, &c. 5 trary name at the unity of distance, be F : then the forces acting on the south pole of the needle will be, M in the direction x; p p — 7 , in the direction s be the angle which the axis of the needle makes with the meridian, or the azimuth of the point of equilibrium, and we shall have, (s y= (R— p)*+ r‘+ 2 r(R—f) (j yjf— (R + f>y+ r2— 2r(R + f) cos. 9 ; ^ 0Y= (R + P)2+ r2+ a r(R + P) Substituting these values in the equation (A), it becomes, R-p s + (A) cos. (p ; cos. *| t 2 r (R p) (R —p)*+ r2 cos.

) cos. > < I + — — > 1 r/ M i (R + p)2+i ^ = 0 (B) (R+p)*+» From this equation the value of F in terms of M may be found for any values of cp, the distances R, r and p being known ; and if we suppose M constant during the observations, the variations in the intensity of the force F may be obtained from the observed variations in the value of (p. If the angle (p does not differ from a right angle by more than io° or even 20°, by expanding the several fractions, no sensible error will arise by limiting the series to a few of the the intensity of magnetic forces , &c. 7 first terms, and we shall in these cases thus obtain a much more convenient equation for computation. Since 1 + — . a cos. ft -4- a 2 cos.2 ft -f 3 ' 5 '4 a3 cos.3ft ^ ^ .i 2 • 4* • o (i — a cos. ip) and i (i -f- a cos. tp) 3 2 2.4 * ' 2 . 4 3 • 5 • 7 • 9 + 2 . 4 . 6 . 8 a4 cos.4 ft + &c* 4“ (1 — a cos. 4 3. ;b a'cos.'p + &c. r — F . -I 7 — £ — rr | a + 3 • 5 • -7- ' (R f) , s . cos.8

= 0 f neglecting the terms which contain the fourth and higher powers of cos. ft, Taking one of the cases which I investigated, and from which the others do not differ very considerably, the values of the co-efficients of cos. ft in the denominators of the frac- tions in the equation (B) are .25691 and .15951 ; so that the greatest of the terms neglected would be 3--5-^7-3-x(.25691 )4. cos.4 ft and -^f67- 3 9 x ( .15951 )4 cos.4 ft. Now, supposing that ft is 70°, if these terms are employed in determining the value of F, it will be 218.7705 . M, and 218.8184 . M, if they are neglected ; making a difference of ,0479 M, or only affecting the fifth figure in this extreme 8 Mr. Christie on the effects of temperature on case. If, instead of expanding the fractions, we computed them in the form which they have in the equation (B), we could hardly be supposed to obtain the absolute values of F more nearly than this ; although in either case the relative values would be obtained to a much greater degree of accu- racy. In the observations which I made, the values of

was 82° 37', the value of F was 222.5630 M, employing the terms containing cos.4 9S + 0.3664 + 0.4286 +°*4I75 +0.3814 +0.2473 0.1268 O. 1247 O. 1004 0. 1279 O.II93 O.II38 O.1413 The differences in the deduced values of the variation of ~ for a change of temperature in the magnets of i° in the last column, are not greater than we may suppose to have arisen from small inaccuracies in the observations, or slight changes in the terrestrial intensity during the time in which they were made ; the latter indeed appear to have taken place, since, at the same temperature, the value of

) = 0. (*2). As before, I calculate the following table from this equation. MDCCCXXV. D 18 Mr. Christie on the effects of temperature on Table of the Magnetic Intensities corresponding to different Tem- peratures of the Magnets. Mean Tempe- rature of the Magnets. DifF. of Temp, in successive observations . Mean of the observed values of 80 28 81 14 75 40 77 44 218.5687 218.7269 2 1 7 * 3° 1 4 217. 9040 -1- 0. 1582 + 1 *4255 4-0.6026 0.0920 0. 1430 O.I182 ^ F There is only one, the first, of the values of A . which differs much from those already obtained, but the difference of the temperatures in the observations from which it is de- rived is so small, that any errors would be rendered very sensible ; and if the thermometers happened not to indicate the precise temperatures of the magnets at the times of ob- servation, it would be quite sufficient to account for this dis- crepancy. In his paper on the daily variation of the horizontal and dipping needles under a reduced directive power, Mr. Bar- low has described some anomalies which he observed between the daily changes in the direction of a needle when placed in the house and when in the open air, arc! also the steps which he took to discover their cause. He mentions, “ that in certain positions of the needle towards the east and west, the daily motion, although it proceeded with the same deter- minate uniformity in both cases, yet it took place in different directions ; passing in the one instance from the east, or west, towards the south, and in the other towards the north, at the 19 the intensity of magnetic forces , &c. same corresponding hours of the day, the motion in both instances being equally distinct, regular, and progressive/'* These anomalies, I also noticed, although, as I have men- tioned in my former paper, I did not find the reversion, in the directions in the two cases, to take place with the same regularity and uniformity that Mr. Barlow observed it to have. In that paper I also stated my opinion, that these anomalies had arisen from the differenee in the changes of temperature in the magnets when in doors and when in the open air, and that the observations in the two cases would be found to agree when they were freed from the influence of difference of temperature in the magnets. As I had already made observations in doors, in which I noted the temperature of the magnets, it was now my intention to make corresponding observations in the open air, in order that by reducing the obervations to the same standard of tem- perature, their agreement or disagreement might be put be- yond doubt. For this purpose the whole apparatus was placed in my garden, exposed to the sun and air, on a table having its legs driven firmly into the ground ; and for several days I observed, at stated intervals, the positions of the points of equilibrium ; when I had an opportunity I also made experi- ments, similar to the preceding, for the purpose of determin- ing the value of A to be applied to the correction of the observations in doors and in the open air. On adjusting the magnets to the needle, I again found that * In the Postscript to this paper, Mr. Barlow, to whom I had communicated my views with regard to the effects of temperature, refers to the experiments which I had made, for the explanation of these apparent anomalies. 20 Mr. Christie on the effects of temperature on their intensities had increased, owing, I consider, to the same circumstance as before, and I therefore increased their dis- tances from the needle ; but after making the first days ob- servations, and comparing them with those made in doors, I found it necessary slightly to diminish these distances, in order that, at the same temperature of the magnets, the si- tuations of the points of equilibrium might more nearly agree in the two cases. During the observations of the first day, the distance of the nearest ends of the magnets from the cen- tre of the needle were 15.62 inches : so that the value of R is here 21.58 inches, and the equation C becomes, M — F (.004441190 + .0007549085 cos.2 0.12300 on the Diurnal changes in the positions of the Points of Equilibrium ) Mean 65.171 .13097 F To apply the value of A . thus determined, to the cor- rection of the observed directions of the needle, for the changes which took place in the temperature of the magnets, let A

) j (F + A F) = o, whence cos.*(? + A*)=i. {p^nr-P}. (E) This formula, though sufficiently simple, is not in the most convenient form for calculating the values of A are to be derived, conse- quently they cannot be calculated to the greatest accuracy. But if p be expanded, the first figure of F — P (a Fl* being in the 5th place of decimals, the first figure of - — — F / A will be in the 9th place, and the first figure of - — ~~ will be in the 13th place; and therefore we should obtain the value of F — P true to the 11th place of decimals, or true to (a fP 7 places of figures when we neglect the term - — f . Now in the cases which I had to compute, the first two figures in the value of were the same for all the arcs, and conse- F«f / ' E MDCCCXXV. 26 Mr. Christie on the effects of temperature on quently by using these, the value of F ^A~F — P for the de- termination of cos.* (

5 3° 45 84 00 *5 30 45 85 00 *5 30 45 86 00 / 2 I . 249 21.815 22.421 23.071 23.770 24.524 25-338 26.217 27.169 28.204 29-33+ 30.569 3i-923 33-4H 35.063 36.894 38.936 40 . 047 41 .224 42.474 43.805 45.222 46.733 48.347 50.075 51 .928 5 3 • 9 1 8 56.060 58.371 60.871 63-579 66.518 69.717 / 0.566 0.606 0.650 0.699 0.754 0.814 0.879 0.952 1 -°35 1 . 1 30 1 -235 1 -354 1 -491 1 *649 1.831 2.042 1 . 1 1 1 1 • 1 77 1 .250 1 -331 1 •4I7 1 .51 1 1.614 1 .728 1.853 1 .990 2. 142 2.311 2.500 2.708 2*939 3-199 / 0.040 0.044 0.049 °-°55 0.060 0.065 0.073 0.083 0.095 0. 105 0. 1 19 0.137 0. 1 58 0. 182 0.21 1 0.066 0.073 0.081 0.086 0.094 0. 103 0. 1 14 0.125 °.»37 0. 152 0.169 0. 189 0.208 0.231 0.260 / 0.004 0.005 0 006 0.005 0.005 0.008 0.010 0.012 0.010 0.014 0.018 0.021 0.024 0.029 0.007 0.008 0.005 0.008 0.009 0 . 0 1 1 0.011 0.012 0.015 0.017 0.020 0.019 0.023 0.029 From these tables, interpolating as before, I constructed the two following. 36 Mr. Christie on the effects of temperature on III. Table of the increments in the Azimuths of the Points of Equi- librium corresponding to a decrement ofVin the Temperature of the Magnets, calculated at intervals of 6' in the Azimuths from from 74 to 82°, and of 3' in those from 82° to 86°; the distances of the centres of the Magnets from the centre of the Needle being 2 1 ,52 inches : to be applied to the correction of the observed Azi- muths when the Observed Temperature of the Magnets is above the Mean Temperature to which the observations are to be reduced.

Dif. A

O N C 4 3° No observation. u. 6 00 61.00 81 20 79 26 0 24 w 29.74 61.50 < 7 30 60.50 81 36 80 04 0 18 w 29.74 60.25 9 45 59-75 82 04 80 42 0 14 w 29.74 61.25 fcuO 6 00 59 00 83 26 81 32 0 06 w 29.75 59-75 c g 7 3o 59 75 83 10 81 52 0 08 E 29.75 59.50 t-i O 9 00 59 75 84 36 83 20 0 16 E 20.74 59.25 .s 10 30 60 50 86 00 83 5° 0 14W 29-75 59-75 rt' 0 10 61 10 83 12 80 42 0 46 W 29.76 61.75 s d 1 30 61 50 82 40 80 22 0 54 w 29.77 62.50 .12 O 3 00 61 50 82 00 79 52 0 36W 29.80 61.75 so ^ 5 00 61 50 81 42 80 08 0 14 w 29.81 62.10 1 30 63.00 81 34 79 54 0 46W 30.02 64.30 § d 3 00 62.60 81 32 79 44- O 34 w 3°. 02 64.40 o rG O 4 30 61.75 8* 34 80 08 0 10 w 30. 02 61.75 +-' d 6 00 61.OO 81 40 80 38 0 04 w 30.02 60.25 7 30 60.20 8 1 30 80 04 0 06 w 3°. 02 59.50 < 9 4° 11 25 60.00 60.00 81 58 81 40 80 20 80 00 0 08 w 0 02 E 30.03 3°.°4 59.50 60.60 6 07 59-75 82 30 8i 42 0 14 E 3°.°7 61.00 do C 7 30 60.10 83 12 81 52 0 04 E 30.07 59.00 c 9 00 60.50 83 28 81 52 0 00 W 3°.°9 62.00 o 10 25 61.00 83 40 8 1 42 0 24 W 30.09 64.75 0 00 61.20 8 3 34 81 22 0 44 w 3°-°9 66.00 1 30 61.50 82 04 80 06 0 52 w 3°-°9 66.25 'S a 3 00 62 . 30 80 48 79 °4 0 46 w 30.09 66.90 oo o 4 30 63.25 80 56 79 46 0 12 W 3°-°9 66.50 G 6 00 63.00 80 44 79 38 0 08 w 30.09 65.50 it! 7 3o 62.00 80 54 79 18 0 18 w 30.19 60.25 < 9 45 1 1 20 6°. 75 60.50 81 24 81 42 79 36 80 12 0 10W 0 io W 30.19 30.20 58.50 60.50 6 05 60.30 82 10 80 50 0 02 E 30.22 60.50 do c 7 3° 61.30 82 12 80 38 0 02 W 30.23 59.40 C 9 00 62.00 82 30 81 40 0 12E 3°-23 62.75 1 O 10 30 62.25 82 46 81 50 0 02 W 30.24 64. 25 0 10 64.00 82 04 80 22 0 40 W 30.24 65.50 S « 45 63-5° 81 58 79 42 0 36 W 30.24 65.40 *G jz 3 °o 63-75 80 52 78 44 0 28 w 30.24 65 -75 G o O 4 3° 64.00 80 10 78 38 0 06 w 30.24 66.75 G 5 55 63-5° 79 5° 78 16 0 18 w 30.24 66.00 OJ 7 22 63.20 80 28 78 44- 0 16 w 30.24 65.00 W-. < 9 40 11 10 62.25 62.00 80 52 81 00 79 °4 79 26 0 I6W 0 16W 30.25 30.26 6:. 00 63-25 44 Mr. Christie on the effects of temperature o?i Table of observations made within doors, fyc. Date and time of observation. Tempera- ture of the Magnets. Point Westerly. s of Equilibr Easterly. ium. South. Barometer. Therm. attached. h. m. 0 O / O / O 04 E 0 / O tob 6 IO 62.OO 81 50 80 12 O 30.27 63.00 G • fH 7 3° 62.50 81 56 80 26 O 08 E 30.28 62.00 u • O 9 oo 63.00 82 56 8l 18 O 06 E 30.28 64.50 N S IO 3° 63.40 82 32 80 40 0 16 W 30.27 65*75 CO o oo 63.66 81 32 79 34 0 24 W 30.28 66.00 I 3° 63*75 81 04 79 02 0 32W 30.28 66.33 cd . 5 G 3 oo 64.20 80 IO 78 38 O 30 w 30.28 66.33 ^ o 4 3° 65.00 80 IO 78 36 0 20 W 30.28 67.75 C/D ^ 5 55 65.00 79 40 78 24 0 16 W 30.27 65.66 £ 7 30 64.66 79 44 78 20 O 16 w 30*27 63.50 < 9 2 5 63*33 79 54 78 50 0 16 w 30.26 61.66 1 1 3° 63.00 80 28 79 00 0 16 w 30.26 64.00 In all the observations which I have made, I have consi- dered the magnetic meridian to be the line of direction of a needle at the time when that direction is most stationary, that is at about seven o'clock in the evening ; and in arranging the magnets for the foregoing and similar observations, I have not only always found much difficulty, hut have seldom succeeded, in determining so accurately the axes of the magnets, and adjusting them so precisely in the meridian, that, at that time, the needle should be held in equilibrio exactly at south, and also at points towards the west and east equidistant from the north, which evidently ought to be the case with a perfect adjustment. Partly from this dif- ficulty in adjusting the magnets, of which those who have attempted similar arrangements will be best aware, and partly from the changes which, even during the evening, take place in the direction and intensity of the terrestrial forces, the east and west points of equilibrium, in the fore- going observations, are not, during the evening, at equal 45 the intensity of magnetic forces , &c. distances from the north, nor is the south point exactly at south. In order to reduce the situations of these points to their distances from what ought to be considered as their meridian, I take the mean of the azimuths of the westerly point at the evening observations, which is 8i° 27', and also of the corresponding azimuths of the easterly points, 790 57'; half their difference will be the mean error in the point which has been considered as zero of the compass with reference to these points : so that if 45' be subtracted from each of the azimuths of the westerly point, and added to those of the easterly, these points will be reduced very nearly to what would have been their positions had all the adjustments been perfect. With regard to the southerly point of equilibrium, the mean of the evening observations gives its position 1 2' W ; this therefore should be subtracted from the westerly and added to the easterly, in order to reduce the observed devia- tions to those from the meridian. These reductions I have made in the following table, preparatory to the reduction to be made in consequence of the changes in the temperature of the magnets. Table of the preceding observations reduced to their Mean Magnetic Meridian. 46 Mr. Christie on the effects of temperature on •joioj qwog sqi jo suoijisoj uesj^ O00 N O 00 VO 00 0 00 N VO xfr* ty-* N tJ- ty^ xj- •-« fsj r^j p-« ,-,__ONN>-«0000 'OOO'+O'l'O+Nl-tt- -rf-oo . • .......... lyoVO nONNOONN — NOO -h— i — ONNNOOOOO 00000000000 OOOOOOOOOOOO • 8 a “C • x: 4-* 3 0 _VO O00 N -4- N vf M N N tJ- ONNOno-tf-NOOOO NO O 00 ti- N O OO OO ■+ -t- -tt- -.N — O-N-OOOOO CD °o 0000000000 OOOOOOOOOOOO *3 cr «J CO N cr\ K (S N m fO <^1 t-r\ — 1 mty-iOl^-tv-)i-. 0 ly-i Lrv LO— ON-ctJ-NNOOP'N'4- vO W Um O aJ w „nnt*--^-i-.--,oooo °co ooooooooooxoooooooo •— 4 O >— • n <-• 0 On On On On On On On co 00 00 00 co M c *-« p-i U*\ N l/M^ Q\ ^ N <-r% <-• N u-% p- 1 u/~» N -4 ^ ty*\ p-4 C4-> r- On to irN Lr^ On On cn Ohm^-^-mNN l^~s O 0 * NN^u^N^h^OOOO Ozo oooocococoooccooooco p-4 p-4 n »4 O O ON ON 00 CX) On ON 00 00 on 00 cc oc •sjsuSej^ oqj joainilijaduiOjL, Olola.00000000 O rv. lav — tn ia ^ O O • •••••••••• On On On 0 ^ ^ ^ O u ir\ tr>sO NO VO O NO NO O OOOOvOLTNOOO'Ot^O O Lri 0 '^-'O rv N 0 O vo too N N t^i X mix t)- ir, ii~\ rh t<"> txi vovovovcvoovovovovovovo 8 3 *G • w 3 0 C/3 0 / 0 16 E 0 16E 0 00 0 14W 0 22 W 0 16W 0 14W n. 0 12W 0 06W 0 02W O -tj- O OO t}-vo vo VO -4- tJ- -tj- — m-hNN — OOOOO OOOOOOOOOOOO tr\ N 3 cr W u- O « 0 (3 CO i_/-\ >— » co *-4 cn 0\£> — < O ("v. " *-0 uoN N *-4 »-» t^“N ctf NN^o*-4^00>00^ °ooxooxcooooo ^ oo oo oo O tyiMUM^NNONtt; - 0\0v — ty-iNNt^lONNNON^ — « — nN — OOvOvOvOvOiO oc 00 00 00 co 00 r\ 00 to .s £ s £ cr\ ON *-• •-« ^ cn iy\ h on CN M CO O f N rt--0 CO • • •• • **o Nc/i^n-hO.OOw 0 OO 00 CO OC CO 03 00 O 00 CX) 00 t-r> *-s~\ >— « ON c<"5 LO cn k I r\ C^ M ^ O »-4 P-4 O N O ^ O ►“« ►_ p-4 ►-« rj p-4 *-4 O On On On O O 00000000000000 fv K t^x 00 •sjsuSei^ oqi J03in}Ei3duj3X u->roOOOOO<-n N t<-> — O O — lav O • •••••• • • f _ 00 On 0 *-* ■— * *+ *-< O On 0 l-o LoO NO VO NO NO VO VO *-o OOOLnOOLTNOOOLt-,0 rt^roONOLor^Oty^NNO •••••••••••• O ** N N xj- r^O cy> c^5 cr> C4 (sj NOtONOvONONONOVOVONONONO 8 .2 .c *-* 3 0 -+00 N +vO VO <4 -4-0 N + ~ — Q — O — N N — O OO VO CO CO OO O Tj-OvOOOVO N N OOOO— NNOOOOO rO c/3 O O O O C O O O O 0 0 0 OOOOOOOOOOOO '3 cr W (4-t O a ~ C\ONO\rNO\NNfcrc(N. *-4 p-h to cr\ rj“ rt~ i-h (v| N N N ^ ON H CO -4 —1 COp-4 OOOLotoONOTf-ONty^ CO Tf- rf- ri *-4 N O ^ ^ ^ Ooo oocooooooooooooooooo ON M NNNN — — OOOVOOO OOOOOOOOOCOOOCOO f^-OO 00 00 C/5 4-* .s 4-* C/5 ON ^4 to p-h »-« — • co cr co •"* -N — 0’-<'+0"NN0>-^> — vo co O' — t^f\ — mO\3\N OO — LoOiyoOO vr\ O t^i L-, (2 £ iflmN mO - " “ °0O CX30000CX5 00 00 00 00 00 00 NNNNN — — OOvOOO 0000000000000000 t^oo 00 00 •spuSsp J0 3injEJJ M3qj JlU3X O'Oii-iu-vOOOOOO1^' 0 VO 0 000 M M r^i • •••••••••• r^oo 00000 on co 0 10 to 10 tONO *ONO NO VO lo to O O O L^ OOO *y~l O O L/O O O tj-o O O to rv to 0 ..f.. ....... O0“"NtnNNt^)rT)N0O 'O'OVO'O'OVOVOVO'OVOVOVO e a £ 3 0 VOOOC^VONVONOVONO NNC^hhNhOO^O w w w ^ ^ ^ ^ ^ VO\ONNNO'tP-0'i--‘-0'!l- N — — — oorJ-moooOO -O C/3 0 0 0 0 0 0 0 0 0 0 0 0 OOOOOOOOOOOO *3 a4 td • 4«rf a W . 10 r^. «o to on »o co 'O — NOOOO-’i-NThO r^, r^. t'-. — ov — tc >n "•. Ch 0 rtooON 0 lo ■+ to N 0 of- Lo c<-> 0 n CO co Th r*- N h-i -4 O ^ M u00 OOGOOOOOXOOOOOOXOO OO r» NNNNNOOvOOOOO 00 00 00 00 00 00 r^-00 oo oo oo oo N .5 4-4 (S N U->1^U->N 0-1O >-oN ioNtoioO\0\tOn 0\ to 0\ 0\ Tt-N TJ-U0-4- — 0 — LON -4*0 0, £ _NNcocoN*-«C^'-4N'-4N °oo cocooooooooooooooooo — NNNN-OOONOvO- 0000000000000000 t\00 00 •sj3uSep\j sqi J0 3JIU)E3dUJ3X OOOOOw-iO«-oOOO u-> 0 0 LOO N ^ N L-iO O • •••••••• • • 1 00 On ON 0 ON ON Os ON ON On CO 0 to to to NO to to to to to to to loOOOOOOloOloloO — LOO N Lo to N Ot-^N 0 OOO — — — ftOroroN — — loVO vOVOvOVOvOVOvOvOVQvO • B .2 x: 4-J 3 c ^00 ONONNNNOOVCON O-’OOcoNO-*^'-* 0 WWWW^^WWWW vo vo 00 N OO tJ- N xf-OO vo t}- ■-•N — ONtONOOOO — r2 C/3 OOOOOOOOOOOO OOOOOOOOOOOO "3 cr w <4- 0 4-4 C/5 On « *— « 10 to »-4 i.r 10 *-4 K ^0 >OlO« rt“ 0 O N COCO»-4 ro to >0 ro O O to ro Ov to lo tONOOthtoNLoNTj-O-^- . w •>— •** °oo cooooocooooococoooco NNtoto— OOO — O — O 000000000000000000000000 May 22 .£ *0 a. 4-4 C/5 0 £ — OviaONOnwii^^1^1^ ON ' N 10 to w O « — '—1— — — 0000-‘-< OCOOOCCXJOCOOOf OOOOOOOO CTj LO — — OV— Ov N Ovltv tA to to — lAvJ"tt-UVt)-v(-v(-tAvh»t Lo N — NN — OOOOO — 0 000000000000000000000000 •S33a2Ep\[ sqj jo PiruEi3dui3x uoO <0 10 O Lnu-iO O O 10 O O — NtoO ION n0>0 OOhmOOOI>m w ty-' <0 VO VC VO VO 'O VO VO >o>o O O O O O O O U-I OOOO O O Oma ia O vO t^-O N O O •••••••••».. OOO — NtrvN — — OOO lav VO VOvO'OvOVCVOvovovovo •UOIJEAJ3SqO JO 3LUIX eoooodoooooo C O to O to 0 rr,Q to 0 mm • O X. vo n On O ^ « tn t}-vo in On OOOOGOOOOOOO O to 0 tA 0 too tA O tAtA N O vo K a, 0 y - tA rf-vo Ov — — t— < _ 47 the intensity of magnetic forces , &c. To reduce these observed positions of the points of equili- brium to their true positions, that is, those which they would have had if the temperature of the magnets had been the same at each of the observations, it is necessary to apply a correction by means of Tables I. and II. ; and that the nature of this reduction may be evident, I shall give an instance of the process at length of applying the tables to the correction of the observations, when the temperature at which they were made was below the standard temperature, and also when it was above that temperature. As the observations were made with the magnets at temperatures varying nearly equally above and below 6o°, I consider that, the standard temperature to which to reduce them. The two following are instances of this reduction. ist. Observed temperature below the standard temperature. 24th May, 6h oom A. M. Westerly. Easterly. Points of Equilibrium 83° 27 8311 at temp. 570 Correction for i° Temp. Table II. — 47.002 — 45-397 Points of Equilibrium • 82 39.998 82 25.603 at temp. 58° Correction for i° Temp. — 42.581 — 41.380 Points of Equilibrium 81 57.417 81 44.223 at temp. 590 Correction for i° Temp. — 39.244 — 38.316 Reduced Poiuts of Equilibrium 81 18.173 81 05.907 at standard temp. 6o°. 2nd. Observed temperature above the standard temperature. 29th May, Noon. Westerly. Easterly. Points of Equilibrium 82000' 81034' at temp. 63° Correction for i° Temp. Table I. 42.820 + 40-5i7 Points of Equilibrium 82 42.820 82 14.5 17 at temp. 62° Correction for i° Temp. + 47-329 -f 44.241 Points of Equilibrium 83 30.149 82 58.758 at temp. 6i° Correction for i° Temp. + 53-7*3 + 49.296 Reduced Points of Equilibrium 84 23.862 83 48.054 at standard temp. 6o°. 48 Mr. Christie on the effects oj temperature on By processes similar to these, making use of Table I. or II. according as the observed temperature of the magnets is above or below the standard temperature 6o°, the observed positions of the points of equilibrium are reduced to what would have been their positions had the temperature of the magnets been 6o° at each observation. the intensity of magnetic forces , &c. 4: hie of the positions of the Points of Equilibrium at ivhich a Magnetic Needle was retained at differed * during the day , by the joint action of two bar Magnets and of Terrestrial Magnetism, reduced to thei positions at the Standard Temperature (60°) of the Magnets . Note. The observations were mad n doors. May 22. £ O nJ T3 *-• ii O a3 "O c o E o-o it S t ~ 9 81 80 81 81 82 82 83 83 83 81 * 17 4‘ 00 70 25 82 83 84 83 81 *83 80 81 80 81 25 41 01 4i 57 52 82 82 83 82 81 82 30,80 iSiSo 0380 06 2 58 47 47 45 53 34 31 57 4i 5 4-0 29. 0.00 0.40 1 .00 82 4782 5881 36 81 4381 >3—2.75 00 — 3.00 48' — 2.00 09—2.3° 38j— 3-75 >7i — 3 • 3° 45; — 2.00 30—0.75 33 ,50 82 01 82 2482 20 82 5 7 82 03 82 53 85 0685 31 84 25 83 26 82 40 82 21 83 47 82 20 81 48 82 21 81 5281 38 81 20:81 13 81 06 80 47 81 1681 16 25. o CT3 G 8 in O w E Q. O it £ t 5 56 45 44 22 05 44 East. o 81 82 83 82 8l 81 8l 39 26 26 °3 5° 26 >3 No observation. •1 .00:81 1 1 80 46 . 5°8 1 4-0. 25 81 10)81 1081 08 18 3°- -0.30 -1.30 -2.00 81 82 83 37 2C 1 2 ,25 83 4*00 84 4 ■3-5083 ■3.75! 82 4.00,81 •3.5081 ■3.20,81 2.25 81 ■2 . 00 8 1 44 21 45 29 45 02 36 28 81 82 47 16 84 05 84 29 84 04 82 44 81 81 4i 43 80 57 81 20 81 81 07 23 26. 4- l) , 0 £ o 3'*- o Bt C fl) QJ *-* C. CLO PH 8 4- i°.oo 4-0.2 4-0.25 — 0.50 582 10 50 5o 50 50 -1 .00 0.0c Points of Equilibrium. West. East. o 81 83 85 83 83 82 81 81 80 80 58 15 82 39 54 18 01 55 >9 5° O 81 36 26 83 85 82 82 52 08 1581 81 81 80 49 80 1 2 06 33 5° 1 7 58 35 31- -2.00 -2.50 -3.0c -3*4° -3*67 -3-75 -4.20 -5.00 -5.00 “4 -3 -33 -3.00 67 8 82 82 84 84 83 82 81 82 81 1 81 81 24 54 42 25 17 82 44 53 46 38 01 28 82 82 83 82 81 27 82 82 81 81 81 >5 54 29 58 4> 03 51 23 04 47 32 31 Mean true positions of the Point! ^-of Equilibrium. Westerly. o 8l 82 83 83 82 82 81 81 81 80 80 26.2 20.8 14. 46. 43-6 04.4 4* 683 883 15.0 20.8 56.2 58.8 Easterly. o 81 82 South, as before. 82 81 28.40 19.80 13. 20 34‘2jo 02.0 0 581 8l 8l 8l 80 22.6 16.8 O 08.0 I4.4 05 .40 46. 9 14. oE 14.8 E 15 .2 E 02.0 V 24.0 V 25.6 V 14.8 V 01 .0 V 02. 8 E 03 .2 E 01.6V 81 82 83 84 83 83 82 82 81 81 81 81 82 82 83 484 83 50.4 24.0 28.2 13 55.2 00.6 1 1 .2 08. 4 35 *8|8i 16.8 81 16.8 21.8 82 81 82 81 81 °3*4 30. 8 39‘° 19.0 25.4 18.4 43.2 >3‘2 47.6 24.2 12.2 17.6 15. 6E 16. oE 16.0 E 02.4 V 22.0 V 28.4V 22.0 V 02.4 V 01 .4 V 02 .4 V 00 . 4 V 00. 8 E In taking the mean, I reject this observation as evidently irregular. CCXXV. H 50 Mr. Christie on the effects of temperature on To obtain from these corrected observations the diurnal variation of the terrestrial magnetic intensity, I take half the sum of the mean easterly and westerly arcs at different hours during the day as the mean azimuths of the points of equi- librium at those hours, and substituting these azimuths suc- cessively for (p in the equation (a), M — F (.004690814 + 000829329 cos.9 (p) = 0, I obtain the values of M in terms of F at those hours : dividing each of these values by the minimum value of M, which in every case appears to happen at about ioh 30m in the morning, I obtain the relative terrestrial magnetic in- tensities at the times of observation. These results are con- tained in the following table. 13. Table of the mean Terrestrial Magnetic Intensities at different hours during the day , deduced from the preceding observations. Note. The observations were made within doors. § O'S Mean of the Observations of May 22, 23, 24, 25, 26. Mean of the Observations of May 27, 28, 29, 30, 31. Mean of the two sets. s £ .ts 0 F-h £ Azimuth of Terrestrial Azimuth of Terrestrial Terrestrial O the Points of Magnetic the Points of Magnetic Magneric Equilibrium. Intensity. Equilibrium. Intensity. Intensity. h. m. 6 00 0 1 81 27.3 I .OOI75 0 7 8l 56.9 I .00170 I .OOI73 7 3° 82 19.9 I .OOIOO 82 27.4 I .00128 I .OOI 14 9 00 83 13-9 I .OOO31 83 33-6 I.OOO46 I .OOO39 10 30 83 40.5 I .OOOOO 84 16.2 I .OOOOO I .OOOOO Noon. 82 22.8 I .00096 83 4° *3 I .00038 I .00067 1 30 81 43*5 I .OOI51 82 39.5 I .00112 I .00132 3 00 81 29.1 I. OOI73 81 57.2 I .OOI7O I .OOI72 4 30 81 11. 5 I .OOI99 82 10.8 I .OOI5I I .OOI75 6 00 81 17.7 I .OOI9O 81 41.7 1 .OOI92 I .OOI91 7 3° 81 00.9 I .00216 81 20.5 I .00224 1 .00220 9 3° 80 52.6 I .OO229 81 14.5 I.OO233 I .OO23I 1 1 20 81 19.7 I .00225 I .00225 51 the intensity of magnetic forces , &c. # From the mean obtained here, it appears that the terres- trial magnetic intensity was the least between 10 and 11 o'clock in the morning, the time, nearly, when the sun was on the magnetic meridian ; that it increased from this time until between 9 and 1 o'clock ip the evening; after which it decreased, and continued decreasing during the morning until the time of the minimum. Having by this reduction of the observations made within doors, determined the nature of the changes in the direction of the needle in that situation, independent of the changes which took place in the temperature of the magnets, and thence deduced the diurnal changes in the intensity of the terrestrial forces acting upon the needle, I shall now detail similar observations which I made in the open air, for the purpose of comparing with them, when these had also been cleared of the effects due to changes in the temperature of the magnets, in order to determine how far there was any thing anomalous in the directions of the needle when in doors and when in the open air. I have already mentioned that, for the purpose of making these observations, the apparatus was placed on a table fixed firmly in my garden, the mag- nets being placed in earthen pans containing water. The observations were made in the same manner as those in doors, excepting that, as the magnets were here liable to greater changes of temperature, their temperatures were noticed at the beginning, and also at at the conclusion of each of the observations : they are contained in the following table, where the time set down is that at which the observation commenced, the time occupied in making the whole of each being from four to six minutes. 52 Mr. Christie on the effects of temperature on Table of observations, made in the open air, on the Diurnal Changes in the positions of the Points of Equilibrium at which a Magnetic Needle was retained by the joint action of Terrestrial Magnetism, and of two bar Magnets, having their axes horizontal and in the Magnetic Meridian, and their centres at the distance 21.52 inches from the centre of the needle. Date and Time of Observation. Temperature of the Magnets. Points of Equilibrium. Temperature of the Magnets. Mean Tempe- rature of the Magnets. Barom. Therm. attached. Slorth. South. West. East. South. North. South. h. m. O O O / O 0 O O O 0 fcb 6 °5 55-2 54.O 85 5° 85 02 0 20 E 54.8 54.O 54.50 3°- 23 58.2 • — c 7 24 55.2 55.2 85 18 84 24 0 20 E 55.6 55.6 55.40 3°- 23 57- 1 N u o 8 53 57*3 56.7 85 32 83 38 0 06 E 57-4 57.O 57.10 lO 3o No observation. CD o °5 61 .8 60.0 82 06 80 18 0 34W 61.8 60.0 60.90 30- 20 58.2 d i 26 62.5 61 .0 81 02 78 46 0 44W 62.5 61 .0 61.75 30. J9 59.8 5 2 56 63.8 62.0 79 H 77 58 0 28W 63.8 62.0 62.90 30- *9 60.6 ’4-> ON d 4 26 63.0 61.0 80 00 78 58 0 20W 62.8 6i .0 61.95 30- 18 59-5 CD ,4-» 6 IO 59.0 58.0 81 36 80 20 0 00 58.8 57.8 58.40 30. 18 56.8 <4-h < 7 25 56.0 55.O 83 08 82 06 0 06 E 55.8 55.0 55-45 9 00 55 6 55.8 82 34 81 3o 0 12W 55-3 55-5 55-55 30. 17 55-7 6 12 55-7 55-5 82 5° 82 °4 0 12 E 55-5 55-3 55-5° 56.75 fab 7 25 55 -2 54.8 84 12 83 02 0 18E 55-5 55 • 1 55-15 3°. 1 1 c • H 9 00 66.25 64.0 77 52 78 08 0 18E 66.25 64.0 65-13 30, 1 1 60.25 CD t-l o IO 27 68.0 66.0 77 18 76 40 0 20W 68.0 66.0 67.00 3°« 1 1 63,0 3 s o 12 71.0 68.8 77 04 74 42 0 26W 71.0 68.8 69.90 30- °9 64.3 i 26 70.7 69.0 75 24 74 20 0 38W 70.7 69.0 69.85 30 °9 64.6 X 4-» d 3 00 70.0 68.4 75 20 74 02 0 32W 69.8 68.3 69.14 3o- 08 65 . 1 o N o o 4 3° 69.0 67.5 75 16 74 28 0 16W 69.0 67.5 68.25 3°« °7 65.8 c Ut 6 00 67.6 66.3 75 42 74 54 0 02 W 67.6 66.3 66.95 3°- °7 64 . 8 7 3° 65.8 64.2 76 18 75 38 0 02W 65.8 64.2 65.00 3°- 08 64.0 < 9 00 61 .5 60. 1 79 H 77 38 0 joW 61.4 60.0 60.73 3° °9 60.0 5 5° 56.8 55.0 81 81 28 0 26E 56.6 54.8 55.80 3° 10 60.4 bb 7 26 56-3 55-7 81 46 81 20 0 22 E 56.1 55-7 55-95 30 •13 57-5 a 9 00 55-4 54.8 82 48 82 54 0 08 E 55-4 54.8 55. 10 3° 15 57.8 • CS IO 26 56.5 56.0 82 48 82 36 0 06W 56.7 56.0 56.30 3° *5 57-7 r-+ O 5 o 00 58.6 58.0 81 50 80 40 0 24W 58.8 58.0 58-35 3°« 16 58.5 3 ' i 30 60.0 58.8 80 08 78 52 0 26W 60.0 58.8 59.40 3° 16 58.6 4-» 1 1 58 57-5 55.6 83 52 82 24 0 26 W 57-4 55-5 56.50 30.22 55-8 S c 0 1 29 56«3 54.8 83 1 8.8 1 54 0 48W 56.5 54.8 55.60 30.22 56.7 ‘ 1 0 2 58 57.0 55.8 81 32 80 34 0 40W 57.0 55.8 56.40 30.21 57-4 s (M ^ 4 21 57.0 56.0 81 5280 44 0 18W 57.0 56.0 56.50 30.20 56.7 5 57 54.8 54.2 82 38 8 48 0 00 54-8 54.2 54.50 O . N O 56.2 <3 7 28 53-5 52.4 83 44 8 08 0 06 w 53-5 52.2 52.90 3°-I9 56. 1 8 53 52.0 5 1 .0 84 54 8 52 0 00 52.0 51 .0 5 1 *5° 30.19 56.4 6 01 54-7 53-7 82 52 82 46 0 10E 54-5 53-4 54.08 30. 16 55-3 Co 7 28 55.0 54-5 83 52 82 58 0 20 E 55.2 54-5 54. 80 3o-i5 54-8 c 8 55 56.25 55-4 82 52 82 46 0 02 W 56.25 55-4 55-83 30.14 55 • S Ui 0 10 25 56.5 54-75 83 10 82 50 0 14W 56.5 54-75 55-63 30.14 55.0 0 H 57-9 55-9 83 28 81 00 0 40W 58.2 56.2 57-05 30.10 56.2 p 1 29 58.5 56.0 81 34 79 54 0 40W 58.5 56.0 57-25 30.11 55-4 2 59 57-7 56.5 80 52 79 20 0 28 W 57-7 56.5 57.10 30. 1 1 56. 1 N | 4 3° No observation. ™ G u 6 00 No observation. 7 42 52-3 5i-5 83 08 82 34 0 04W 52.3 5i-5 51.90 30.10 5 6.7 < 9 00 50.8 50.6 84 22 83 44 O CO 50.8 50.4 50.65 30. 10 52.8 The mean of the azimuths of the westerly point at 7b sora in the evening is 8i° 28', and of the easterly at the same time 8o° 48'; so that to reduce the situations of the westerly and easterly points to their distances from what ought to be considered as their meridian, 20' must be subtracted from each of the azimuths of the westerly point, and added to each of those of the easterly, similarly to what was done with the observations made in doors. The mean of the ob- servations gives the position of the south point at the same hour o'. 4 W., or so nearly in the meridian, that the obser- vations of this point require no reduction. The observed 54 Mr. Christie on the effects of temperature on azimuths, so reduced to their mean meridian, are to be cor- rected for the difference between the standard temperature and that of the magnets. By means of tables III. and IV, repeating the processes described for the reduction of the observations made in doors to the standard temperature 6o°, I reduce these observed positions of the points of equilibrium to what would have been their positions had the temperature of the magnets been 6o° at each of the observations. These reductions are successively effected in the two following tables. the intensity of magnetic forces, &c 5 S3 "a a <5j I •juioj tpmog aqj jo suoiqsoj uB3j^ co N O O W N ff) tn o N tfi M • •••••••••• ONX -lOtor^NN-.-iCO ►ii-«__^rr)c<-)i- > rb cr 0 O N Uc u *-o 0 w v*-« W 0 w »-« O OS CO CO N 0 °x X OO 00 X X tH 0 O X X C/) *-t • (S N N 0 00 N X N C CO ro N 0 CN m 0 O 0 «2 4J N N N l-H 0 £ £ N Ox OO X X X X 00 X OO •SJ3U§BJ\[ 00 0 rn ao 0 0 in aqj jo ajtuBj 0 • X X • so 0 N •-H Osso -aduia t uBarvr *-0 U-\ fN tH rn -H 0 O 0 ao a/~\ i.r\ in anv in CH-I a • Ho 1° "b a S3 JU 'b a ' * !*i ' Hj © ' "Vi '"S3 © o ""a 5° a a a • -~1 'Hi S3 ■ » a S3 S3 SN n M s 3 3 O' W o O, W W ^ ^ 3 O in k W r*-X VOVO00 ooo h O O N tJ- -+• «H O no o o o o u £ rt - t> u to e ,0 O o £ oooooooooo N ct N OO -4- -cr •+■ tJ-X X N to Tf* <-< to O O N hh COX i-hNNO'-hNcO'*- co r-^oo 00 00 x oc 00 00 00 •4-th N co •chsO + N00 N NX N -h p-> tfl >ri >« tf|M •sj3u8ej\[ sqi jooinjBi -sduisj ussjyq COX NcONi-i'-iNcn'4- X tHX X X X X X X X N •o O to O O tH hh to SO OOOOO ■+ io to Omo 7- -4- On so 10O so -4- N O N Points of Equilibrium. South. SO N X SO rt-SO rj- rf-so 0 NNOONNNOOOO °ooooooooooo East. 00 O -hJ-SO O N 0 N •<+• N X u*t 0 >h 0 tr>N Lrttrt _ « -1 tn N H Os OSX ON O — °X X X X X Fn (h tHOO X 4-> 8 sosoxx ox Thox ox N N N N W + c _ *-i n. n n i— t Os OX On O f °X X X X X N N N NX X •spui 5U) JO -aama^L 3eIM ajnjEJ UE3JV Oty-\OOt>-sOOtr>OOti-s X ON ~ CO t^N -thso T}- N O so • •••••••••• . mn m>vo 00 CN O OO aO m 0 lo ir\ in i_o u^> ar> us us us *ns s 3 3 a* W <2 3 O m NXX OO X N VO N N o •-ii-.H.NNroco'-'OO'-' OOOOOOOOOO O O w A t*l O lO p-H — < Q O ijv+ ir\ to O (J\X M N ON O tO to to to to N O Cs OX SO to O o I/-* to SO OOOOSoSOOO o — x so X X O so O t 'N+trtjjWOMH+NliN ^ uo O CNX Os O N « °X X X Q x Ch NX X X Vi 44 .2 ’5 Ph West. OX N _SO N xt-OSOX ■<+■ 'WlA M ® sr ItN ^ in •hJ-«-i its rh t r\ — O X Os « N N C X XX X X tH NX X X •sjouSejm aqj jo ojnjBJ -aduiaj^ UE3JM OOO O L/N O Its O tT| O t-riTf-i-i Ov N. ON ON ■+ -+X • • • ••••••• -rb >n N 0 ** N ^ 00 *n »n °in m in VO 'O 'O VO immn •aoijEAjasqo cOOOOCOOOOOO C OcoO MOtoOwOwiO JO 3UJIX 0 j3so N On O ^ « co •thso tn On Hi ri OH © Sh & "S3 Ho S3 "S3 © a • OJ a •Ho © a >> a a c © a) Ho <~o O c3 h»h C M "S3 QJ HhO "a Ho a a 1° a o bn ^ Sv in *2 -o n 0 — S a rp a. r-1 Ho ’> Ho <3j a I Ho a brj a> a s; '"H H <0 a o a to a rs> «i 'fe >> so Oi • «^> o so a a o • »o Ho a a Ho a Ho a S §• C: s >1 a o O ft, a -a HO Ho ■h3 O -23 a a a -a "a **» a as a "a ^ a> hj -a a Ho =0 to a a o • no a so a H> HO o -a a a 0) ca o c V a -c HO +J Ho • ni SO a sa a> a Mean true Positions of the Points of Equilibrium. South as before. 0 , 0 19.0 E 0 18.0 E 0 i i .3 E O 10. 7 W / 0 25 . 3 W 0 37 • 3 w 0 32. oW 0 12.7 W 0 01 .3 W 0 01.3W 0 03 . 3 W Easterly. wnO Nt'IM^NNf'NNN • •••••••••* - O C>"" t-H Ih nONO On O « OnOnJI S^XX °NM NCO X NNn o «H. m. J0J P3JD3JJ0D ajnjEjaduiax JO 3DU3J3JIQ NOCHtHUr\LoOOOOl-C' ON N MO\ NX _ * « cr, .......OO.. °tnMAr}- 'j-N N N lZ X ON + + + + + + + + + N N Points of Equilibrinm. East1 X coso On sO Noo X 'l- (h '.o^ioOncosoO'-oO'T- ^ § ON O - O OnX ONX OnX °.3< tHXXX N N N N N N West. rt OncoO soOnN ►- io — On *• > so •cJ-'d-O O •”< co O O so l— « >1 J! CnO w i- O OnOnCN OnX o £ t^x XXX NNNNN JOJ p»)03JJIO0 sjnjEJaduiax JO 30U3J3JJIQ Oi-oO'-oOOOOOOO ^ N NX uo it-SO so so -< «-o °*Z so-^J-O 0 + 00 in NX + 1 4-++ + + ++ + N Points of Equilibrium. East. Oh + m o rt-X X X SO SO *■ N ct O co O co O -T-i-i N . OnOn O O Oxxx NX X ° tH r^X XX NNNNNN West. ioOH0-0\NSDo <-osO 'O — COoitoNNO-d-ON On On O' O O Os OnX NX X O N N IN-X X NNNNNN JOJ P3JD3JJ0D 3JtlJEJ3duJ3X JO 33U3J3JJIQ O'oOOsoOOsoOOso N O ON tHSO SO oh so co o co O ^b ^b rr> *—<0 0^ in'O +++++++++++ 20. Points of Equilibrium. : East. *" rb ^b ^b O Ov »n no Os ON + -< - n N rb O ’"i O O *-• 0 On O — O Onoo co co oo oo oo t^oo oo oo r-H r>H West, x hh co ci co "« to co On n n ' CO O N +• N 1-0 N •-• O On O O O — OsX X x x O' ° NX XXX NNNNNN JOJ P3J03JJOD 3jnjEJ3dtU3X JO 3DU3J3JJ1Q O to co O O to rh to i-o O to lox hh O Onx i-i n On O tn O ^b ^b r\ On On Cnoo vo Lr^ O + + 1 1 II 1 1 1 1 1 June 19. Points of Equilibrium. East. n m o ^ n *— i • rb O ^ '*b ^ O ^bN',b'^"N ^ hh i-h g o qn o On On On °co oo oo .i; oo oo oo West. SO N Os rt CO tHSO to O tH CO O N co >• N + N + N to + u -._mcjn-hCOOOsOn Ox XX^XXXXX N N JOJ P3J33JJ0D 3jnjEJ3dtU3X JO 3DU3J3JJ1Q OOOoO UNOtoOtoO •oso ON _ On N On Onso to N • • • L Q ••••••# °io + n7o-Nh«+ + +++ | | || +++ oOOOO H.-000000 •U0pEAJ3SqO C O coo co 5 CO o coo coo JO 3U1IX NOnO^ n ^VO r\ On »-* 4 56 Mr. Christie on the effects of temperature on The character of the diurnal changes in the positions of the points of equilibrium is very nearly the same for each day, but, in taking the mean, I can only make use of the observations of the 20th, 21st, 22d, since on the 19th no ob- servation could be made at ioh 3om, and the azimuths are all greater on this day than on any of the subsequent, and two observations were unavoidablv omitted on the 23d. W- ' Comparing the results with those obtained from the obser- vations made in doors, we find them agree as nearly as could possibly be expected. From table A it appears, that when the observations were made in doors, the westerly point receded from the north until half past 10 o’clock in the morning, and approached the north during the remainder of the day until about 9 in the evening ; and from table C, that when they were made in the open air, the westerly point receded from the north until about half past eleven in the morning, and approached it until six or seven in the evening, after which it again gradually receded. This is not a greater variation in the times of the maxima than we find on different days, either in the in-door observations, or in those in the open air. The easterly point appears to have receded from the north until about 10 o’clock in the morn- ing, when the observations were made in doors and likewise when they were made in the open air ; and to have approached it until between nine and ten in the evening in the former case, and until six in the latter. Taking, as before, half the sum of the mean easterly and westerly arcs at different hours during the day as the mean azimuths of the points of equilibrium at those hours, and sub- stituting these for

in which oil is found ; magnified ten diameters. Plate VI. Fig. l. Ova six hours after being spawned on water; natural size. A. one of these ova ; magnified five diameters. B. The same ovum magnified ten diameters. C. Longitu- dinal section of the same ovum ; its contents in a half coagu- lated state, and putting on an organized structure ; magni- fied ten diameters. The rest of the ova spawned at the same time were kept in water, to watch the progress of the formation of the tadpole. One of these was not impregnated, consequently remained unchanged, while the others became gradually more and more organized. This abortive ovum is placed at the top of each cluster with a mark # Fig. 2. The cluster of ova 12 hours after being spawned, diminished by that examined in fig. 1. ; of the natural size. A. One magnified five diameters. B. The same magnified ten diameters. C. The same, forming a longitudinal section ; magnified ten diameters. Fig. 3. Twenty-four hours after being spawned. Fig. 4, Thirty-six hours after being spawned. At this period the ovum has its form considerably changed, and the head and tail of the tadpole are distinctly seen. 86 Sir Everard Home on the changes , &c. Fig. 5. Three days after being spawned. At this period muscular motion is for the first time perceptible. The letter D shows the ovum laid open on one side ; magnified ten times, as in letter C. Fig. 6. Four days after being spawned. The letters cor- respond to these in Fig. 5. Plate VII. Fig. 1. Five days after being spawned. At this period the ova become separated, and the tadpoles begin to leave the ovum. A. Shows a tadpole in the act of extricating itself ; magnified five diameters. B. A back view of it ; magnified eight diameters. C. A belly view. D. A side view. E. A longitudinal section ; all the views magnified eight diameters. Fig. 2. Six days after being spawned, four different views ; magnified eight diameters, as in Fig. 1. Fig. 3. Eight days after being spawned ; all the views magnified eight diameters. Fig. 4- Twelve days after being spawned ; four views of the tadpole ; magnified eight diameters. The animal in twelve days had become so far advanced in its growth to make further progress in the investigation unnecessary, after the splendid figures that are before the public upon that subject in different publications. FMl. 7}-ans.MDCCCXJ£V. Plate V.p. S6. IYa.2 . 'izJlrtiifr d * 9> m, ■mz Bausr dej ' El C 87 3 IV. A general Method of Calculating the Angles made by any Planes of Crystals , and the Laws according to which they are formed. By the Rev. W. W he well, F. R. S. Fellow of Trinity College , Cambridge . Read November 25, 1824. 1. It has been usual to calculate the angles of crystals and their laws of decrement from one another, by methods which were different as the figure was differently related to its nucleus ; which were consequently incapable of any general expression or investigation, and which had no con- nexion with the notation by which the planes of the crystals were sometimes expressed. And the notation which has hitherto been employed, besides being merely a mode of registering the laws of decrement, without leading to any consequences, is in itself very inelegant and imperfect. The different modes of decrement are expressed by means of different arbitrary symbols ; and these are combined in a manner which in some cases, as for instance in that of in- termediary decrements, is quite devoid both of simplicity and of uniformity, and indeed, it may be added, of precision. The object of the present paper is to propose a system which seems exempt from these inconveniences, and adapted to reduce the mathematical portion of crystallography to a. small number of simple formulae of universal application. According to the method here explained, each plane of a 88 Mr. Whewell on calculating crystal is represented by a symbol indicative of the laws from which it results ; the symbol, by varying the indices only, may be made to represent any law whatever: and by means of these indices, and of the primary angles of the substance, we obtain a general formula, expressing the dihedral angle contained between any one plane resulting from crystalline laws, and any other , In the same manner we can find the angle contained between any two edges of the derived crystal. Conversely, knowing the plane or dihedral angles of any crystal, and its primary form, we can by a direct and general process deduce the laws of decrement according to which it is constituted. The same formula are capable of being applied to the investigation of a great variety of pro- perties of crystals of various kinds, as will be shown in the sequel. We shall begin with the consideration of the rhom- boid, and the figures deduced from it ; and we shall after- wards proceed to other primary forms. § 1. The Rhomboid. 2. Let there be a rhomboid, A a , Fig. l. divided into a num- ber of small equal rhomboids by planes parallel to its faces. Let any one of the points of division of each of its three upper edges be taken, as P, Q, R ; and let a plane pass through these three points P, Q,R. Let the small rhomboids which are above this plane be removed, so as to leave a uniform assemblage of cavities. Then, the remaining surface P Q R, being com- posed of the trihedral angles of small rhomboids, if we sup- pose the small rhomboids to become smaller than the least distinguishable magnitude, the surface POR will appear a plane. And if we suppose these rhomboids to represent the 89 the angles of crystals. primary form of a crystalline body, P O R will be a secondary surface deduced from a certain arrangement of these primary elements. Let the three upper edges of the rhomboid, Ax, Ay, A z, be considered as three axes of co-ordinates ; and let the cor- responding co-ordinates be x9y,z. We can then express the plane P Q R by means of these co-ordinates. If, for in- stance, we consider an edge of the small rhomboid as unity, and if AP, AQ, AR contain respectively 9, 6, and 3 of these edges, the equation to the plane P, Q, R, will be ^+i+T = 1: X 9 ' 0 * 3 and if the numbers of small rhomboids in AP, AQ, AR be respectively h, k , /, the equation to the plane will be * 1 T + y_ k • 2 + T — If h, k, l be multiplied by any common quantity m, so that the equation becomes . y mh mk + ^ = 1>orT + T + f = m’ it is clear that the plane P Q R will continue parallel to its former position, and may be considered as deduced from the same law as before. Hence it appears, that in the equa- tion -i -f- ~ = m, the quantity m does not serve to de- termine the position or law of formation of the plane, and may be any whatever. If we make m = o, the plane POR still continuing parallel to its former position, will pass through the point A ; and as we have to consider only the angles made by planes and their intersections, we may in such calculations suppose all our planes to pass through this point A. MDCCCCXXV. N 90 Mr. Whewell on calculating Since therefore the direction of the plane P Q R is com- pletely determined by the three quantities h, k, l, we may re- present it by writing those three quantities thus |-h; y) ;* or, if the equation be px -f V + re = m, we may represent the plane by the symbol (/>; q ; r). 3. According to the law of symmetry which prevails in the production of crystalline forms, if one edge or face of the primary solid be modified in any manner, the other homo- logous edges and faces will be similarly modified. Hence, if one plane exist, other corresponding planes must also exist, and these we may call co-existent planes to the first. Thus if we have a plane P Q R, Fig. 2, and if we take AP' = AQ, and AQ' = AP, we must also have a plane P'Q'R: for the edges Az, Ay being perfectly similarly situated, if one of them be affected in any manner, the other must be similarly affected. Hence, if we have a plane (p; q; r), we must have one (q ; p ; r ). The same is also true of % ; and by considering this in the same manner, it will be seen that the plane [p ; q; r) has the following co- existent planes ( q;p;r ) ( >;?;/> ) ( p;r;q ) ( q;r;p ) ( r;p;q ). That is, there are all the permutations that can be made by altering the arrangement of the three quantities/), q, r ; that the one which stands first in order being always the coefficient of x, the second that of y, and the third that of z. These six planes may be represented by a single symbol * We might represent the plane by (h; k; l), which shows more immediately the law of its formation ; but in all our subsequent calculations we have to use the re- ciprocals, and hence our formulae are simplified by using the symbol (p ; q-,r) where p, q, r are the coefficients of the equation. 91 the angles of crystals . [p, <7> r) ’ it being understood, that when quantities are only separated by commas, they are to be taken in all the ways in which they can be permuted. In the same manner ( p,q ; r) may represent the two planes [p, q; r) (q,p\r), the permutations not extending to r, which is separated by a semicolon. In the case of the rhomboid, however, the per- mutations always include all the three quantities, in conse- / quence of the similarity of its three edges. 4. We have hitherto considered only the planes produced by cutting off the upper angle ; but we may represent in the same manner the plane produced by truncating any other angle. It maybe observed that the angles x,y,z, fig. 3, which are separated from the superior angle A by an edge, are called lateral angles. The angles x' , f , vl , which are separated from A by a diagonal, are called inferior angles. Let p q r, fig. 3, be a plane produced by a truncation at the lateral angles : ocp,xq, xr being h, k , l respectively. Produce r A beyond A, and take AP = xp, AO = xq, AR = xr ; then the plane POR will be parallel to p q r, and may be taken instead of it. Now it is manifest that the equation to this plane is — -j + \ + T = 1 ; and therefore its symbol is f — X’T’-r)* Or if p = L. q == r = the equation is — p r + qy + rz = m, and the symbol ( — p ; q ; r). Hence a plane which cuts off the lateral solid angles is distinguished by having one negative index. In the same manner let p q r, fig. 4, cut off an inferior angle xf, so that x' p s h, x' q = k, x,rz=l: and taking 92 Mr. Whewell on calculating AP = cdp, AQ = x'q, AR = a! r, the plane P Q R will be parallel to p q r, and its equation will be T — T — T — 1; orpx — qy — rz=i: and its symbol ; — -i- ; y) , or (p ; — q ; — r; ) . Hence a plane which cuts off the inferior solid angles is distinguished by having two negative indices. It may be observed, that in both these cases the coexistent planes are given by taking the permutations of p,q,r; and may be represented as before by ( — p , q , r) and (^>, — q ; — r). There will in each case be six ; two for each angle. 5. If one of the quantities AP, AQ, AR, or h, k , /, in any of these cases become infinite, we shall have a truncation of an edge of the rhomboid. Thus if AP, in fig. 2, become in- finite, we have a plane cutting off the terminal edge A x, fig. 5. And since h is infinite, if q=~,r=z -k, the equation of this plane is qy + rz = 1 ; and its symbol (o ; q; r). In the same manner, making x'r infinite in fig. 4, we have, for a plane truncating the lateral edge x'y, an equation px — qy = 1 , and a symbol ( p ; — q ; o ) . The terminal edges of Ax, Ay, Az, are not similarly affected with the lateral edges xy' , z , zxr, x'y,yzf, z? x. 6. Instead of supposing the secondary faces to be produced by removing a part of the rhomboid A a, we may conceive, with Hauy, that this larger figure is composed by adding successive layers of the small component rhomboids to a rhomboidal nucleus ; and that the secondary faces are pro- duced by supposing the magnitude of these layers to de- crease according to any law. And it will be easy to show 93 the angles of crystals. what symbols, according to the notation here proposed, cor- respond to the different laws in the old system. Thus A decrement on the superior angle is expressed by ( p , q, q), A which corresponds to Hauy's symbol p_. 9 _1 On a lateral angle by ( — p,q,q) corresponding to E?; ; ± On an inferior angle by ( p , — q , — q) corresponding to e p ; r On a terminal edge by (o, q , r) corresponding to B? ; On a lateral edge by ( p , — q, o) corresponding to G p • An intermediary decrement thus (/>, g, r), corresponding to (A^B^Cyj and ( p , — q, — r) corresponding to (opD?F -f). The symbols of the faces of the primary form are (p, o, o). 7. There is in fact, however, no necessity to suppose the secondary forms to be produced either by truncation of a primary one, or by addition to it. If we suppose that the small rhomboids, of which A a was assumed to be made up, are continued through all the space round the point A, we may conceive a plane to pass among these, parallel to PQR. And this plane will be represented by (p ; q ; r) indepen- dently of any consideration of the rhomboid A a or the point A ; for if we take any point , and from it draw lines to the plane, parallel to the three edges Ax, Ay, Az, these three lines will be as-h^^-i. And any other plane may simi- larly pass among the small rhomboids, and be represented by (/>' ; q' ; /). And if we obtain any solid figure contained by such planes, we may, by supposing those of the small 9* 94 Mr. Whewell on calculating rhomboids which lie without this plane to be removed, have a proper representation of a secondary crystalline form con- stituted by the aggregation of primary ones. Before we proceed to the calculations founded on this mode of viewing the subject, we may observe, that by in- creasing or diminishing the three indices p , q, r in any ratio, the plane represented by them is not altered. Thus (p ; q; r) ( np\nq\nr ) &c. are the same plane. Hence (p ; q ; q') is the same as ( T- ; 1 ; 1 j (p ; p ; o) as (1 ; 1 ; o) ; and the primary faces are (1,0,0). 8. Prop. To find the dihedral angle contained between two planes (p;q;r) [p‘ ; <7'; r'), the dihedral angle at the ter- minal edges of the primary rhomboid being a. If there be three co-ordinates any how situated so that the dihedral angle at the axis x between the planes xy and xz is a. ; the dihedral angle at the axis y, /3 ; and at the axis 2, y : and if d be the cosine of the angle which a line perpendicular to the plane yz makes with x ; e the cosine of the angle which a line perpendicular to xz makes with y ; f the cosine of the angle which a line perpendicular to xy makes with % : and if Q be the angle of two planes whose equations are Ax -f- By + C z = m, A' x + B'y + C z =2 m' : we shall have (see Transactions of the Cambridge Philosophical Society, Vol. II. P. I. p. 200) A A' , BB' , CC' d7 T e7 ' f* 95 the angles of crystals. In the case of the rhomboid, since the dihedral angles are equal, a, jQ, y are equal; and hence also d,e,f are equal. Hence . AA/+BB/+CC/-(A/ B + AB'+A' C+AC'+ B' C-f BC') cos. * cos. 6 = — — — — , */ ] (A*-f Bz-f C#— 2 (AB-f AC-f BC) cos. a) (A'3+B'2+C/a— 2 (A' B' + A'C'+B'C') cos.«.) j And if we put^>, q, r, p ', 9' ; r' for A, B, C, A', B', C', we shall have the angle. If we have to find the angle of two planes resulting from the same law, (/>'; 9'; r') will be a permutation of (p ; q ; r) ; and the denominator of — cos. 6 will be p1 + 91 + — 2 (/>? + ^r+ COS. a. We shall take examples of the use of these formulas. Ex. 1 . To find the angle made by two planes of carbonate of lime resulting from the law* (4, — 5, — 5). (Chaux Car- honatee Cuhoide of Hauy). The primary form of carbonate of lime is a rhomboid in which the angle ot is 105° 5', and therefore cos. a. = — .2602. Two of the secondary planes will be (4 ; — 5 ; — 5) and ( — r, ; 4 ; . — 5), and if 0 be the angle contained by these COS. 0 e= — 15 — 5 1 COS. a 66 + 30 COS. a = 88°. 18. or cos. 6 = 5 — 17 x .2602 22 + 10 x .2602 = .0297 A variety of other rhomboids may be produced in this and other substances by other laws. In all cases, if two of the indices of the symbol be equal, as (p, q, q), there will only * That this law is what Hauy calls a decrement on the inferior angles of 4 in breadth to 5 in height, and is in his notation represented by the symbol e JL. The angles obtained in the text differ slightly from these given by Hauy in con- sequence of his having assumed the angle of the primary rhomboid of carbonate of lime, = 1040 .28/ .40'', for the convenience of using the cosine rz — _L. 96 Mr. Whewell on calculating be three coexistent planes ; and if each of these planes be repeated, we shall have three pairs of parallel planes con- taining a rhomboid. If the three indices in the symbol ( p , q , r) be all different, we shall have six planes, and repeating each of these, we shall have a dodecahedron consisting of two six-sided pyra- mids. To this case belongs the following example : Eoc. 2. To find the angle of planes in carbonate of lime, resulting from the law (1, — 2,0). (Decrement on the lateral edges by two rows in breadth. Symbol D2. Chaux Carbonatee Metastatique. Hauy.) Two adjacent* planes are (1 ; — 2 ; o) (1 ; o ; — 2), and preserving the same notation as before — cos- 6 = 5+4‘cos.» = — -2525 , 0 = 104° 38'. By other laws we should find other dodecahedrons and their angles. But in many cases we have two laws, pro- ducing two sets of faces, and it may be required to find the angle between those of one set and of the other. Ex. 3. To find the angles of planes (2, — 1,— 1) and (1,0, o). (Decrement by two rows in breadth on an inferior angle, combined with the primitive faces. Symbol es P. Chaux Carbonatee Imitable. Hauy). Adjacent faces* are (2 ; — 1 ; — 1) and 1 ; o ; o) : and a 2 -J- 2 COS# Gt / I “f- COS# CC Ant cos. 6 = 77-73-- .) = 2 V — — - = . 7022 ; 6 = 1 34° 37'. 9. We proceed now to the inverse problem ; having given the angles of the secondary crystal to find the law of its planes. And we shall first suppose the secondary form to * It will be shown afterwards how we may determine of co-existent planes which are adjacent. 97 the angles of crystals. be a rhomboid ; in which case, as has already been observed, two of the indices in the symbol are equal. Prop. Knowing the dihedral angles of the secondary rhom- boid, to find the symbol of its planes, Let (p,q,q) be the symbol of the planes, 9 the angle of (p;q;q) and (q;p; q). a _ 2pq + f— (p% + *pq+ 3 9*) C0S’ « p--\- 2 q* — 2 (2 p q -f- q 2) cos. a Here cos. 9 being known, we have a quadratic equation to determine q in terms of p , which as the proportion q : p only is wanted, is sufficient. The equation will be p 2 (cos. 9 — cos. a) -f- 2/> q (l — cos. OL — 2 cos. OL cos. 9) + q* ( 1 3 COS. a -f- 2 cos. 9 2 COS. a cos. 9) = 0 There will be for each value of 9 two values of — and there- p fore two laws according to which the same secondary form may be produced. It is to be noticed however, that the direc- tion of the primitive faces, and consequently of the cleavage will be different in the two cases. iq. Prop. It is required to find according to what law we shall have a rhomboid similar to the primary one. Here 9 = cc: therefore the first sum of the above equation vanishes, and the remaining part will be verified either by q = o, or by p( 1 — COS. oc — 2 COS.3 «) + #(l — COS. a — 2 COS.2 a) = O, or q= — 2 p. Therefore ( l, o, o) and ( l, — 2, — 2) each give 9 = cc. The first indicates the primary face, and the form is the pri- mary form. The other indicates a decrement by 2 in height on the inferior angle, which it appears gives a rhomboid iden- tical with the primary rhomboid. MDCCCXXV. O 98 Mr. Whewell on calculating 11 Prop Knowing the lateral angles made, at the termi- nal edges, by the planes of any bipyramidal dodecahedron to find the symbols. If we have planes ( p , q, r) they will generally form a bipy- ramidal dodecahedron, and the six angles at the edges of each pyramid will be alternately greater and less. If p, q,r be the order of magnitude of the indices, p being the great- est, the order of the faces will be that represented in fig. (see hereafter the section on the arrangement of faces). Hence faces occur in the order (/> ; q ; r) ( q\p\ r) (/*; p ; q) See. : and if 0 be the angle of the two first, and 0' of the next, we shall have zp q + r2 — ( q1- f 2 p r -f 2 qr) COS. u cos. 0 = COS. V = px q* 4- r1 — 2 (p q + pr qr) cos. « z q r p * — (?*+ r4 -f- 2 p q -f zpr) cos. * p1 + — 2{pq-\-pr + qr) cos. « from which equations we have to determine q and r in terms of p. To eliminate in these equations would lead to expressions of four dimensions, and it will generally be simpler to find q and r by trial. If we assume for p any number, as 12 ; q and r, which generally bear to it very simple ratios, will in most cases be whole numbers, and may be found by a few trials. And if the ratios of q and r to p involve quantities which are not divisors of 12, still the trials made on this supposition will indicate nearly the values of q and r ; and by trying other values for />, we may obtain them accurately. If two of the indices, as q, r be negative; the order of the faces will be (/> ; — r ; — q) ( — r ; p\ — q) ( — q ; p ; — r), &c. and the rest of the process will be the same as before. 12. Prop. Knowing the angles made by any plane with two primary planes, to find its symbol. 99 the angles of crystals. Let (p ; q; r) be the plane, and (o, 1 , o) (o, o, 1) the two pri- mary planes ; 9 and 9' the given angles .-. cos. 9 : i-(r + r) cos. . V | — 2 (P 9+ Pr+ q r) cos. a | cos. 9' = r — ( P + q) cos. a V | Pl+q1l+ rx—z (pq + pr+qr) cos. a. j whence q and r must be found in terms of p, as in last pro- position. Or we may find them directly thus. Since one of the three />, q , r is indeterminate, assume/>24-^3+ rz«*~Q(p q-\- pr-\-qr) COS. a = 1. cos. 9=q — r cos. a — p cos. a ; cos. — q cos. a — p cos. ct. Eliminating, we have q sin.2 a = cos. 9 + cos. a cos. Of + p cos. cx (l + cos. a) ; r sin.2 a = cos. 9' + COS. a COS. S+p COS. a (l + COS. ex). If we substitute these values in the assumed equation multi- plied by sin.4 cc, viz. [p*+ q*+ r3- — z(pq +Pr + qr) cos. sin.4a= sin.4« we shall have a quadratic equation in p ; and hence p , q , r are found. 13. Prop. To find what laws will give prisms parallel to the axis of the primary rhomboid. For this purpose the planes must be parallel to the axis ; and the equation of a plane must be consistent with the equa- tions of the axis, which are y = x, z — x. Let [p ; q ; r ) be the plane ; p oc + qy + rz = o is the equation to it, supposing it to pass through the origin; and since jy = x, z=x ; we ha ve px-\-q x-{-r x=o :.pz=. If r=:q,p = — 2 <7 ; the planes are ( — 2, 1 , 1) and the ioo Mr. Whewell on calculating secondary rhomboid becomes a regular hexagonal prism. (Example. Chaux Carbonatee Prismatique. Hauy.) In other cases the secondary form is an irregular hexago- nal prism, the angles being equal, three and three alternately. 14. Prop. To find the symbol of a plane which truncates any edge of a given form. Let two faces (p; q;r) [p'; q'; r') meet, and let (P ; Q ; R,) be a plane which truncates the edge formed by their inter- section : the plane must be parallel to this intersection ; and the equations to the intersection must be consistent with the equation P oc + Q^ + R* = o. Now for the intersection we have p z + q y + r z = °> p' % + q'y + r'% = 0 whence [pep — p'q] x — [q r' — q'r)z, (p'r — piJ)x = [q r' — tfr)y. Multiply Pjc + Qy + R^=oby(^ r' — q'r) and substitute, and we have P (1 r> — 4r) + Q (p1 r — P r1 ) +R(/> q'—p’q) = o. And if P, Q, R fulfil this condition, (P ; Q ; R) will be a plane truncating the edge as required. 15. Prop. To find the symbol of a plane which truncates an edge of any secondary rhomboid. This is a particular case of last Prop, when instead of [p ; q ; r) [p'; q r'), the planes are (p>q',q)(q\p',q)- Hence the equation of condition becomes F(q*—pq) + Q (q2—pq) + R(p2—q2)=° or Vq + Qq — R[p + q) = o Hence if R = q, P -|- Q ~p -|- and with this condition, (P ; Q ; q ) is the plane required. Ex. Required the planes which truncate the edges of the rhomboid produced by the law (3, 1 1). Here p -f- q = 2 ; the values which may be given to 101 the angles of crystals. P, Q are any number whose sum is 2. Thus (1, 1, — 1) (2, o, — 1) are truncating faces. (This rhomboid truncated by these two planes occurs in Hauy's Chaux Carbonatee Progressive. Fig. 41-) The plane thus determined will always be parallel to the intersection of the two planes ; but in order that it may trun- cate the edge, it must meet both of them on the really exist- ing part of each plane. This condition is easily introduced in each particular case. 16. In order to express, by means of the symbols already introduced, any crystal whatever, we may write down the symbols of the faces by which it is bounded ; indicating by the punctuation the permutations which are allowed. It will be convenient also to mark the number of the faces which arise from these permutations. In the rhomboid, when all the three indices are different, this number will be six. When two are alike, it it will be three. Thus (6) (/>, q, r) may indi- cate that the crystal has six faces arising from the law ex- pressed by (/>, q , r) and (3) (/>, p , r) may represent a crystal with three faces arising from the law (p,p,r); which is what would, according to Hauy, be called a decrement on an angle at the summit. It often happens that faces in a crystal are repeated ; that is, that there are faces parallel to one another, one of which may be considered as a repetition of the other. In that case we may distinguish them by placing a 2 before them as a multiplier. Thus 2 (3) (/>, p , r) indicates a rhomboid pro- duced by repeating each of the three faces represented by ( p , p , r). This is in fact the mode in which a rhomboid is always produced. In the same manner 2 (6)(p, q, r) is the 102 Mr. Whewell on calculating symbol of a dodecahedron, which results from repeating each of the six planes (p, q, r). §. 2. The Quadrangular Prism. 17. The quadrangular prism may be right or oblique, and its base may be a square, a rectangle, a rhombus, or a pa- rallelogram. But in all cases we may take one of its angles, and make that the origin of co-ordinates ; and taking two of our co-ordinates along two edges of the base, and the third along the length of the prism, we shall be able to express the secondary planes in the same manner as in the case of the rhomboid. There will however be some additional con- siderations to introduce, since the edges of the prism may be of different magnitudes ; and its angles not being symmet- rical like those of a rhomboid, we shall no longer have the same coexistent planes which we had in the former case. In order to introduce the first consideration, let x and y, fig. 6, be the co-ordinates in the direction of the edges of the base, and z in that of the length of the prism. Let the space bounded by the co-ordinate planes be filled with small similar prisms, and let their edges in the directions x,y, z be a , b, c respectively. Let a secondary plane POR be formed, by taking away h prisms along the edge x, k along y, and / along % ; then the lengths of AP, AO, AR will be h a, kb,lc. respectively ; and the equation to the plane will be ha » kb * lc 1> If we call —, A ; B ; C ; we shall have the angle be- tween any two planes by the formula, Art. 8 ; putting for ft, y and for d, ej , their values. But if we make ~, — py the angles of crystals. 103 ~ = q, y = r, (p ; q ; r) may still be taken for the symbol of the plane. In this case -A, are the co-efficients of the equation to the plane, and are to be used for A, B, C in calculating the angles which the planes make with each other. We shall use the following terms ; a rhombic prism is one whose base is a rhombus : an oblique rhombic prism , fig, 8, is one in which the sides are not at right angles to the base, the angles of the sides, as BA 2, CA z being equal. A doubly oblique prism , fig. 7, is one in which the angles of the sides at the base BA z, CA % are unequal. Prisms are called square or rectangular when their bases are so : and when the base is a parallelogram with unequal sides, and angles not right an- gles, the prism is called oblique-angled. Besides these we have a prism which we may call the oblique rectangular prism* fig. 9, in which besides the two rectangular ends we have two sides, as cz and the opposite one, also rectangles. 1. The doubly -oblique Prism, fig. 7. 18. In this, since the angles are all different, no one of the solid angles (A, B, C, D) is similar to another. Hence if a plane be formed on one of the angles, there is no plane ne- cessarily formed on another angle ; consequently a plane as [p ; q; r) or (p ; — q ; — r) does not necessarily imply any co- existent plane, and the symbol is to be written with the mark (;) between the indices, to show that no permutations are allowed. Let the edges of the subtractive prisms in last article be a, * We might consider B z as the base of prism, by which means it would be a right oblique angled prism. But the method adopted in the text seems to be more natural and simple. 104 Mr. Whewell on calculating in the direction AB, b in the direction AC, c in the direction A z. Then putting 3Lf -L, -1 for A, B, C in the formula, Art. 8, we shall have the angles made by secondary planes. Conversely, knowing the angles made by secondary planes we may determine A, B, C, as before, and when we have found in crystals the same substance, various values of A, B, C, we have q B b r C c m p Aa ’ p A a ’ and a, b, c are to be assumed, so that q : p and r : p may be numerical ratios as simple as possible. 2. The oblique rhombic Prism , fig. 8. 19. In this case the angles 2AB, z AC, and the sides AB, AC are equal ; and consequently the two faces z AB, z AC are symmetrical ; and whatever secondary plane is formed with reference to one, we must have a co-existent plane cor- responding to the other. Hence, if we have a plane ( p;q ; r) we must have a plane (q ; p ; r) and we may express both these by the symbol (p, q ; r) the (,) indicating that the co-or- dinates x and y may be exhanged, z remaining the same. And this is true whether/), q, r be positive or negative. Here having found p , q, and r we have ha, ka, Ic, because a and b are equal, and their values are to be determined as before. 3. The oblique rectangular Prism, fig. 9. 20. Here the solid angles A and C are similar in all re- spects, A being contained by two right angles BAC, CA z and the angle BAs;, and C by the angles DCA, AC 0, oCD equal to them. Hence whatever plane be formed on A, we must have a coexistent plane on C, agreeing with it, except 105 the angles of crystals. that the ordinate in AC is in the opposite direction : that is (/> *> <2 ; r) (P ; — q ; r) are co-existent planes. These may be included in the formula (p ; ±q-, r ). 4 . T/n? right oblique-angled Prism, fig. 10. 21. It is obvious that the opposite angles A and D of the base of this prism are similar in all respects ; and with any secondary plane formed on one of them, we must have a co-existent similar plane on the other. That is, we must have a second plane, when x and y are negative, as they were positive in the first. Hence (/> ; q ; r) ( — p ; — q ; r) are co- existent planes ; and we may express them thus (+/>; ± q,r) it being understood in such symbols that the upper signs are taken together, and the lower together. 5. The right rhombic Prism, fig. 10. 22. Here, the opposite angles A, D are similar, and also the adjacent sides. Hence with a plane (/> ; q; r) we have co-existent planes ( — p ; — q ; r) (q ; p ; r) ( — q ; — p; r). These may be included in the symbol (±p, ±q ; r) the upper signs being taken together as before, and/), q being permutable as is indicated by the comma. 6. The right rectangular Prism, fig. n. 23. Here the four angles A, B, C, D are similar. Hence (/> ; q; r) has co-existent planes (— p ■ q ; r) (p ; — q ; r) (— p ; — q ; r) These may be included in the formula the signs being taken in horizontal pairs. P MDCCCXXV. 106 Mr. Whewell on calculating 7. The right square Prism. 24. In this case, besides the co-existent planes which we have in the last figure, we shall have those which arise from considering that the sides AB, AC are symmetrical, that is p and q are permutable. Here the symbol is / J ^,±9; r) this will give eight secondary faces. 8. The Cube. 25. This differs from the last in having the edge in the direction % similar to those in x andy. Hence/), 7, r may be permuted and the symbol is | */>, ^ q, r) which gives 24 se- condary faces.* There is no necessity to vary the sign of r, for the plane (/> ; q ; — r) is the same as ( — p ; — q ; r). § 3. The regular Tetrahedron and Octahedron. 26. In this and other cases where the figure is bounded by more than three planes we shall make three of the primary faces co-ordinate planes, and the remaining primary faces will be expressed by different symbols. Also the co-existent planes will be differently represented accordingly as they are on one angle or another, and we shall in each case have to determine the different forms which will thus occur. Let A x y z, fig. 12, be a regular tetrahedron, and let Ax, Ay, A z be three co-ordinates. * In some cases however, we have only half the number of faces which the law of symmetry would give. Thus in the case of the pentagonal dodecahedron derived from the cube, the law is (2, 1, o); but the faces which occur are (2; 1 ; o) (1 ; o; 2) (o; 2; 1) which by the changes of sign become 12. The other 12 which arise from the symbols ( 1 ; 2 ; o) (2 ; o ; 1) (o ; 1 ; 2) are excluded. 107 the angles of crystals. Let a plane p qr be formed on the angle A ; then, since all the angles are symmetrical, we must have a coexistent plane at any other angle, as x. Let A p = h, A 7 = k, A r = / ; and let a? P = h, x Q = k, x R = l ; it is required to find the equation to the plane PQR Draw x M andy K parallel to PO and we have, if A x = a, xK = xy . ••• AK = «(i — x)1 % Also AM = Ay . ^ = 1 ~ T Similarly if x N be parallel to PR, we shall find AN = — i Hence the equation of the plane N x M is v+o-4)i+('-!)T=>; or t + (t— + Hsi = f- And the symbol of this plane will be And the plane PQR is parallel to N x M, and will have the same symbol. If y =/>, y *= q,j = r, the symbol of the plane PQR will be ( p ; p — q ; p — r). In the same way we shall have at the angles y and z , planes (q—P'*qm> V — r)and (/>— -r; q — r; r). But the edges Ax, Ay, Az are also similar, and therefore p,q,r may be permuted in any manner. Hence we have these co-existent planes (/>. 7. 0. (P’P — ^P — r), ( q —p, q,q-r), ( r—p , r— q, r). io8 Mr. Whewell on calculating It being understood that in each parenthesis the indices which are separated by commas may undergo any permutation. The first symbol (p, q,r) gives 6 planes, and the three others also 6 each, making in all 24. If the primary form be known to be a regular tetrahedron, it is evident that the first symbol ( p , q, r) must be understood as implying also the rest. But in order to express all the planes we may include them in one symbol thus {(/>»?. r)(P’P— a>P — r)&c-} the &c. implying the coexistent planes. 27. Prop. To determine the symbol of the planes which truncate the edges of a tetrahedron. The plane truncating the edge oc is (o ; q, r) : and hence by last article the general symbol includes the planes (0,9, r), (q,q,q — r), ( r,r — q,r ) which gives 12 planes. We omit (o, — q, — r), which is identical with (o, q, r). If q r the planes are expressed by (o, q, q), which gives 3 planes ; but in order to truncate the six edges, each is used twice, and the symbol is 2 (3) (o, q, q). The regular octahedron is bounded by the same 4 planes as the tetrahedron, each being used twice ; and its symbol is 2 (4) { (l,0,o) (l, 1, l)J. Its edges are also parallel to the edges of the tetrahedron, each being used twice. And any plane which can be deduced from the octahedron, may with equal simplicity be deduced from the tetrahedron. 28. Prop. In the regular tetrahedron to find the angle contained by planes (o, 1, 3). 109 the angles of crystals. The plane angles of the tetrahedron are 6o° ; and hence, to find its dihedral angles, we have to find the angle of an equilateral spherical triangle whose sides are 6o°. If a be this angle, we have cos. a = cotan. 6 o . tan. 30 = tan.2 30 = — . 3 Let 0 be the angle of the planes (o, 1, 1 ) ( 1, o, 1), and we have by the formula — cos. 0 = — ~ 3 cos‘ a = o because cos. = 2 — 2 COS. ec 3 Hence the angle of the planes is a right angle. And in the same manner the angles made by the other planes will be right angles. The figure will be a cube bounded by the 3 planes (o, 1,1) twice repeated. Irregular Tetrahedrons arid Octahedrons. 29. If we have an octahedron composed of two right quadrilateral pyramids, similar and equal, set base to base, we shall call this a right octahedron ; and it will be termed square , rectangular , or rhombic , when the base is so. The tetrahedron, from which the right rectangular octahedron is derived, may be called the direct symmetrical tetrahedron ; and that from which the right rhombic octahedron is derived, may be called the inverse symmetrical tetrahedron , on account of properties which will be explained immediately. Also, all the planes which can be derived from the octahedrons, may be derived more simply from the corresponding tetra- hedrons ; and we shall find the coexistent planes, and the angles made by the faces, in the same manner as in the previous cases. 110 Mr. Whewell on calculating > § 4. Direct symmetrical Tetrahedron and rectangular Octahedron . 30. Let A .ryz, fig. 13, be a tetrahedron, and let all its edges be bisected, and the bisections joined by lines drawn in the faces. We shall thus have an octahedron DEFGHK. If we consider EFHK as the common base of the two pyra- mids of which the octahedron is composed, when EFHK is a rectangle, the octahedron is called rectangular ; and when EFHK is a square, the octahedron is called square. Let EFHK be a rectangle, the octahedron being a right one. Then all the faces of the octahedron will be isosceles triangles, of which DEF, DHK, GFE, GHK will be equal to each other, and the other four also equal to each other. Also, it is easily seen that the triangle Ay z has its sides double of those of EFG, and is similar to it ; and similarly x y z has its sides double of KHG. Therefore the two tri- angles Ay z, xy z are both isosceles, (y z being the base,) and are equal in every respect ; and similarly y Ax and z Ax are isosceles triangles equal in every respect. Hence the solid angles at y and % are equal in every re- spect, and also those at A and x. And a plane passing through A x and through the middle of y z would divide the tetrahedron symmetrically into two equal portions. Hence we have called this the direct symmetrical tetrahedron. We may suppose the solid angle A to be filled with paral- lelepipeds, the planes of which are parallel to the planes A xy, A xz, A y z, in the same manner as the solid angle A, fig. 1. And by removing these parallelepipeds according to any law, as in fig. 1, we obtain a secondary plane, of which the symbol and the equation may be known from the law. Ill the angles of crystals. 31. But since the solid angles at A and at x are symmetri- cal, for every plane at A we shall have a co-existent plane at x * of which we shall find the equation. We may as before suppose A x, A y, A z, to be co-ordi- nates, and with any plane p q r at A we shall have a co-exist- ent plane PQR at x, such that x P, x Q, x R are equal to Ap , Aq, Ar respectively. ^ Prop. The symbol of pqr being (p\q\r) to find the symbol of PQR. Let the small component parallelepipeds have the edge in direction A x = a, and the edges in directions Ay, A z each = c (these being equal). Also, let A x == n a , Ay = A z = n r.f And let the plane pqr be obtained by taking away h molecules in the direction A.r, k in the direction Ay, and / in the direc- tion A z. Therefore Ap = ha, Aq = kc, Ar— l c: and the equation to the plane p qr is . X _l JL = t • h a k c * l c ’ * The parallelepipeds of which the solid is supposed to be made up at x, are not in the same position with those of which it is supposed to be made up at A. Those at x are bounded by planes parallel to Axy, Axz,yxz, as those at A are by the planes which meet at A. If the crystal be divisible according to all the planes of a tetrahedron or octahedron, there are four different kinds of parallelepiped of which it may be conceived to be composed, corresponding to the four angles A, x, y, z. And we may take any one of these kinds with equal propriety. In fact, the mode of conceiving secondary planes to be formed by removing parallelepipeds, is an assumption to be considered right only so far as it exhibits the dependence of secondary planes upon the simplicity of the ratios p : q: r. f If we suppose A xy z to be made up of parallelepipeds. Ax, Ay, and A z having equal numbers of them, planes parallel to xyzw ill pass through all their angles. And if instead of parallelepipeds, we suppose that we have only points in space where the angles of the parallelepipeds would be, the planes which are determined by any adjacent three points will be the four planes, A xy, A x z, Ayz, xyz. 112 Mr, Whewell on calculating or if /> = ■*-, ? = X’r = T> Pi + 1 T + 4 = 1’ the symbol of which is [p ; q ; r). Draw y O, a; M parallel to PQ, meeting A x and Ay. Then ^ xy.x P nc.ha n ha X O — ^ c ^ AO = A x — x 0 = na(i — y) A M = ^X'-Ay : ^ AO na . n c ~ r na(,-_ 7i A ~h' Similarly if .r N be parallel to PR, AN = Hence the equation to the plane x M N is ns, 1 ' k l n c * ' l j nc orp-j + CP—i) t+ ( P—v)t—P and the equations to planes p qr and PQR x , y i 2 P~+(i i + ‘iT = 1’ c are *J-4- ( £ — a 1 -- -1- ( £ \ z and their symbols are (p ; q ; r ) , (p\p — q; p — r) . Also the edges Ay, A z are symmetrical ; and hence we have two other co-existent planes (p ; r; q) [p — r; p — q). These are included in the formula |(/> ; q, r) (p ; p — q,p — r)| The solid angles at y and z are also symmetrical ; and a plane being supposed to be formed at y as before, we must have a co-existent plane at z. Let p' cf r' be a plane cutting off the angle y, and 6 being the edge of a molecule in the direction y z, let y p\ y q', yr' =hb, he, Ic respectively, and let z P', z Q', zR! =y pr, y (/, y r' respectively. Then p ' q1 r' US the angles of crystals . and P' O' R' will be co-existent planes ; and the condition of their co-existence is included in the preceding symbol. The quantities a , b , c are as na, n b, n c, that is as A x, yz and Ay. Or, referring to the octahedron in fig. is, they are as FH, FE, and FD. The square Octahedron. 32. When EFHK, fig. 13, is a square, A.r, yz will be equal, and the solid angles aty and * will be symmetrical to those at A and x, and will be similarly affected. Hence for a plane at A there will be co-existent planes at y and z. Prop. To find the symbols of co-existent planes in this case, If we take z P', zQ', zR',=yp', y q', y r',= Ap, A q, A r re- spectively, we shall, as in last article, find the equation of the planes p' q' r', P' O' R' to be and since /) = -k <7 = -h r = A these are equivalent to (?-' )-7+li +(?-^)f = T Hence with a plane (/> ; q ; r) we have co-existent planes (q — r; q ; q—p) and (. q — r; q—p; q)> But we have also a co-existent plane (/>; r; q) and therefore also (r — q ; r ; r — />) and (r — q ; r — /> ; r) Hence in the square octahedron we have co-existent planes which may be included in this symbol {(/>; r)(P’’P—r>P— )} All which are implied in (/>;3° 37' and YXE = 180 — 90° 40' = 84° so7 r. sin. YE=sin. XY. sin. 84°2o' e=sin. 43° 2 1'; e= .6864532 The two planes of which we have to find the angle, are (2 ; o; i)(i ; o; o).. Hence by the formula, Art. 8, 2 cos. 0 — COS. 6 = -I— .JO. = _zf-d cos. 0 To find 0, let tan. w = -£^?C0J‘ 13 — — zf— — cotan. (i ; and ’ a sin. j3 d sin. 0 1 we shall have, — cos. 6 = = sin. « . 6 = 90° 4- w. By the values above given, we shall find u = 6o° 4S7 and 6 = 150° 43'. The value given by Mr. Phillips is 150° is'. It may be observed, that (2 ; o ; 1) is the side adjacent to the primary plane (1 ; o; o); and that we obtain sides adja- cent to other faces by taking corresponding co-existent planes from the formulas in Art. 32. Thus the primary faces (1 ; o ; o) have adjacent secondary faces (2 ; o ; 1) and (2 ; 1 ; o). The primary faces (o ; 1 ; o) have adjacent (1 ; 2 ; o) and (1 ; — 1 ; The primary faces (o ; o ; 1) have adjacent (1 ; o ; 2) and (1 ; 1 ; — The primary faces (1 ; 1 ; 1) have adjacent (2 ; 1 ; 2) and (2; 2; 1) Here instead of ( — 1 ; o: — 2) &c. we have written (1 ; o; 2) &c. which represents the same plane. § 5- Inverse symmetrical Tetrahedron and rhombic Octahedron. 36. Let A xy z, fig. 16, be a tetrahedron ; and let its edges be bisected, and an octahedron formed as before. In this octahedron, let EFHK be the rhombic base; and the two 117 the angles of crystals. pyramids which compose the octahedron being right ones and equal, it is evident that the four lines DE, EG, GH, HD will be equal, and the four lines DF, FG, GK, KD. Now A x is double of FH, and xy of HK. Hence Ax=yz. Similarly Ay = x z, and A z = xy. Hence it appears that the four triangles which form the sides of the tetrahedron have their sides equal respectively, and are therefore equal and similar. Hence the four solid angles A, x,yt z, are con- tained by equal angles, and are symmetrical. Thus the angles x Ay, y A z, z Ax are equal to A x z, y x z, A xy. And this tetrahedron may be called an inverse symmetrical tetrahedron. From the law of symmetry, whatever plane is formed at the angle A, we must have a coexistent plane at each of the angles x, y, z, the equal and opposite edges being similarly affected. 37. Prop. A plane (p ; q ; r) being known, to find the co- existent planes. Fig. 17. Let A x, Ay, A z be n a, n b, n c. Ap, Aq,Ar=ha, kb, Ic ; and p= •j,q= -p ^ = T’ x P, x Q, x R are ha, kb, l c. Draw y O, x M parallel to PR. = xy ■7R==nc- = — ’AO=na(1 — r) AM=Ax4 = -4=— AO h r -T '~J Similarly if x N be parallel to PQ, AN = — — , ■ . 1 F '~J Hence the equation of the plane x NM, which is parallel to PQR, is 118 Mr. Whewell on calculating ±\JL = p \ nc orp-j +(p — r) t +{P — ?)f —nP and its symbol is [p ; p — r\p — q). In the same manner the angle y gives a plane ( ; q ; r),(p ; P — r ; p — q),(q — r- ; q ;q—p ), (r— ? ; r—p ; 4 These four planes would truncate symmetrically the four faces of one of the pyramids which compose the octahedron, and planes parallel to them would truncate similarly the planes of the other pyramid. 38. Prop. To find the portions cut from the edges of the octahedron by the plane [p ; q ; r). Let the plane P, Q, R, fig. 16 and 18, meet DK, DE, DF, DH in S, T, U, V. Draw QL parallel to DE. Then DS=DP.4§ = DP.^=DP.^- AP ha q a QL = AQj± = kb±=kc,AL = AQ^=kb.^. = ka-,PL=(h k) a DT = DP.^ = DP,, PL (4 — k)a = DP . — L- . L q — p a Similarly DV and DU would be DP ~ and DP . p r — p b a Hence DS, DT, DU, DV are as -1- . b, — l— c, — — b, -! c. Hence for the four co-existent planes the edges cut off are respectively as b c_ b c_ q ’ q — p’ r — q’ r 9 b c b c r — p ’ r ’ q ’ q — p ’ b c b c — - ■ * q 9 r ’ r — p9 q — p 9 b c b c r~p’ q-p’ T* the angles of crystals 119 The calculations would be nearly the same as in the case of the square octahedron, article 35. We should have to calculate d , e,j from the angles of the octahedron. Thus in sulphur, according to Mr. Phillips (p. 361) we have inci- dence of GEF on GEK = 106° 30 ; .-. angle at A x = 730 30 = y GFHonGFE = S5° 5; angle at Ay = 94° 55 = P GHF on DHF = 143° 25 ; .*. angle at A z = 36° 35 = u And if we construct a triangle, of which the three angles are a, jQ, y, and draw arcs from these angles perpendicular on the opposite sides, the sines of these arcs will be respectively d , e,f. And by first finding the sides of the triangle by spherical trigonometry, these may be calculated. § 6. The regular triangular Prism. Fig. 19. 39. This is a right prism, having for its base an equilateral triangle. It includes the regular hexagonal prism by re- peating the lateral faces. Prop. To find the co-existent planes. By the law of symmetry, for every plane on one angle A, we must have co-existent planes on x,y. Letpqrbezny plane whose symbol is (/> ; q \ r), and the lines A p = h, Aq = k, A r—l, when p — q r—-j- Then we shall have a plane POR where xV = h, x Q = k, x R== l. Draw rMjO parallel to PO. Similarly if x N be parallel to RP, AN = A^r.^ = 4-c=:— . J x P A r Hence the equation of the plane x MN is xO — xy. ^ = ^\fAx = xy = Ay = i. k I - V 120 Mr. Whewell on calculating x + Lj1y— 7*=i or px+ (p-q)y — rx=p. its symbol, or that of PQR, is (p; p — q; — r). Similarly, aty, we shall have a plane ( q — p ; q ; — r). Also, since the edges Ax and Ay are symmetrical, we have a plane (q; p ; r). And hence the co-existent planes are (P'>q>r){p\p — 9; — r)(q— p\q\ — r)(q;p;r)(q; q — p; — r) (p — q ; p ; — r). Which may be included in the symbol | (P,q;r) (p,p — q; — r) (< hq—p; — r )} § 7. The rhombic Dodecahedron. 40. If we take a regular tetrahedron w x y z, fig. 20, and from its centre of gravity A draw lines Aw, Ax, Ay, A z, the angles made by any two of these lines will be the same. And by taking planes passing through any two of these lines we shall have six planes symmetrically disposed, each of which will make an angle of 1200 with four others. A figure bounded by planes parallel to these planes, each taken twice, and symmetrically disposed, will be the rhombic dodecahedron. We may consider the three lines A x. Ay, A % as axes of co-ordinates ; and any plane p qr which cuts them must have co-existent planes cutting any two of them and A w. Also, as the lines Ax, Ay, A z are similar, in a plane ( p,q,r ) we may present the indices in any manner. 41. Prop. To find the symbols of co-existent planes in the rhombic dodecahedron. Let a plane p qr cut w A produced in O. Let x, y, z be the co-ordinates of the point O. The equations of the line Aw ar e y = x, z = x. And if the equation to the plane 121 the angles of crystals . p qr be p x + qy + rz = m , we shall have the co-ordinates of the point O by combining these equations. Hence we have px-\-qx-\-rx — m, or i = ^ + But if the co-ordinates x,y,z be projected upon AO, we shall have AO = Ax cos. x AO -f- Ay cos. y AO A % cos. % AO. And since cos. x AO = cos. y AO = cos. z AO = y, AO = Z+l+J. = x . ,.AO = — =—. 3 P + ? + r Now let P'x + q'y + r'z = m be the equation to a plane which cuts Ax, A y. Aw in the same manner in which {p\q\ r) cuts Ai, Ay, A z. Therefore the portion cut off from ry A produced will be ™yrrr Also the portions from Ax and Ay, are . Hence i = p m m p'+ ?' + r‘ ~ ••• p'=p, (l'=q ; q \ r) has co-existent planes (p, q, r). And making — p + q + r= s, we have the planes (P> q> r) (P > q> s) ( p, r, s) ( q > r> 4 Each of these symbols gives six permutations, so that we have in all 24 co-existent planes. § 8. On the arrangement of secondary faces. 42. When crystals have faces determined by the laws con- sidered in the preceding pages, they will have the form of polyhedrons bounded by polygons ; and in order to deter- mine the dihedral angles, &c. it will be necessary to know mdcccxxv. R 122 Mr. Whewell on calculating in what order the faces occur, and which are adjacent. This may be done in the following manner : Let A I fig. 21, be any parallelepiped of which the edges Ax, Ay, A z are a, b, c. Let an ellipsoid be described, of which the center is I, touching three planes of this parallele- piped in D, E, F. If we suppose any secondary plane, de- duced from this parallelepiped, to be drawn so as to touch the ellipsoid in P, the situation of the points P will determine the position of the planes. Let A x + + C z = m be the equation to the plane. The equation to the ellipsoid will be («— *)a , (b— yY I (c—zY a4 ■ bz "• c* And that the plane may touch the ellipsoid, the differential co-efficients and must be the same in both. Hence fdy\ A bz m (a—x) . /dz\ A (a— x) B a 4 ( b — y) ’ [dxj C a1 (c — z) ‘ Therefore a — x b — y A a% TF a — x c — z Afl* C c2 ' And substituting in the equation to the ellipsoid we have l / \a . B 1 bz , Va , C‘ / az (d X) “t“ Az a4 (a ”1“ A* a4 A a Cz c2 —x) a x V (A1 az + Bz bz + Cz c4) B6 y — Y (A* bz + C4 c2) and c — z=z Cc Y (A4 az + B1 bl -f C4 c4) Knowing the position of the points P for all the planes, we have the polyhedron, on the supposition that it is made such that the ellipsoid can be inscribed in it ; which is always pos- sible by supposing the planes to move parallel to themselves till they touch it. We shall see more clearly the position of the points P if 123 the angles of crystals. we suppose it to be determined by angular distances like the longitude and latitude on a globe, assuming as the axis of the ellipsoid that about which the figure is symmetrical. 43. (1) In the rhomboid. Here A x= Ay = A z = 1, suppose IA be taken as the axis ; and a plane API being drawn, let the angle between this plane and I Ax be called the longitude (x) of the point P ; and let the complement op AI P be called the latitude (p) of P. Let the co-ordinates of P be called X, Y, Z. Then the plane API has a point A, of which the co-ordinates are 0,0, o ; a point I, of which the co-ordinates are 1,1,1; a point P, of which the co-ordinates are X, Y, Z. Hence its equation is (Y — Z) x + (Z — X)y + (X — Y ) z = o. And the equation to I A x is y — z = o. Therefore by the formula for the angle of two planes, Art. 8, — 2X + Y + Z — (2 X — Y— Z) cos. « cos. x = — 7—7 — yj > 2((Y-Z)*4(Z— X)* + (X— Y)2+2(X1 + Y*4Zl-XY — XZ-YZ) cos. a If the symbol of the plane be [p ; q ; r) its equation is px + qy + r % — m\ and hence a — X cos. X — 7"(;>»4 r*y and similarly for Y and Z. Hence (2 /> — (f — r) (1 4 cos, a) 2 \/ | (/>*+?*+ r pq — pr — qr) (1 + cos. a) J 2 p — q — r / , \ 2 \f ( px 4 q1 -f r7 — p q — p r — q r) ' * ^ ' COS. ocj. To find ^ ; if we draw PM perpendicular in AI, and call IP, r, we shall have IM = r sin. and [x will be greater as IM is greater. Now if IM, NO, OP to the co-ordinates of P measured from I, and if we draw perpendiculars from N and O on IA, wfe shall see that IM = (a — X) cos. £ -f- (a- — Y) cos. £ + (a — Z) cos. £ where £is the angle which AI makes with A x, Ay or A z. 124 Mr. Whewell on calculating rs By these formulas we may determine the arrangement of any set or sets of secondary faces. Thus if we have a symbol (p, q, r ) in which p > q, q > r; we have 6 faces. The expres- sion for r sin. p, is the same for all : hence they are all at the same distance from the summit B. And cos. x will be greater as 2 p — q — r is, or as sp — (y> + g-|- r) is so. Consequently the values of cos. x taken in order of magnitude will corre- spond to (p; q ; r) (q ; p ; r) (r ; p ; q). The other three values be the same, viz. ( p ; r; q) ( q;r;p ) (r; q ; p)\ and indicate longitudes on the other side of A x. The arrangement of the planes is represented in fig. 22. It is to be observed that as the order of the first index is p , q, r, beginning from x, the order of the second index is p , q , r beginning fromjy, and of the third/), q , r, beginning from z. 44- (2) In the Prism. Let the line IF, fig. 21, parallel to A z, be taken for the axis of the ellipsoid ; and let the posi- tion of P be determined by (x) the longitude which is measured by the angle between the planes FID and FIP ; and by (x the latitude, the angle PIN. It is evident that tan. x will be greater as is greater. Let (p\ q\r) be the symbol of the plane, and its equation will greater ; because a and b are constant for the same substance. Also sin. [x is greater as PN is greater ; that is, as + And the values of IO, ON, NP, will be p a qb r c IS SO. the angles of crystals. 1 25 And hence we may arrange the faces in the order of their longitude and latitude. We might in the same manner find the position of the planes for other primitive forms, but what has been done will generally be sufficient. § 9. On the angles made by edges. 45. If we have two lines referred to any co-ordinates, of which the equations are y = Ax, 2 == B.r; jy = A!x, z = BT ; and if the plane angles of the faces be known ; viz. the angle which x makes withy = ) ( I — X — J— ^ 2 COS.

; q; r) which will express its position without determining its distance from the origin : p, q, r may be positive, o, or negative. By the law of symmetry with respect to the angles and edges of primary forms, if one secondary plane exist, certain others must also exist, which are hence called co-existent planes. Some of these are obtained by permuting the order of the letters in the symbol (/>, q, r) ; and the instances where this the angles of crystals. 127 permutation is allowed may be distinguished from those where it is not, by separating the letters p , q, r in the former case by a comma, and in the latter by a semicolon. The other co-existent planes in each primary form will be seen in the following table. Table of planes which exist if (p ; q ; r) exist. In the rhomboid - (A A 0 The doubly-oblique prism (p;q ; r) The oblique rhombic prism (A A • r) The oblique rectangular prism (. p\±q ; r) The right oblique-angled prism (±p> ±g; r. The right rhombic prism (± A ± q ; '•) The right square prism (+ A ~h \ + q-,r) The cube - /+ , + f +A ± A r) The regular tetrahedron and regular oc- tahedron - (A A r) (A P — H>p — r) *(?— A A (P ; a 0 ( pip — r,p — q ) ’(? — r; q>q—p) (r—q; r—p, r) The inverse symmetrical tetrahedron and rhombic octahedron. > (piqir) {P'-p — r-,p — q) (q — r;q;q—p) (r — 7 ; r — p ; r) 128 Mr. Whewell on calculating The regular triangular prism ; - (p, q ; r) (p’p— . » — />+?+>•. r) (— P + q + r, 7 , r) A crystal may be represented by uniting the symbols of the planes of which it is composed. And it will be conve- nient to represent by a figure in brackets thus (6), the num- ber of faces which arise from each symbol. Also frequently the crystal has parallel planes; in which case one of them may be considered as a repetition of the other ; and the plane thus doubled may be indicated by writing a 2 before it. Thus the form of borate of magnesia, called by Hauy magnesie borated defective , may be thus represented. Primary ; a cube. Secondary; 2 (3) (1 , o, o) + 2 (6) (± 1 , 1 , o) + (4) (± 1 , 1 , 1) Indicating — a cube 2(3) (1,0,0), formed by repeating each of the primary planes (1, o, o) ; Modified by 6 pairs of planes (±1,1,0); truncating the edges ; And by 4 planes truncating angles, which are not repeated. Hence the opposite angles are not symmetrically affected. The situation of planes with respect to each other, may be determined by assuming a certain point as the pole of the crystal, and measuring the latitude and longitude of the cen- tre of the plane with respect to this pole. If we suppose an ellipsoid of which the three axes are as the three edges a, b, c of the primitive form, we may suppose secondary planes to 129 the angles of crystals. be in their natural position when they are drawn so as to touch the ellipsoid ; and we may consider as the centre of the face, the point of contact. The latitude and longitude (/a and x,) of this point, are given by the formulas which follow. In the rhomboid, the axis of the rhomboid being the axis of the crystal cos. x varies with 2p ~ q ~ r V ( r*— pq — pr — qr) sin. i* p 4- q 4- r V (pl+ qz+ r In the prism, the axis being the axis of the prism tan. x varies with — p sin. 1 1* L V ( p 1 + ?* + r%) And hence the situation of the planes is known. Also if any ol the planes, instead of touching the ellipsoid, be nearer to or farther from the centre of the crystal, the order of the planes will not be altered. Having thus determined what planes are adjacent, we find the angles which they make, by the formulas given Art. 8. In the rhomboid (/>; q ; r) (p ; q; r) being the planes, 6 their angle, and & the dihedral angle of the primary form, 1QS g py' + qq' + rr'— ( p'q -f q'p -f p'r + + q'r -f r'q) cos. * d (p1’+fz+rZ— 2pq+pr+ qr cos. a) r,%—2p'q,+p'if+ q'r'cos.u) This is true also for the tetrahedron, and for the right rec- tangular prism, making cos. a = o. In the other cases we have a formula involving the three dihedral angles of the pri- mary form. We can also find the angles contained between any two edges by first finding the equations to the edges, and then employing a formula given, p. 125. mdcccxxv. S 130 Mr. Whewell on calculating the angles of crystals. The inverse problem, knowing two dihedral angles of the secondary figure to determine the symbols of the planes, is resolved by the same formulas. In the case where the angles made with the primary planes are given, we have a direct solution. In the other cases we find the indices of the symbol of trial ; and if the limits of the present paper allowed it, it might be shown how we might, after some trials, proceed directly to find the law. P. S. The greater part of the formulas in the preceding pages were calculated before my notice was directed to a paper by Mr. Levy, in the Edinburgh Philosophical Journal for April 1822. Mr. Levy there employs the principle which is the basis of the investigations now given, viz. the mode of expressing a secondary plane by means of its equation to three axes coinciding with the edges of the primitive form. From this principle he deduces, with great simplicity, the law of a secondary plane in a particular case; viz. when the intersections of that plane with two known planes, are parallel to their intersections with two others.* In order however to deduce the general formula, a new and different series of theorems is necessary, as appears in the course of this paper. W. W. • It may be observed, that the resuit in this case is easily obtained from the for- mula in Art. 14. * I \ • Fhil. Thans. MDCCCXKV. Flat? VIE. p.i3o. ■ ~ -~1 2i9 85>4 82,6 80,9 79>3 79>5 7°>9 7i>9 70,3 + I>5 — 2,8 ~ *>7 — 1,6 + 0,2 — 8,6 + — 1,6 -f* o>45 — 0,84 — 0,51 — 0,48 + 0,06 — 2,58 + 0,30 — 0,48 The image of the cross wires not being perfectly distinct, I limited the aperture to three-quarters of an inch, and thus 157 a floating colimator. obtained a much better image. These observations were made in extremely damp weather, and the support had been kept for a few days in a very dry place. 2d Set. Divisions of Microm. Difference. Error in Sec9. I affecting th* Horiz. point. Dec. 8 O raised - 3**6 After an hour’s interval Lanthorn close to wires 1 6,6 *9*9 + 3*3 + 0,99 - After an hour - Out and replaced, S first Ditto, - E first Ditto, - O first O raised and carried S raised and carried Ditto, read again - - Carried box, kept as level as possible S raised and carried - - Out and replaced, S first 8,8 >3 *7 *3*i 13A ”>5 11 >7 10,7 5>2 3*5 °>5 + 4*9 — 0,6 0,0 — 1,6 + o,z — 1,0 — 5*5 — D7 — 3»° + 1*47 — 0,l8 — 0,00 — 0,48 + 0,06 — 0,30 — 1,65 — 0,51 — 0,90 The wooden float being designed merely for preliminary experiments, and it not being my intention to introduce any errors but such as might arise from moving the float or agi- tating the mercury, I had a float made of cast iron eight inches long, four wide, 0,2 thick, and weighing 2 lb, 5 oz. troy. The telesccope was tied firmly to the Y s. 158 Captain Kater's description of Experiments with the Iron Float. 3d Set. Divisions of Microm. Difference. irror in Secs. affceting the Horiz. point. Dec. 9 Previously to moving 3 raised - 57,7 5L5 Sot sufficient mercury ; added more. Out and replaced S first 0 raised and carried 3 raised and carried, escaped from the } grooves ) Out and replaced, the surface at once in ) contact - - - j Out and replaced, O first Out and replaced, E first Out and replaced, S first Out and wiped the mercury, S first Out and replaced, E first Out and replaced, S first Out and carried, S first Out and wiped, S first 4 7>I 43- 3 44- 3 46,6 46>5 44,2 43>8 43A 42,1 4I>9 37>5 37,4 ~ 3>8 + 1,0 + 2,3 — 0,1 - 2,3 — 0,4 - 0,7 — 1,0 — 0,2 - 4,4 — 0,1 // — - 1,14 + 0,30 + 0,69 + 0,03 — 0,69 — 0,12 0,21 — 0,30 0,06 1,32 — 0,03 On returning after an hour’s interval Out and carried, S first Out and carried, S first Out and carried, S first Out and carried, S first - O raised and carried Agitated by raising and depressing the 7 end of the box 3 Out and carried, S first 42»4 4°>7 42>7 43-1 42,1 39’1 No Var 38,0 ~ 1,7 + 2,0 + 0,4 — 1,0 — 3,0 — i,i 0,51 4- 0,60 + 0,12 — 0,30 — 0,90 — °>33 Left the lanthorn close to the wires for | three quarters of an hour and returned $ Out and agitated mercury, S first O raised and carried Out and wiped mercury, S first 39-3 38-6 4L3 39’1 — 0,7 + 2,7 — 2,2 — 0,21 + 0,81 — 0,66 Lanthorn taken away and returned in an 7 hour and a half / Lanthorn left close to the wires, returned 7 in an hour - - J 45>° 50,8 Agitated by tapping the box 51,6 Returned in an hour Out and wiped mercury, S first No Var. 55>8 + 4>2 + 1,26 a floating collimator. 159 Experiments with the Iron Float. 4th Set. Divisions of Microm. Difference Error in Sec*, affecting the Horiz. point. Dec. 10 Out and replaced, S first - Ditto, and agitated the mercury, S first Ditto - - - ditto Ditto - - - ditto Ditto - - - ditto Ditto - - - ditto 84>5 90,3 89.8 88,7 87> 3 84.9 + 5»8 — °>5 — 1, 1 — i>4 — 2,4 // + i,74 — 0,15 — 0,33 — 0,42 — 0,72 5 th Set. Out and agitated mercury, O first Ditto - - ditto Ditto - - ditto Ditto - - ditto Ditto - - ditto Ditto - - ditto An acccident suspected 84>3 83»9 82,9 83,2 85,0 79»z — 0,4 — 1,0 + o-3 + i.>8 — 5>8 n — 0,12 — 0,30 + 0,09 + °>54 — »>74 The surface of the mercury being very dirty, it was care- fully strained through a paper funnel. 6th Set. Out and replaced S first Ditto - - ditto Ditto - - ditto Ditto - - ditto Ditto - - ditto Ditto - - ditto 81.0 80.9 78.9 7 8,5 78.0 77.0 — 0,1 2,0 — 0,4 — 0,5 — 1,0 — 0,03 — 0,60 — 0,12 — 0,15 — 0,30 The mercury carefully strained through a paper funnel, and the support oiled and rubbed dry. i6o Captain Kater/s description of Experiments with the Iron Float. - ■ — i — -i 7th Set. Divisions of Microm. Difference. Error in Sec’, affecting the Horiz. point. Dec. 1 1 Out and replaced, S first Ditto - - ditto Ditto - - ditto Ditto - - ditto Ditto - - ditto Ditto - - ditto i7>3 12,4 15,8 16.7 10.7 15.8 — 4>9 + 3>4 + 0,9 — 6,0 + // — !>4 7 + I >02 + 0,27 1,80 + 1>53 Experiments to show the effect of turning the box round . 8th Set. Previously to moving - Turned quite round - Back again - Turned round - Back again - 16.7 16,4 19,0 15.8 1 3>7 — 0,3 + 2,6 — 3,2 — 2,1 // — 0,09 + 0,78 — 0,96 — 0,63 The micrometer wire not being perfectly horizontal, the cross was brought precisely to the same part at each experi- ment. gth Set. Previously to moving - Turned round - Back again - Turned round ... Back again - - - Turned round ... 1 1,0 ic,3 10,2 10,5 U 8,1 l''» —1 M tT) 0 O O N 0 1 1 + 1 1 # • 7/ 0,21 — 0,03 + 0,09 — 0,63 O.O9 The side and subsequently the whole float, whilst replac- ing, pressed gently upon the mercury. a floating collimator. 161 10th Set. Divisions of Microm. Difference. Error in Sec*, affeeting the Horiz. point. Dec. 1 1 Out and replaced, S first Ditto - ditto Ditlo - - ditto Ditto - - ditto Ditto - ditto Ditto - - ditto 95.7 9 6>7 99,5 98,2 97,o 97.7 + 1,0 + 2,8 — 1,3 — 1,2 + 0,7 + 0,30 + 0,84 — 0,39 — 0,36 + 0,21 The float pressed upon the mercury as before, and the mean of the readings of both angles of the cross wires taken. i ith Set. Out and replaced, S first Ditto - - ditto - - - Ditto - - ditto - Ditto - - ditto - Ditto - - ditto - Ditto - - ditto - - - 97,4 98,1 100,5 93,8 95, 0 94,6 + 0,7 + 2,4 — 6,7 + 1,2 — 0,4 // + 0,21 + 0,72 — 2,01 + 0,36 — 0,1 2 In the preceding experiments it may be seen that by far the greater number of the results are negative, or that the readings of the micrometer for the most part gradually de- crease. I felt much at a loss to account for this, and at first supposed it to have been occasioned by the vicinity of the lamp to the Y supporting the cross wires ; but I found on trial that this was not the fact ; indeed in that case the effect would have been the reverse of what was observed. I can in no other way account for it than by supposing that as the weather was very damp and cold, my approach to the stand which supported the micrometer, caused the legs which were mdcccxxv. Y 162 Captain Kater’s description of next me to expand ; a supposition which appears to be in some degree corroborated by the micrometer giving an in- creased reading on my return, after having been absent for some time from the Observatory. Whatever may be the cause, it constantly operates in one direction, and seems to be the principal source of the errors which are observable. I now wished to ascertain whether by encreasing the length of the float, or by adding to its weight, the length being the same, I should attain greater accurary. I therefore procured two other cast iron floats, the one twelve inches long, four wide, and a quarter of an inch thick, and the other of the same dimensions as that before described, except that its thickness was half an inch, and its weight 4 lb. 8oz. troy. Iron pins were fixed in the sides of these floats in place of the grooves, and grooves to receive the pins were attached to the sides of the box. The box in which both floats were used was fourteen inches long and six inches wide. Before I made trial of the new floats, I browned that used in the preceding experiments by rusting it with nitric acid, and then rubbing it with oil ; imagining that I might thus diminish any small affinity which the iron might have for the mercury. With the float thus browned, the following experiments were made. a floating collimator. 1^3 / Iron Float browned. 12th Set. Division of Microm. Difference. Error in Sec", affecting the Horiz. point. Dec. 28 Out and replaced, S first Ditto - - ditto Ditto - - ditto Ditto - - ditto Ditto - - ditto Ditso - - dttto 20,0 20,5 l9>9 19,0 1 S>9 20,3 + 0,5 — 0,6 — 0,9 — 3U + 4»4 // + 0,15 — 0,1 8 — 0,27 — °>93 -f i>32 13th Set. Out and replaced, O first Ditto - - ditto Ditto - - ditto Ditto - - ditto Ditto - - ditto Ditto - ditto 22,2 15.8 17.8 z3>5 22,6 16,4 — 6,4 + 2,0 + 5>7 — 0,9 — 6,2 // — 1,92 -f- 0,60 + i>7i — 0,27 — 1,86 I now made the following experiments with the long float, the rough surface of which had been made smooth by rubbing it with wax. Long Float. 1 14th Set. Dec. 29 . * Out and replaced, S first Ditto - - ditto Ditto - - ditto Ditto - - ditto Ditto - - ditto Ditto - - ditto 3 no 32,0 34>8 3^6 37 >3 33>l + 1,0 + 2,8 — 3>2 + 5,7 — 4,2 + 0,30 + 0,84 — 0,56 + D7i — 1,26 164 Captain Kater's description of t Experiments to show the effect of turning the box round. 15 th Set. Divisions of Microm. Difference. Error in Sec3, affecting the Horiz. point. Dec. 29 Previously to moving Turned round, (much agitation) Back again - Turned round - Back again - Turned round - 3 3>3 32,5 346 3 no 31,2 3°>4 — 0,8 — 0,9 — 0,6 + 0,2 — 0,8 // — 0,24 — 0,27 — 0,1 8 4 0,06 — 0,24 I now laid aside the long float to try the short heavy float. Short heavy Float. 1 6th Set. Out and replaced, S first Ditto - - ditto Ditto - - ditto Ditto - - ditto Ditto - - ditto Ditto - - ditto 57>2 59>7 60,6 56,1 58,0 57>6 + 2,5 + 0,9 — 45 + 49 — 0,4 + 0,75 + 0,27 — 435 + 0,57 — 0,12 17th Set. Out and agitated the mercury, S first Ditto - - ditto Ditto - - ditto Ditto - - ditto Ditto - - ditto Ditto - - ditto 67.0 65,5 68.1 647 60,7 66,0 — 45 + 2,6 — 3>4 — 4>° + 47 // — 0,4; + 0,78 1,02 1,20 + 441 The utmost care taken. The mercury carefully strained. a floating collimator. 165 Short heavy Float. i 8th Set. Divisions of Mierom. Difference Error in See®, affecting the Horiz. point. Dec. 30 A.M. Out and replaeed, S first Ditto - ditto Ditto - ditto Ditto - ditto Ditto - ditto Ditto - ditto 32,1 34>9 34>7 33>2 34>2 31,8 + 2,8 — 0,2 — 1,5 + 1,0 — 2,4 + 0,84 — 0,06 — °>45 + 0,30 — 0,72 Experiments to show the effect of turning the box round. 19th Set. Previous to moving Turned round Back again - Turned round - - - Back again - - - Turned round 31,0 33>2 33>9 32,6 3°>7 3»>3 + 2,2 + 0,7 — 1’3 — l>9 + 0,6 -f 0,66 + 0,21 — o,39 — °,57 + 0,18 Mercury carefully strained. 20th Set. Out and replaced, S first Ditto - — ditto - - Ditto - — ditto - - Ditto - ditto - Ditto - ditto - - Ditto - ditto - 21,1 27.0 22.1 25,7 24,4 53>6 + 5,9 — 4>9 + 3>6 — i,3 — 0,8 if + i»77 — i,47 + 1,08 — 0,39 — 0,24 Great care taken that the side of the float should be in contact with the mercury its whole length, previously to putting down the surface. 166 Captain Kater's description of 2 1 st Set. Divisions of Microm. Difference. Error in Sec8, affecting the Horiz. point. Dec. 30 A.M. Out and replaced, S first Ditto - ditto - - Ditto - ditto - Ditto - ditto - - Ditto - ditto - Ditto - ditto - - 25. 1 24.1 24,8 20.6 23.1 21.6 — 1,0 + 0,7 — 4,2 + z>5 — i>5 // — 0,30 + 0,21 1,26 + 0,75 — o,45 2 2d Set. Jan. 1 Out and replaced, S first - Ditto - ditto - - Ditto - ditto - - Ditto - ditto - Ditto - ditto - - Ditto - ditto - 25.9 *9>4 21.9 21,4 23>5 21,9 — 5>5 ~h 2,5 — 0,5 + 2,1 — 1,6 — '1,65 + 0,75 — 0,15 -j- 0,63 — 0,48 Having caused the long float to be ground smooth, and browned it by rusting it with nitric acid, and rubbing it with oil, the oil was very thoroughly cleaned off, and the follow- ing experiments made with the greatest care. 4 Long float browned. 23d Set. L Jan. 2 Out and replaced, S first - - Ditto - ditto - Ditto - ditto Ditto - ditto - Ditto - ditto - - Ditto - ditto M 2,7 2,1 3>4 3>3 5>7 + 1,3 — 0,6 + — 0,1 + 2,4 + o,39 — 0, 1 8 + 0,39 — 0,03 + 0,72 i a floating collimator. Long float browned. 167 24th Set. Divisions of Microm. Difference. Error in Sec’, affecting the Horiz. point. Jan. 3 Out and replaced, S first - - Ditto - - ditto - - Ditto - - ditto — - Ditto - ditto - - 51.1 49*4 4 8*7 50.2 — i*7 — 0,7 + i*5 // — 0,51 0,21 + 0,45 25th Set. Jan. 3 Out and replaced, S first - - Ditto - ditto - - Ditto - ditto - - Ditto - ditto - - Ditto - ditto — — Ditto - ditto - - 57*5 56*7 60,3 57*4 5 9>° 58,1 — 0,8 + 3*6 — 2,9 *4 i>6 — 0,9 // — 0,24 + 1>°8 — 0,87 + o>48 — 0,27 26th Set. Out and replaced, S first - - Ditto - - ditto - - Ditto - - ditto - - Ditto - - ditto — - Ditto v- - ditto - - Ditto - - ditto - - 63>3 63,6 61.1 59*6 60,9 61.2 + 0,3 “ 2*5 — M + »*3 — °*3 + 0,09 — o*75 — 0,45 4- 0,39 — 0,09 Of the one hundred and fifty one results in the column indicating the errors affecting the determination of the hori- zontal point, only twenty-eight are found exceeding one second ; viz. one of 2", 58, another of 2", 01, ten between two seconds and one second and a half, and sixteen between a second and a half and one second ; the remaining one hundred and twenty-three errors being all less than one second. But as it is not to be supposed that an observer would be satisfied with a single determination, when he has the power in a very few minutes of attaining far greater accuracy, I shall 168 Captain Kater's description of now show the effect that would result from using the mean of a few of the preceding observations. Wooden Float. Error in Seconds. t Mean of the first four - - // — 0,34 1st Set. < Mean of the second four - — 0,67 , 0 f Mean of the first five - + 0*36 2d Set. < Mean of the second five - — 0,66 Iron Float. c Mean of the first five - — 0,16 Mean of the second five - — 0,40 3d Set. < Mean of the third five - — — 0,02 ( Mean of the last six - 0,00 4th Set. Mean of five - - -f 0,02 5 th Set. Mean of five - - — 0,31 6th Set. Mean of five - - — 0,24 7th Set. Mean of five - - — 0,09 8th Set. Mean of four - - — 0,22 9th Set. Mean of five - - — 0,17 10th Set. Mean of five + 0,12 1 ith Set. Mean of five - - - — 0,17 Iron Float browned. 12th Set. Mean of five - -f- 0,02 13 th Set. Mean of five - - — °>35 Long Iron Float. 14th Set. Mean of five - - + 0,13 15 th Set. Mean of five - - - — 0,17 Short heavy Float. 16th Set. Mean of five - - -f 0,02 17th Set. Mean of five - - - — 0,10 1 8th Set. Mean of five - - — 0,02 19th Set, Mean of five - - — 0,02 20th Set. Mean of five - + 0,15 2 1 st Set. Mean of five - - - — 0,21 22d Set. Mean of five - - — 0,18 Long Float browned. 23d Set. Mean of five 4- 0,26 24th Set. Mean of three — 0,09 25 th Set. Mean of five — + 0,04 26th Set. Mean of five - - — 0,16 169 a floating collimator. On examining the above table, it appears that by taking the mean of a very few results, the greatest error, if the experiments with the wooden float be rejected, is four-tenths of a second, consequently the place of the horizontal point may be speedily determined by the use of the collimator, to the utmost degree of accuracy which the astronomical circle employed, is capable of attaining. The results obtained by turning the collimator round with- out removing the float from the mercury, might have been expected to have been very nearly, if not wholly free from error ; but as this does not appear to be the fact, and as the errors are all in defect, they seem to have been influenced by some constant cause, which, as before remarked, I believe to have been expansion of the stand of the micrometer in consequence of increased temperature. When the float is removed in order to transport the box containing the mercury to the opposite side of the observa- tory, the manner of replacing it, so as to occasion the least error, seems to be that of bringing the edge of the side of the float first in contact with the mercury, and then gra- dually lowering it. This mode of removal can be necessary only when the collimator is used with a portable circle ; but in a fixed observatory a plank should be laid, or a sort of railway contrived from one support to the other, on which the collimator should be either slid or passed along on rollers without removing the float from the mercury ; by this ar- rangement the greatest, and perhaps the only source of error would be avoided.* * It may perhaps be found preferable to have two boxes with mercury, and to carry the float from one to the other. MDCCCXXV. Z 170 Captain Kater’s description of There appears to have been some advantage gained by using a longer float, and it certainly was improved by being browned, as previously to that operation, small particles of mercury were observed, occasionally to attach themselves to the float, which was not the case afterwards. # It may not perhaps be considered altogether superfluous to give in a few words the manner of using the collimator. The instrument being placed on the north or south side of the observatory with its telescope pointed to the centre of the circle and nearly in its plane, it is to be directed, so that the wires of the telescope of the circle may be seen through it, when reciprocally the cross wires of the collimator will be visible through the telescope of the circle, and the collimator is to be so placed, that the cross wires may appear in the centre of the field of view. The place of the box should then be carefully marked, to ensure its being at once restored as nearly as possible to the same situation. The collimator is then to be removed to the opposite side of the observatory, and the same process repeated, the situ- ation of the box being here also carefully marked. In observing, the star having been taken and the readings of the microscopes registered, the telescope is to be depressed to the collimator, and the angle formed by the cross wires carefully bisected. The collimator is then to be taken to the opposite side of the observatory, and the cross wires again bisected ; the mean of the readings at the bisections will give the inclination of the collimator to the horizon, and the diffe- rence between this and the apparent inclination at either po- sition of the collimator will be the correction to be applied to the mean of the readings registered at the bisection of the star. 171 a floating collimator. For example, let the mean of the readings of the bisection of the cross wires when the collimator is to the south of the instrument be 7'. 30" of altitude, and when it is to the north 8'. 40". The mean of these readings 8'. 5", is the true incli- nation of the collimator to the horizon, and the difference be- tween this and 7'. 30" (o'. 35") must be added to all altitudes taken to the south, or subtracted from those to the north of the zenith. The instrument I have described may be called the hori- zontal collimator , but another and in most respects a prefer- able arrangement may be employed, similar to that suggested by Professor Bessel. The telescope may be firmly fixed in a position perpendicular to the float, and I should then name it the vertical collimator .* This must be placed directly under the telescope of the circle ; and though not in a convenient position for observing, it yet possesses the very great advan- tage of obviating the necessity for carrying the collimator from one- side of the observatory to the other, nothing more being requisite than to turn the float half round in azimuth, and to take the readings of the microscopes when the angle formed by the cross wires is bisected in each position of the collimator, the mean of which will be the place of the zenith point. This is the construction which appears best calculated for a public observatory ; but in addition, it would perhaps be adviseable that it should be furnished with a horizontal colli- mator, having a Hoar of increased length. It is intended that * The float of the vertical collimator should be circular, and an opening be made in the bottom of the tube of its telescope to throw light on its cross wires by means of an inclined plane mirror. 172 Captain Kater’s description of the horizontal collimator should remain stationary, and that the usual course of observations should be referred to it, its inclination to the horizon having been previously determined, and its permanency, when thought requisite, being examined by means of the vertical collimator. As it is not necessary for the telescope of the collimator to have a tube, the object glass and the cross wires in the hori- zontal construction may be fixed in two uprights cast in one piece with the float. The distance of the object glass from the cross wires must be capable of the nicest adjustment. This may be effected by a screw cut on the outside of the tube in which the object glass is set, and a collar, by means of which after it is adjusted, it may be firmly secured in its proper place. There should be short pieces of tube screwed on each side of the upright, to protect the cross wires from injury, and also to contain the eye glass, which is convenient, as well for illuminating the wires, as for placing the colli- mator in the proper direction. This construction appears to promise the most perfect invariability of relative position be- tween the line of collimation and the float. The box should be sufficiently deep to include the whole instrument, and should have apertures made in the ends, opposite to the ob- ject glass and to the cross wires. It is scarcely necessary to add, that it should also have a cover to exclude dust from the mercury, and a piece of ground glass or oiled paper should be placed between the cross wires and the lamp by which they are illuminated. The accurate adjustment of the cross wires is a point of extreme importance. Upon whatever portion of an object glass parallel rays fall, they are converged precisely to the 173 a jloatmg collimator. same point in its focus, and consequently, whether the colli- mator be placed above or below the axis of the telescope of the circle, so long as the cross wires continue visible, the image will suffer no change of position. This affords an ex- cellent method of discovering any want of parallelism in the rays; for if on placing the collimator as much above the axis of the telescope as possible, without losing sight of the cross wires, the image appears elevated above the horizontal wire, or if on placing it below the axis, the image appears to have descended, it is a proof that the rays falling upon the object glass of the circle are not parallel, but that they converge, and consequently that the cross wires of the collimator are too far from its object glass, and vice versa. It is necessary that this adjustment should be made with the utmost care. It might possibly be supposed that the accuracy of the collimator would be augmented by increasing the length of its telescope, but this is not the case. It is the direction of a ray passing through the cross wires, and the centre of the object glass of the collimator, which is the subject of observa- tion ; and the direction of this ray is as definite in a telescope of an inch in length, as in one of ten feet focus. The degree of precision with which any variation in the horizontal incli- nation of this ray can be estimated, depends upon the length and power of the telescope employed to view the cross wires, and not upon the length of that of the collimator. There is an inconvenience however in using a telescope of too short a focus, as the cross wires are very much magni- fied, and consequently appear not so well defined ; in addi- tion to which, if a permanent point of reference be required, there might be some fear that the relative positions of the 174 Captain Kater’s description of float and telescope might suffer derangement, and the direc- tion of the ray be consequently changed. I may here point out an advantage, and not the least valu- able, which this instrument presents, that of enabling the observer, by varying the inclination of the float, to bring a different part of the arc into use, and thus to check erro- neous division of the circle : this may readily be done by securely fixing weights to either end of the float. * I shall now proceed to give a description of the manner in which the floating collimator may be applied to the zenith tube. The first zenith tube was I believe constructed for Dr. Tiarks. It was a telescope hanging in Y s upon pivots pro- jecting from each side of the tube near the object end, and furnished with a wire micrometer : to this telescope a plumb line was attached. When the star was upon the meridian, and of course suffi- ciently near the zenith to be seen in the telescope ; it was bisected by the micrometer wire, and the divisions regis- tered. The telescope was then inverted in the Y s, re-ad- justed by means of the plumb line, and the following even- ing the star again taken, when the mean of the readings of the micrometer gave its zenith distance. In the construction of the superb zenith tube 25 feet long, now making by Mr. Troughton for the Royal Observatory at Greenwich, I understand it is intended that the axis of the tube shall be the centre of motion, and the plumb line be * The above advantage may be considerably extended by the collimator being so constructed as to allow the inclination of the telescope to the float to be varied at pleasure. 17 5 a floating collimator. suspended at the side. When the observations have been made a sufficient number of times with the plumb line on one side, the tube will be turned half round, and the observations repeated with the plumb line on the other side. The mean of both giving the zenith distance as before. In this construction the zenith distance cannot be obtained in one evening ; for were the telescope to be turned half round after the first observation, so much motion would be communicated to the plumb line, that there would not pro- bably be time to re-adjust the instrument before the star would have passed out of the field of view. As it is highly desirable that the completion of the obser- vation should not be postponed, I endeavoured to effect this in a very fine zenith tube, which was constructed under my directions by Mr. Dollond for Colonel Lambton, and in another for Sir Thomas Brisbane, by placing the plumb line in the centre of motion ; but these various forms are still subject to one or other of the inconveniences which have been detailed in the preceeding parts of this paper, and which it is the object of the floating collimator to remove. The accuracy of the instrument I am about to describe, will depend upon the goodness of the telescope and of the wire micrometer employed. Exclusively of these it is within the reach of every observer, as the whole arrangement may be completed without difficulty and at a very trifling cost. Expence may contribute something in point of convenience, but can add nothing to its efficiency. To a firm wall, at a sufficient height, let a shelf be fixed and supported by a bracket at each end. In the middle of this shelf let a circular aperture be made, rather larger than the object glass of the telescope. Precisely beneath, and at a 176 Captain Kater/s description of little distance from this aperture, the telescope is to be securely fastened to the wall in the direction of the zenith. This may perhaps be conveniently done by two irons driven into the wall, terminating in rings, into which the telescope may be passed and clamped. A box of sufficient size to contain the floating collimator being prepared with a circular aperture in the bottom of it, a very little less than that in the shelf, a piece of tube made of sheet iron, varnished brass, or even tinned plate, well painted or varnished, of a size to fit very tightly * into the aperture of the box, must be passed into it and secured so as to project above the bottom on the inside an inch or two, and on the outside two or three inches more than the thickness of the shelf. The part of the tube outside the box must be passed through the hole in the shelf, and the box may then be readily turned about the axis of the tube as a centre. The side of the box being placed nearly in the direction of the meridian, its position must be determined by a pin driven perpendicularly into the shelf, so as to come in contact with a pin projecting from one corner of the box near the bottom, and in the direction of one of its sides. The box is then to be turned half round in azimuth, and a pin is to be fixed in the opposite end of the box in con- contact with that in the shelf. By this contrivance, the box may be turned at pleasure half round the azimuth. The float should be of cast iron, with a hole in the middle an inch larger in diameter than the tube. It is to be fur- nished with pins, and the box with corresponding grooves to steady it, as before described. An arm of plate iron is to be fixed to the float, its edge being at right angles to the surface. This arm is to project over the aperture, and to ter- minate in a small tube at the centre, to receive a telescope not 177 a floating collimator. larger than that of a sextant furnished with crossed wires,* and having its object glass next that of the zenith tube. To any convenient part, either of the shelf or of the wall, a support must be fixed, to which a circular screen of blackened tin may be attached by a joint, so as to be elevated to the vertical or lowered to the horizontal posi- tion at pleasure. In the centre of this screen a hole is to be made rather smaller than the telescope of the collimator. The screen is intended when in use to occupy a horizontal position, just above the crossed wires of the collimator, and to exclude false light from the object glass of the zenith tube. In order to illuminate the wires of the collimator, a small plane reflector, which may be of planished tin, is to be at- tached at a convenient angle to the upper side of the screen over its aperture. This may be made to turn stiffly upon a hinge to vary its inclination. Having put a sufficient quantity of mercury into the box to enable the float to act freely, the screen must be turned up and the micrometer adjusted, so that a star may pass along its moveable wire. The screen being then restored to its horizontal position, the crossed wires of the collimator will be distinctly seen when the arm carrying its telescope must be bent till they appear in the centre of the field of view, and the telescope of the collimator must be turned in its tube till the opposite angles of the crossed wires are bisected by the micrometer wire. These adjustments may be considered as permanent. To determine the zenith distance of a star, it must be * A small black dot upon mother-of-pearl forms a very neat object instead of the crossed wires, but from some trials, I fear it cannot be made sufficiently small, MDCCCXXV. A a *78 Captain Kater's description , &c. bisected by the micrometer wire at the time of its passing the meridian, and the division of the micrometer head read off and registered. The screen being then turned down, the angle formed by the crossed wires of the collimator is to be bisected, and the reading of the micrometer registered. The collima- tor is then to be turned half round, the angle again bisected by the micrometer wire, and the reading noted. The mean of these bisections is the place of the zenith, and the difference between this and the reading when the star was bisected, is the star’s zenith distance. ft is evident that the operation for finding the place of the zenith may be repeated at pleasure, and consequently that the error, if any, in the zenith distance, may be ultimately refer- red to inaccurate bisection of the star, or imperfection of the screw of the micrometer. I may remark, before I conclude, that a telescope,* similar to that I have used in the horizontal collimator, may be em- ployed as a meridian mark for a transit instrument when a distant one cannot be obtained, and that the crossed wires afford an excellent object for the adjustment of the line of coflimation. For this purpose, the telescope must be firmly fixed in the proper position. I attempted some years since to effect this by means of a convex lens, having cross wires in its focus, but as it did not occur to me to use an eye-glass, I was unable to place it in the proper direction, and after many unsuccessful trials I laid it aside.-f * The length of the telescope is here important to accuracy. f Since this Paper was written, I have discovered that in the year 1785, such a meridian mark was actually used by Mr. Ritten house, who employed for the pur- pose the object glass of a telescope thirty-six feet long, in the focus of which was placed a metal plate, having several concentric circles drawn upon it. See Transac- tions of the American Philosophical Society, vol. ii. Phi/.. Trans. '\fDCCC-XXV: / C 179 3 P VIII. Notice on the Iguanodon , a newly discovered fossil reptile , from the sandstone of Tilgate forest , in Sussex. By Gideon Mantell, F. L. S. and M. G. S. Fellow of the College of Surgeons , &c. In a Letter to Davies Gilbert, Esq. M. P . V. P. R. S. &c. &c. &c. Communicated by D. Gilbert, Esq. Read February 10, 1825. Sir, I avail myself of your obliging offer to lay before the Royal Society, a notice of the discovery of the teeth and bones of a fossil herbivorous reptile, in the sandstone of Tilgate forest ; in the hope that, imperfect as are the materials at present collected, they will be found to possess sufficient interest to excite further and more successful investigation, that may supply the deficiencies which exist in our knowledge of the osteology of this extraordinary animal. The sandstone of Tilgate forest is a portion of that exten- sive series of arenaceous strata, which constitutes the iron-sand formation, and in Sussex forms a chain of hills that stretches through the county in a W. N. W. direction, extending from Hastings to Horsham. In various parts of its course, but more particularly in the country around Tilgate and St. Leo- nard’s forests, the sandstone contains the remains of saurian animals, turtles, birds, fishes, shells, and vegetables. Of the former, three if not four species belonging to as many ge- nera are known to occur, viz. the crocodile, megalosaurus, plesiosaurus, and the iguanodon, the animal whose teeth i8o Mr. Mantell on the iguanodon, form the subject of this communication. The existence of a gigantic species of crocodile in the waters which deposited the sandstone, is satisfactorily proved by the occurrence of numerous conical striated teeth, and of bones possessing the osteological characters peculiar to the animals of that genus ; of the megalosaurus, by the presence of teeth and bones re- sembling those discovered by Professor Buckland in the Stonesfield slate ; and of the plesiosaurus, by the vertebras and teeth analogous to those of that animal. The teeth of the crocodile, megalosaurus and plesiosaurus, differ so materially from each other, and from those of the other lacertas, as be to identified without difficulty ; but in the summer of 1822, others were discovered in the same strata, which although evidently referable to some herbivorous rep- tile, possessed characters so remarkable, that the most super- ficial observer would have been struck with their appearance, as indicating something novel and interesting. As these teeth were distinct from any that had previously come under my notice, I felt anxious to submit them to the examination of persons whose knowledge and means of observation were more extensive than my own ; I therefore transmitted spe- cimens to some of the most eminent naturalists in this coun- try, and on the continent. But although my communications were acknowledged with that candour and liberality which constantly characterises the intercourse of scientific men, yet no light was thrown upon the subject, except by the illus- trious Baron Cuvier, whose opinions will best appear by the following extract from the correspondence with which he honoured me. “ Ces dents me sont certainement inconnues ; elles ne sent from the sandstone of Tilg ate forest, Sussex. 181 point d’un animal carnassier, et cependant je crois qu’elles appartiennent, vu leur peu de complication, leur dentelure sur les bords, et le couche mince d’^mail qui les revet, a l’ordre des reptiles. A Tapparence exterieure on pourrait aussi les prendre pour des dents de poissons analogues aux tetrodons, ou aux diodons ; mais leur structure interieure est fort diffe rente de celles la. N'aurions-nous pas ici un ani- mal nouveau, un reptile herbivore ? et de meme qu'actuelle- ment chez les mammiferes terrestres, c'est parmi les herbi- vores que Ton trouve les especes a plus grande taille, de meme aussi chez les reptiles d'autrefois, alors qu'ils etaient les seuls animaux terrestres, les plus grands d'entr’eux ne se seraient-ils point nourris de veg^taux ? Une partie des grands os que vous possidez appartiendrait a cet animal, unique, jusqu'a present, dans son genre. Le terns co?ifir- mera ou mfirmera cette idee, puisqu'il est impossible qu’on ne trouve pas un jour une partie du squelette reunie a des por- tions de machoires portant des dents. C’est ce dernier objet surtout qu'il s’agit de rechercher avec le plus de perseve- rance/* These remarks induced me to pursue my investigations with increased assiduity, but hitherto they have not been attended with the desired success, no connected portion of the skeleton having been discovered. Among the specimens lately collected, some however were so perfect, that I re- solved to avail myself of the obliging offer of Mr. Clift, (to whose kindness and liberality I hold myself particularly in- debted) to assist me in comparing the fossil teeth with those of the recent lacerta* in the Museum of the Royal College of Surgeons. The result of this examination proved highly 182 Mr. Mantell on the iguanodon, satisfactory, for in an Iguana which Mr. Stutchbury had pre- pared to present to the College, we discovered teeth possess- ing the form and structure of the fossil specimens. In the annexed drawing, Plate XIV. examples of the recent and fossil teeth are represented, and the peculiar characters of each accurately shown ; a description of it in this place will render the subsequent observations more intelligible. Fig. 8 represents a portion of the upper jaw of the iguana viewed from within ; it is magnified four diameters. 9 a shows the inner, and 9 b the outer surface of a tooth of the same, greatly magnified. It may be proper to remark, that the teeth differ considerably in the number of points, and that the eminence at f, fig. 9 a , is sometimes the first or second in the series, instead of being the third, as in the figure. In some teeth the points vary but little in size ; they are more distinct on the edges of the teeth occupying the centre of the jaw, than in the anterior and posterior ones. The skeleton from which the drawings were made is three feet six inches in length. It is said to be the common edible iguana of the West Indies, but I have not been able to ascer- tain its species with certainty. The remaining figures repre- sent different examples of the fossil teeth. Fig. 1. a represents the outer, and fig. 1. b the inner sur- face of one of the largest and most perfect specimens of the teeth of the iguanodon. As the letters of reference in each figure indicate the same parts, they are explained here to avoid repetition. a. Surface worn by mastication, b. The serrated edges. c. Fang broken; the cavity filled with sandstone. from the sandstone of Tilgate forest, Sussex. 1&3 d. Cavity or depression in the base of the fang, the effect of absorption caused by the pressure of a secondary tooth. * e. Ridge extending down the front of the tooth. Fig. 2. This tooth evidently belonged to a young animal ; yet even in this example the apex is worn away, (see a . fig. 2 c .) The ridge extending down the front (see e fig. 2 a) is more or less distinct in every specimen. Fig. 3. A tooth much worn by mastication. The serrated edges and other characters are obliterated, the tooth being worn down to the point marked by the line atg. fig. 1. a. The fang has been removed by absorption ; and the cavity formed by the pressure of the new tooth is very deep. Fig. 4. In this specimen the point is perfect, and it there- fore more closely resembles the recent tooth (fig. 9.) than those above described. 5. Is another example, where the point is but little worn. 6. A large strong tooth less curved than fig. 1 and 2. It probably occupied a place in the posterior part of the jaw. 7. In this figure, the cavity of the base of the fang for the reception of the new tooth is remarkably distinct. The teeth above described, although varying from each other in some particulars, do not present greater dissimila- rity than the differences arising from age, and the situation they respectively occupied in the jaw, would be liable to pro- duce. Like the teeth of the recent iguana, the crown of the tooth is accumulated ; the edges are strongly serrated or * The hollow here described is so constantly found in every example, that it cannot be accidental. From the close resemblance it bears to the cavity forfned in the base of the fangs of the recent iguana, by the secondary teeth, (Vide d, fig. 8) it may be confidently presumed that it is the effect of a similar cause. 184 Mr. Mantell on the iguanodon , dentated ; the outer surface is ridged, and the inner smooth and convex ; and as in that animal the secondary teeth appear to have been formed in a hollow in the base of the primary 4 ones, which they expelled as they increased in size. From the appearance of the fangs in such fossil teeth as are in a good state of preservation, it seems probable that they adhered to the inner side of the maxillae, as in the iguana, and were not placed in separate alveoli, as in the crocodile. The teeth ap- pear to have been hollow in the young animals, and to have become solid in the adult. The curved teeth (figs. 1, 2.) probably occupied the front of the jaw ; and those which are nearly straight, (fig. 3.) the posterior part. It appears unnecessary to dwell longer on the resemblance existing between the recent and fossil teeth. Whether the animal to which the latter belonged, should be considered as referable to existing genera, differing in its specific characters only ; or should be placed in the division of enalio-sauri of Mr. Conybeare, which includes marine genera only, cannot at present be determined. If however any inference .may be drawn from the nature of the fossils with which its re- mains associated, we may conclude, that if amphibious, it was not of marine origin, but inhabited rivers or fresh- water lakes ; in either case the term Iguanodon, derived from the form of the teeth, (and which I have adopted at the sugges- tion of the Rev. W. Conybeare) will not, it is presumed, be deemed objectionable. It has already been mentioned, that of the bones of ovipa- rous quadrupeds found in the sandstone ofTilgate forest, some are decidedly referable to the crocodile, and others to the megalosaurus and iguanodon ; but our knowledge of the 185 from the sandstone of Tilgate forest, Sussex. osteology of the latter is at present so limited, that until some connected portion of the skeleton shall be discovered, it is impossible to distinguish the bones of the one from those of the other. Since, however, the teeth of the iguanodon are not known to occur in the Stonesfield slate, perhaps such of the bones from Tilgate forest as resemble those figured and described by Professor Buckland, in Vol. I. Second Series of the Geological Transactions, may be attributed to the mega- losaurus ; while others not less gigantic may be assigned to the iguanodon. That the latter equalled, if not exceeded the former in magnitude, seems highly probable ; for if the re- cent and fossil animal bore the same relative proportions, the tooth, fig. 1. must have belonged an individual upwards of sixty feet long ; a conclusion in perfect accordance with that deduced by Professor Buckland from a femur,* and other bones in my possession. The vertebrae, as in the greater part of the fossil saurians, differ very materially from those of the recent iguana, cro- codile, &c. They are not concave anteriorly, and convex posteriorly, but have both faces slightly depressed, resem- bling in this respect the vertical column of one of the fossil crocodiles of Havre and Honfleur. But among the recent lacertae there are some, as the Proteus of Germany, the Syren of Carolina, and the Axolotl of Mexico, in which the vertebrae are deeply cupped at both extremities ; and since the fossils in question are clearly of the saurian type, hav- ing the annular part united to the body of the vertebra by * Vide Professor Buckland’s notice on the Megalosaurus. Second Series, p. 391. 2 B Geol. Trans. Vol. I. MDCCCXXV. i86 Mr. Mantell on the iguanodon, &c. suture, the discrepancy alluded to does not appear to be sufficiently important to invalidate the accuracy of the opi- nions which I have attempted to establish. I have the honor to be, Sir, your most obedient Servant, Gideon Mantell. Castle Place, Lewes, Jan. i, 1825. Jfid. Zbans. MD C CCZXV. Tiate XIV. p. iM. T((f7/ o/ /fig IGUANODON a newly discovered FOSSIL dFTAfdJ, /from tfie Sandstone of TIL GATE FOREST, in SUSSEX. 2. a z.i> Sr Portion o/ the Lair of tfir fi/U/2 ?/d , /bar times mtit/nr/red . ' f>uSl7 ¥ SClilpf C 187 ] IX. An experimental enquiry into the nature of the radiant heat - mg effects from terrestrial sources. By Baden Powell, M. A. F. R. S. of Oriel College , Oxford. Read February 17, 1825. (1.) The nature of the heating effect emanating from lumi- nous hot bodies has been distinctly shown to be, in many particulars, very different from that evolved from non-lumi- nous sources ; but the ideas commonly entertained on the subject, are far from being precise and distinct. To gain if possible some ground for establishing more clear views, is the object of the following enquiries. (2.) Professor Leslie, in his well known and elegant expe- riments, (Inquiry concerning Heat, &c. chap, iii.) has fully established the theory of the effect of screens on radiant heat ; and these effects give some of the most important criteria for examining the nature of radiating agents. Those experiments apply only to the heat evolved from a non-luminous source. It therefore naturally becomes the subject in question, whether the interceptive power of glass is not limited to a certain temperature, or state, of the radi- ating source ; and to this point accordingly the attention of several eminent observers has been directed in many well known investigations, among which those of M. De La Roche are justly regarded as the most important and com- plete. In these experiments it appears, that a greater effect 188 Mr. Powell’s experimental enquiry into the nature oj is produced on a blackened thermometer when a glass screen is interposed, in proportion as the body under trial approaches nearer its point of luminosity, or becomes more intensely luminous. (Biot, Traite de Phys. tom. iv. p. 63 8.) (Ann. of Philos. O. S. vol. ii. p. 163.) Both M. De La Roche and M. Biot (See Biot, iv. 6 12.) seem disposed to view the results obtained by the former upon the supposition of one simple agent, the principle both of light and heat. This is at first radiated as heat ; at a cer- tain point it begins to assume the form of light, when the interceptive power of glass decreases in proportion to the increase of luminosity. (3.) As long as the hot body continues below the tempera- ture of luminosity, the partial or total interception of the effect is precisely the same phenomenon as that described by Professor Leslie in his experiments on screens and explica- ble in the same way ; (Phil. Trans. 1816, Part I. On new Properties of Heat, Prop. 40.) And the apparent transmis- sion of a portion of the effect must be referred to the same principle, as is clearly shown by Dr. Brewster, who has established, apparently beyond contradiction, the imperme- ability of glass to simple radiant heat upon quite indepen- dent principles. (4.) Above the temperature of luminosity we must have recourse to further considerations. The hypothesis of M. M. De La Roche and Biot appears to be nearly the same as that of Professor Leslie (Inquiry, p. 162). And it certainly has the merit of simplicity and satisfactory explanation of the phenomena. But it is an opinion which has not received direct proof ; and it is also obvious, that the phenomena may the radiant heating effects from terrestrial sources. 189 be explained without it ; for we may just as well account for the facts, by supposing two distinct heating influences, one associated in some very close way with the rays of light, carried as it were by them through a glass screen without heating it ; the other being merely simple radiant heat, affected by the screen exactly as the radiant heat from a non- luminous body. (5.) In order to ascertain which of these suppositions is true, it will not be sufficient to observe the effects produced by the intervention of a screen alone. We must combine this method with an examination of the relations of different sorts of heat to surfaces. These relations have been shown to dif- fer according as the bod}^ is luminous, or not ; in the one case, the direct heat affects bodies in proportion to the dark- ness of their colour , without regard to the texture of their surface : in the other, the magnitude of the effect depends solely on the absorptive texture without reference to colour. I use the term “ absorptive texture/' to signify that peculiar state of division in the particles of the surface, which has been shown, by Professor Leslie and others to be most sus- ceptible of the influence of simple radiant heat, and always to give a proportionally greater radiating power. The question then is entirely one of facts ; and involves no hypothesis as to the nature either of light or of heat. The object is simply to ascertain by experiment, whether, of the total heating effect radiated from a luminous hot body, the portion intercepted by a transparent screen is of the same nature as, or different from the part transmitted in its rela- tions to the surfaces on which it acts. (6.) In conformity with this view of the object proposed, 190 Mr. Powell's experimental enquiry into the nature of the general principle of the following experiments is this : taking different luminous hot bodies, to expose to their influ- ence two thermometers presenting, one, a smooth black sur- face, the other an absorptive white one : thus obtaining the ratio of the total direct effect on the two, we may compare it with the ratio similarly observed, when a transparent screen is interposed. (7.) This principle of experimenting was applied with one or two variations : and though in the abstract sufficiently simple, it will in practice require an attention to several con- siderations. I shall therefore proceed in the first instance to the detail of the different particulars; then give the results of the experiments in a tabular form ; and lastly, recapitulate the conclusions, and make a few general remarks. I. (8.) In the following set of experiments two common thermometers were employed. The diameters of their bulbs were, thermometer A, 0.6 inch, ; B, 0.55. A, was coated with a wash of chalk and water, and B, with indian ink. In order to compare the effects to be observed with those of simple radiant heat, I ascertained the ratio of the effects of the latter on the two bulbs thus coated, by a few preliminary trials ; and found it to be very nearly one of equality, or perhaps the effect of the white rather greater than that of ihe black. The two thermometers were graduated to quarters of cen- tigrade degrees ; and were both fixed on one mounting with their bulbs detached about one inch from its lowest part, and at the distance of about three-quarters of an inch from each other. (9.) In the 2d set of experiments they were fixed into the the radiant heating effects from terrestrial sources 191 top of a box, the front of which was open, so that the glass screen could be applied to it or not, as required. When the screen was not used the box would acquire more heat, and radiate it to the bulbs in a small degree ; which affecting them in the inverse ratio of their diameters, would diminish the ratio of their risings. That this diminution was very trifling, and not at all sufficient to account for the observed difference of ratio will be evident, because the 1st set was made with- out employing the box, the thermometers being suspended at a distance from any object which could radiate heat to them ; and in this set the difference of ratio is quite as con- spicuous. This remark applies likewise to the possible com- munication of heat by the air. (10.) We must also take into consideration the effect due to the glass screen. When we consider the two bulbs as heated only by that part of the radiation which is transmitted through the screen, the screen may be regarded simply as a third body placed near the two bulbs ; and whether it pos- sesses a higher or a lower temperature, there will be a ten- l dency to bring all three to an equality in proportion to the difference of temperature, and in the bulbs, dependent on their diameters modified by the state of their surfaces. This effect arises from simple radiant heat, whilst that derived from the luminous hot body, is evidently following a different law with regard to the surfaces. It will easily follow from what has been already shown, that such a secondary heating effect will be of a kind tending to diminish the ratio other- wise obtaining between the effects on the two bulbs. If the effect were of a cooling nature, the same thing would also take place : for I ascertained that the radiating powTers of the 192 Mr. Powell's experimental enquiry into the nature of coatings employed, deduced from the observed rates of cool- ing, were in a ratio which happened to be almost exactly the inverse of that of the diameters ; but this effect is pro- bably always small, and I have roughly allowed for it, as will be seen immediately ; taking the temperature of the screen by a small thermometer having its bulb in contact with the central part of the surface. II. (11.) I now proceed to state the results, which will be most conveniently exhibited in a tabular form. 1st Set. Incandescent iron. Distance 7 inches. Glass screen. Experiment. Rise of Thermometer in 1 min. centigrade. A. White. B. Black. 1 1.25 2.5 2 1.2 5 Mean 1.25 2.75 Allowing for the screen ? (as below. 3 * 2.5 No screen. 1 7.5 9.75 2 6.5 7.75 Mean 7. 8.7 5 Difference of exposed and screened results. 6.25 the radiant heating effects from terrestrial sources . 193 (12.) Argand lamp without its chimney. Distance 3 inches. Glass screen. Experiment. 71 Rise of Thermometers in 1 min. centigradge. A. White. B. Black. 1 •75 1.75 2 •5 2.25 3 •75 2.25 Mean .66 2.08 Allowing for the screen. .41 1.83 No Screen. 1 2 3 1.75 1-75 2. 3-5 3.25 3-5 Mean 1.83 3.41 Difference of exposed ) and screened results, j 1’^4" 1.58 tt MJDCCCXXV. Cc 194 Mr. Powell's experimental inquiry into the nature oj (13.) IId. Set. Incandescent iron. Distance 6 inches. Glass screen 2 inches from bulbs. Experiment. Temp, of screen be- fore experiment by thermometer in con- tact. Rise of Thermometers in 1 min, (centigrade.) Temperature of screen after ex- periment. A. White. B. Black. 1 16.5 1. 1-5 25.5 2 1 6.5 •5 1.25 23.75 3 17 • 5 1-5 24.5 4 17 • 5 1. 22.25 5 17 • 5 1. 22.25 Mean .6 1.25 Effect of the screen alone, heated above 250. 1 .25 .25 2 .25 .25 The former result diminished 1 _ _ for this effect. / ’3b 1 . Incandescent iron. No screen. 1 3- 35 2 3- 4. 3 2.75 3.5 4 3-3 3.75 5 3.3 4. Mean r- 2.95 3-75 Difference of the exposed and } screened results. J 2.6 2.75 0 the radiant heating effects from terrestrial sources. 195 (14.) Flame of an Argand lamp without its chimney. Distance 3 inches. Glass screen 1.5 inch from bulbs. • a CD 6 • H £* OJ Temperature of screen before expe- riment. Rise of Thermometers in 1 min. (centigrade.) Temperature of screen after ex- periment. Dl. X w A. White. B. Black. 1 17 I.25 2.25 I 23. 2 1.2 5 2.25 3 1-75 2.2 5 4 I.25 2.75 5 1. 2.25 Mean 1.3 2.35 Effect of the screen alone heated above 250. .25 .25 The former result diminished ) t r from this effect. ) ‘ ^ 2.10 Lamp. No screen. 1 2.25 3- 2 2.5 3.25 3 2.25 3. 4 2.2 5 3.25 5 2.5 3.5 Mean 2.35 3.2 Difference of the exposed and screened results. [ 1.3 1.1 196 Mr. Powell's experimental inquiry into the nature of (15.) In these experiments it will be evident upon inspect tion, that the ratio of the effects produced on the white and black bulbs, is in every instance considerably greater when they were affected only by that part of the total heating in- fluence which is transmitted through a transparent screen, than when they were exposed to the whole. This then would indicate, that on the removal of the screen some new heating power was brought into action which affected the ratio by the addition to each of its terms, of quantities in a ratio expressed by that of the difference of the exposed and screened results above given. This ratio is evidently one differing a little from equality, and agreeing nearly with that of the diameters of the bulbs inversely. (16.) The experiments now detailed will probably be con- sidered sufficient to substantiate the conclusion ; but in re- searches of this kind, where great numerical precision is unattainable; it seemed desirable to give the experiments that confirmation which they wanted in point of intrinsic accuracy, by frequent repetition and variation. With this view I made a great number of trials with a large differential thermometer ; the bulbs were about one inch in diameter and nearly three inches apart. The bore of the tube was about tTq of an inch. Many of the experiments made with this instrument I shall not mention, as, although all agree- ing to confirm my former conclusions, they were complicated by several unnecessary conditions. (17.) In order to obtain results in the most simple manner, it was desirable to get rid of any action on one of the bulbs, and to expose only the other ; the instrument thus acting simply as an air thermometer. The effects on each bulb, one the radiant heating effects from terrestrial sources. 197 being painted with indian ink, and the other coated with white silk pasted on, when exposed, might thus be compared with those through a glass screen. I first tried the experi- ment by placing the bulb in the focus of a spherical tin reflector about six inches diameter; by this means the source of heat could be placed at a sufficient distance to preclude any effect from the glass screen. (18.) The experiment was again varied by placing a large opake screen before the instrument, in which was an aper- ture through which one bulb might be exposed. To this aperture a piece of glass could be applied ; each bulb was presented both with and without the glass. (19.) In all these experiments it is evident, that any heat- ing effect arising from the screen, would tend to diminish the ratio of the black and white effects; and this not being allowed for in the statement of the result, the difference be- tween this ratio and that of the exposed effects will be in reality greater than appears. The result are comprised in the following table. Lamp. Bulb in the focus of a reflector. Coatings white silk, and indian ink. Experiments. Screened. Exposed. White. Black. White. Black. 1 5 8 11 15 2 4 9 13 15 3 6 11 12 14 Mean in 30 sec* . 5 9 3 12 15 198 Mr. Powell's experimental inquiry into the nature oj (21.) Incandescent iron. 1 4 7 11 13 2 4 6 10 10 Mean 4 6.5 10.5 11.5 (22.) Lamp. One bulb covered by an opake screen, the other exposed at an aperture. Dist. 5 inches. Screen 1.5 inch from bulb. 1 4 6 8 11 2 3-5 6 9-5 12 3 4 6 8 10.5 4 3 6 8 12 Mean ini min. 3 -6 6 8.3 11.3 ) Incandescent iron. in 30 sec*. 3 4 12 9 (24.) It is perhaps not worth while to make any formal de- ductions from these results as to the ratios subsisting in the different cases. It will be sufficiently evident upon inspection, that when all due allowances are made, the ratio of the effects upon the white and black bulbs is considerably greater when they were affected only by the transmissible part of the heating effect, than when they were exposed to the whole. The part then which is added on the removal of the screen, is of a nature tending to add to the terms of the former ratio quantities in a ratio much nearer equality : quantities in a the radiant heating effects from terrestrial sources. 199 ratio very nearly that which the effects of simple radiant heat would give. III. (25.) I have above adverted to all the sources of error which occur to me as likely to have affected these results ; and when these are taken into consideration, as well as the nature of the experiments and apparatus, the accordance which the different results exhibit, is perhaps as close as we can ex- pect ; and it appears that all the different sets of experiments agree in showing a very considerable difference in the ratio of the effects produced on a smooth black, and on an absorp- tive white surface, by that part of the radiant effect trans- mitted through glass, and by the total effect. If the total direct effect were the result of one simple agent, the intervention of the glass would, by intercepting some part of it, produce no c .her alteration than a diminution of intensity ; the ratio of the two effects would remain unchanged. This distinction appears to me of some importance towards clearing our ideas respecting the nature of the phenomena, and thus afford- ing an answer to the question originally proposed in refe- rence to some theoretical views, which, though boasting the sanction of high authority, will be untenable if the validity of these results be admitted. (26.) The general conclusions from all these experiments may be thus recapitulated : 1st. That part of the heating effect of a luminous hot body which is capable of being transmitted in the way of direct radiation through glass, affects bodies in proportion to their darkness of colour , without reference to the texture of their surfaces. 2d. That which is intercepted produces a greater effect in 200 Mr. Powell's experimental inquiry into the nature of proportion to the absorptive nature of texture of the surface, without respect to colour. These two characteristics are those which distinguish simple radiant heat at all intensities. Thus then when a body is heated at lower temperatures, it gives off only radiant heat stopped intirely by the most transparent glass, and acting more on an absorptive white surface than on a smooth black one. At higher temperatures the body still continues to give out radiant heat, possessing exactly the same characters. But at a certain point it begins to give out light : precisely at this point it begins also to exercise another heating power distinct from the former ; a power which is capable of pass- ing directly through transparent screens, and which acts more on a smooth black surface than on an absorptive white one. (27.) This last sort of heat, whatever its nature may be, is essentially different from simple radiant heat. It appears to agree very closely with what the French philosophers term “ Calorique lumineux,” and is, according to Professor Leslie's theory, a conversion of light into heat. These views of the subject are certainly gratuitous assumptions. We have no right whatever to identify those two agents, or to suppose that, because a heating effect very closely accom- panies the course of the rays of light, the light is therefore converted into heat ; but the theories above alluded to, seem to regard the whole heating effect of a luminous body as of this latter character. In this particular, the present inquiry has led us to an essential distinction ; and if the experiments are to be relied upon, this peculiar sort of heat constitutes only a part of the total effect. These results do not indeed 201 the radiant heating effects from terrestrial sources. present so simple a theory as that alluded to, but they apply very obviously to the explanation of many phenomena re- corded by various experimenters. (28.) The peculiar heat above spoken of, and which, for the sake of distinction and brevity, we may call “ trans- missible heat,” is similar to that which acts in the solar rays, and which there constitutes the total effect. It is this kind of heat which has been employed as a principle of photometry, on the assumption that it is precisely proportional to the in- tensity of light. Within certain limits this may be the case ; but there are unquestionably circumstances under which the relation is very different ; such for example, as difference of colour in the light : and in general it cannot be assumed to hold good in light from different sources. To show this, there is a remarkable instance in incandescent metal, which produces but very faintly illuminating rays, yet its “ trans- missible heat” is very considerable. I have repeatedly tried the experiment with a small “ photometer,” having one bulb painted with indian ink and the other plain ; the bulbs being in a vertical line ; this instrument whether employed with or without its case, or a glass screen, always gave an effect of about io° in 30" at eight inches distance from a ball of iron heated to the brightest point in a common fire. (29.) In making these last experiments, the effect was always greater when the instrument was used without its case, or a glass screen. This was no doubt in part owing to the greater action of the simple heat now admitted to the instrument on the coated, than on the plain bulb ; but it was also in part occasioned by the circumstance, that the stem going to the upper bulb passes in contact with the lower, MDCCCXXV. D d 202 Mr. Powell’s experimental enquiry , &c. and being a solid mass compared with the thin bulb, is slower in acquiring heat, and therefore cools it, thus increasing the apparent effect on the other. (30. ) In a variety of other experiments which I have tried, using either this “ photometer,” or another having the bulbs at equal heights, various apparent anomalies presented them- selves, all which I found easily explained on the principles here established of two radiations, when connected with the various other considerations to which it is necessary to refer when employing instruments of this description ; but I do not conceive it necessary to enter into' any further details. a From the Pi- ess of JF.NICOL, Cleveland-row, St. James’s, London. PHILOSOPHICAL TRANSACTIONS <■ OF THE ROYAL SOCIETY OF LONDON. FOR THE YEAR MDCCCXXV. % t . PART II. LONDON: PRINTED BY W. NICOL, SUCCESSOR TO W. BULMER AND CO. CLEVELAND-ROW, ST. JAMES’S; AND SOLD BY G. AND W. NICOL, PALL-MALL, PRINTERS TO THE ROYAL SOCIETY. MDCCCXXV. / . » A 4 £ t • ‘ • 0 . ■ . . * ’ CONTENTS. X. On the Anatomy of the Mole-cricket. By J. Kidd, M. D. and F. R. S. Reg. Prof, of Medicine in the University of Oxford. ------- p. 203 XI. Further observations on Planarice. By J. R. Johnson, M.D. F.R.S. - - - - - - 247 XII. On the influence of nerves and ganglions in producing animal heat. By Sir Everard Home, Bart. V. P. R. S. presented by the Society for the Improvement of Animal Chemistry. 257 XIII. An Essay on Egyptian Mummies ; with observations on the art of embalming among the ancient Egyptians. By A. B. Granville, M.D; F. R. S; F. L. S; F. G. S; M. R. I. one of His Royal Highness the Duke of Clarence's Physicians in Ordinary, &c. - - - - 269 XIV. On the temporary magnetic effect induced in iron bodies by rotation. In a Letter to J. F. W. Herschel, Esq. Sec. R. S. by Peter Barlow, Esq. F.R.S. Communicated April 14 tli, 1825. • 317 XV. Further researches on the preservation of metals by electro- chemical means. By Sir Humphry Davy, Bart. Pres. R. S. 328 XVI. On the Magnetism of Iron arising from its rotation . By Samuel Hunter Christie, Esq. M. A. of Trinity College, Cambridge ; Fellow of the Cambridge Philosophical Society ; of the Royal Military Academy. Communicated April 20,1825, by J. F. W. Herschel, Esq. Sec. R. S. - - 347 / Civ ^ XVII. Some account of the transit instrument made by Mr. Dollond, and lately put up at the Cambridge Observatory . Communicated April 13, 1825. By Robert Woodhouse, Esq. A.M. F.R.S. ----- p.418 XVIII. On the fossil Elk of Ireland. By Thomas Weaver, Esq. Member of the Roy al Irish Academy, of the Royal Dublin Society , and of the Wernerian and Geological Societies. 429 XIX. Microscopical observations on the Materials of the Brain , and of the Ova of Animals, to show the analogy that exists between them. By Sir Everard Home, Bart. V. P. R. S. Read at the Society for promoting Animal Chemistry, April 12, 1825. - -- -- -- - 43 6 XX. On new compounds of carbon and hydrogen, and on certain other products obtained during the decomposition of oil by heat. By M. Faraday, Esq. F. R. S. Cor. Mem. Royal Academy of Sciences of Paris, &c. ----- 440 XXI. Account of the repetition of M. Arago’s experiments on the magnetism manifested by various substances during the act of rotation. By C. Babbage, Esq. F. R. S. and J. F. W. Herschel, Esq. Sec. R. S. - - - - 467 XXII. On the magnetism developed in copper and other substances during rotation. In a Letter from Samuel Hunter Christie, Esq. M. A. &c. to J. F. W. Herschel, Esq. Sec. R. S. Com- municated by J. F. W. Herschel, Esq. - - 497 XXIII. On the annual variations of some of the principal fixed Stars. By J. Pond, Esq . F. R. S. Astron. Royal. 510 XXIV. On the nature of the function expressive of the law of human mortality , and on a new mode of determining the value of Life Contingencies. In a Letter to Francis Baily, Esq . F. R. S. &c. By Benjamin Gompertz, Esq. F. R. S. p. 513 APPENDIX. Presents received by the Royal Society from November 1824, to June 1825. Index Meteorological Journal kept at the Apartments of the Royal Society , by order of the President and Council. ERRATA. Page Line 317 o for [117] ” read “ [317] ” at the top of the page. 375 Running title, for “ prevention” read “ preservation.” 439 4 for “ Plate XXVII.” read " Plate XXIX.” 445 3 from bottom, for .** having ” read “ leaving.” 449 18 for “ 1092 ” read “ 8092.” 457 1 from bottom, for “ there were mixtures” read “ these were mixtures.” 463 1 In the column of differences, the numbers should be placed to stand 464 J intermediate between those of the column of parts. Also, dele ** 23.4” in line 8 of the former column, and bring up the remaining differences each a line higher. 492 2 for “ place ” read “ plane.” PHILOSOPHICAL TRANSACTIONS. X. On the Anatomy of the Mole-cricket. By J. Kidd, M. D. and F. R. S. Reg. Prof, of Medicine in the University of Oxford. Read February 3 and February 10, 1825. The following observations contain the principal points of a laborious examination of the anatomical structure of the gryllotalpa, or mole-cricket ; and if I dare hope that that ex- amination has been conducted with any thing like adequate accuracy, I need not apologize for the length of the details with which the account of it is accompanied, since Cuvier has affirmed of an entire volume written by Lyonnet on the anatomy of a single species of caterpillar, that it contains not one word that is useless. Natural science indeed has now arrived at that point, in which individual detail is requisite for the acquisition not only of a surer basis of classification of species, but also of more correct principles of general physiology. Independently however of these considerations, the insect, which is the subject of the present communication, is so singular in its mdcccxxv. E e 204 Dr. Kidd on the structure and habits, and is in some parts of the world so formidable to the agriculturist, as to render its history pecu- liarly interesting. It is described under various names ; as the earth-crab, from its general appearance ; vermis cucurbitarius, from the mischief it does to cucumber-beds. By the French naturalists it is called courtiliere. The best account of the mole-cricket with which I have met is in a well known etymological work by Fosel, pub- lished at Nuremberg in 1749. This account is accompanied by the best engravings also of the external characters of the animal in its different states : and the value of these engra- vings is greatly enhanced by the accuracy with which they are coloured. Rosel says that about the month of June or July, rarely later, the gravid female gryllotalpa excavates a cavity, from 4 to 5 inches beneath the surface of the earth, in which she deposits her eggs in one heap, to the number of three hundred or more ; and dies within a few weeks afterwards. At the end of about a month the young mole-crickets are produced ; and appear, on a hasty survey, to bear a general resemblance to the ant. Between the time of their birth and the com- mencement of winter, the young animals cast their skin three times ; they lie dormant during the winter, deeper in the earth in proportion to the inclemency of the season ; and during this period cast their skin for the fourth time. About May they leave their winter quarters, and at this time are furnished with the rudiments of their future wings, four in number ; which differ remarkably in size and form and po- sition from those of the perfect insect ; in which the inferior 205 anatomy of the mole- cricket wings are folded in a very curious manner, while in the im- perfect insect they are always open. During the month of June or July they cast their skin for the fifth and last time ; after which the wings acquire a per- manent character, and the insect becomes capable of pro- pagating its species. Rosel says that he himself never dissected a 'mole-crcket ; but reports, on the authority of others, that its stomach re- sembles that of the locust, represented in his ninth plate of the series of that tribe of insects. I may here add, from my own observation, that it very closely resembles that of the gryllus viridissimus, and also that of a species of gryllus preserved in the Ashmolean Museum, which answers to the pneumora of Lamarck : it also somewhat resembles that of a locust, marked 614 in the Hunterian collection; and, still more, that of the Cape grasshopper, engraved in the 84th plate of the first part of Sir E. Home's Comparative Anatomy. It appears from Rosel's account, that while very young, these insects are gregarious, but not afterwards ; that they are usually found in the vicinity of meadows and of fields of corn, particularly of barley ; to which they are very detrimental by feeding on the roots, and thus intercepting the due nou- rishment of the plants themselves. I have no doubt of the general accuracy of the foregoing remarks of Rosel, and have little to add to his account of the natural history of this in- sect. I have hitherto met with the mole-cricket in one situ- ation only ; namely, in some peat-bogs, at the distance of a few miles to the west of Oxford. In the neighbourhood of these peat-bogs the insects are familiarly known by the name / 206 Dr. Kidd on the of croakers, from the peculiar sound which they occasionally make ; a sound not very unlike, but more shrill and more soft than that of the frog. This sound, even in the case of a single individual, may be heard at the distance of some yards ; but when made by numerous individuals at the same time it may be heard, as I have reason to believe, at the distance of some hundred yards, provided the air be in a favourable state. I have usually found the insect within a foot and a half of the surface, and in parts where the peat was neither quite dry, nor very moist ; of such a consistence indeed as is most favourable to the mining operations of the animal. The accounts of different authors differ as to the food of the mole-cricket. Having kept several individuals in glass vessels during some weeks, I observed, that of all kinds of vegetable food they preferred the potatoe, while cucumber they hardly touched ; but if raw meat were offered them they attacked it with great greediness, and in preference to every thing else. And, when they had been kept, though even but for a short time without any food, they did not hesitate to attack each other ; in which case the victor soon devoured the flesh and softer parts of the vanquished. As I have not unfrequently found them in their native haunts maimed in various parts of the body, I have very little doubt that, although captivity may increase their ferocity, they are not, even in a natural state, free from each other's attacks. If they are carnivorous, they probably feed on worms, and various larvae, which are abundant in the peat-bogs above-mentioned, for I have re- peatedly found the horny and indigestible parts of insects within their stomachs. Similar relics I have found in the stomach of the pneumora and gryllus viridissimus. The l 207 anatomy of the mole-cricket. two following facts attest in the tribe of insects to which the mole-cricket belongs a remarkable degree of voracity, and an equally remarkable power of abstaining from food. My friend Dr. Macartney, of Dublin, informs me that he has known a gryllus devour a portion of its own body : on the other hand, my friend Mr. Buckland, of this University, gave me, at the commencement of the present summer, a living gryllotalpa, which had been confined during nine or ten months in a tin case, containing a small quantity of garden mould, without the possibility of having met with any other nourishment than such as that portion of mould might be supposed to contain. External characters of the perfect gryllotalpa. In this, as in the case of every other animal with whose habits of life we are acquainted, we see a perfect accommo- dation in form and structure to the circumstances in which the individual is naturally placed. Destined like the common mole to live beneath the surface of the earth, and to exca- vate a passage for itself through the soil which it inhabits, the gryllotalpa is furnished like the mole, with limbs parti- cularly calculated for burrowing ; with a skin which effec- tually prevents the adhesion of the moist earth through which it moves ; and with exactly that form and structure of body, by which it is enabled to penetrate the opposing medium with the greatest ease. At the same time, in order to prevent the necessity of its excavating a track so wide as to admit of the body being turned round in case of a desire to retreat, it is endued with the power of moving as easily in a retrograde as in a progressive direction ; and, apparently to perform the 208 Dr. Kidd on the office of antennae, which warn the insect of approaching danger in its progressive motions, it has two appendages, which might not improperly be called caudal antennae, evidently calculated to serve a similar purpose during its retrogade motions ; par- ticularly as they are furnished with very large nerves. The indifference with which the insect is disposed to move in either direction is manifested by the following experiment : if you touch it towards the head, it retreats ; if towards the other extremity of the body, it advances. The general colour of the animal is such as indirectly to serve as a protection to it, being nearly of the same hue as the vegetable mould in which it lives ; so that it is not very readily distinguished upon being first turned up to view ; and its safety seems to be still farther insured by the appearance of death, which, in common with many other insects, it assumes when suddenly disturbed. This stratagem, for so it may be called, appears to be most decidedly practised by the animal while in captivity ; and if thrown at random out of the vessel in which it has been confined, however unnatural the posture may be into which it has been thrown, it remains as it were in a state of catalepsy during half a minute or more ; the first indication which it gives of recovery from this stupor, invariably consists in a motion of the extremity of the antenna. The general colour of the insect is a dusky brown, passing either into a reddish brown, or into an ochry yellow ; those parts being of the darkest colour which are most exposed to view when the animal is moving in the open air. Every part of the body is to a greater or less degree covered by a kind of down, which seems to be the efficient cause of its capa- anatomy of the mole-cricket . 209 bility of repelling moisture ; which capability is so remark- able, that when the insect is plunged under water, it appears as if cased in silver, or some bright metallic covering : this appearance being evidently derived from a stratum of air, interposed between its body and the surrounding liquid. This down not only serves to repel the adhesion of any moist sub- stance to its body, but also facilitates the motion of the animal, by lessening the degree of friction which would otherwise take place ; and it is owing to the same circumstance that there is an unusual degree of difficulty in retaining a sure hold of the insect, even when dead ; but more especially when alive, and struggling against detention. The degree of force which it commonly exerts on such occasions is very remark- able ; and, from the sensation produced, may easily be sup- posed to be what Rosel says it is, equal to the counterpoise of two or three pounds. The skin or covering of the insect is in some parts nothing more than a thin membrane ; in other parts it resembles soft leather ; and sometimes equals horn or even shell in its degree of hardness. The mole-cricket is more distinctly divisible than most other insects into three separate parts, which I will call re- spectively the head, the thorax, and the abdomen ; although I am aware that the anterior part of that which I call the abdomen is usually considered as a part of the thorax. Of the three parts above-mentioned, the head is not above one- twelfth the length of the whole body ; the thorax three- twelfths ; and the abdomen eight-twelfths. The head is united to the thorax, as the thorax also is united to the abdomen, by means of a loose membrane, which envelopes the muscles that pass respectively from one to the 210 Dr. Kidd on the other ; and it is in consequence of the looseness of these mem- branes that the animal is enabled either to separate the con- nected parts to a considerable distance from each other ; or to contract them so closely together as to hide the interposed membranes from view ; and, from the arched form of the anterior part of the thorax it can draw in its head under that part, much after the manner of a tortoise. The same flexi- bility of the connecting membranes enables the animal to place either its head or its thorax at a considerable angle with the rest of the body ; a movement which is very charac- teristic of this insect, and gives it an air of intelligence; the attitude being apparently that of watching, or listening. The head '* All the upper part and the sides of the head form a hard, thick, horny case, containing the various mus- cles which move the jaws ; and, in order to strengthen this case, two firm bars run transversely across the bottom both of the anterior and posterior margin ; which bars are them- selves united together by a still stronger bar or beam, which runs longitudinally from the middle of the one to the middle of the other. There is nothing very remarkable in the parts which constitute the mouth, excepting the maxillary and labial palpi. In the maxillary palpi there are five joints or parts ; in the labial there are three ; and the last of these joints in each of the palpi terminates in a rounded extremity, like a pestle ; this extremity, which is of a honey-yellow colour, is perfectly smooth, while every other part of the palpi has a rough and hairy surface. In their natural posi- tion the palpi are bent and projected forward, so as to re- semble the fore-legs of a horse in the act of cantering. • Vide Fig. i and 2. Plate XV. 211 anatomy of the mole-cricket. The antennae, which are situated near the articulation of the mandibles, consist of a great number of minute segments; resembling beads of a circular form: the number of these beads, which varies in different instances, is usually from 100 to no; rarely more or less: but it is worth noticing that in examining the two antennae of the same individual, I sometimes found the number of beads greater in one than in the other ; and as the terminal bead differs in its form from all the rest, the result of the examination is less open to doubt than it would otherwise have been. Each bead is united to the one that precedes and the one that follows it by means of a soft, white, very flexible membrane ; in conse- quence of which, and of the number of the joints, the insect can move and bend the antennae with great facility in every direction, excepting at the very root : there the motion is confined by a ridge that only admits of its being directed from behind, forwards, or vice versa. The anterior edge of each bead is fringed with bristly hair; which, surrounding the joint that connects it to the following bead, gives to the whole, when viewed by a mag- nifying lens, the appearance of a sprig of equisetum. The beads are upon the whole larger, in proportion as they are nearer to the origin of the antennae : but here and there, and without any regularity in the variation, one of the beads is either much larger or much smaller than those in the vicinity. Whatever be the primary use of the antennae and palpi, on which subject entomologists are not agreed, their general importance is allowed by all ; and is evinced in the parti- cular instance now before us by the extraordinary attention bestowed upon them by this insect. Those who may be led mdcccxxv. F f 212 Dr. Kidd on the to watch its habits, will repeatedly observe the antennae bent forwards and downwards, by a curious application of the fore-legs towards the mouth : and then by a regulated mo- tion, not unlike that by which the resin is applied to the bow of a violin, they are passed between the maxillae : in order, as it would appear, either to moisten the organs, or to disen- gage from their surface, particles of dust or other extraneous substances which may have accidentally adhered to it. With a more rapid motion the insect from time to time dresses, if I may use the expression, its palpi ; bending them inwards and brushing the surface of their extreme parts by a frequent application of the maxillae. A similar care of the antennae and palpi is observable in the gryllus viridissimus ; with the additional circumstance, that that insect very often passes between its maxillae the curiously padded surfaces of its feet, much in the same manner as a cat licks its paws. The eyes * The gryllotalpa has two compound eyes, as they are called, and two ocelli or stemmata. Latreille uses this expression “ ocellus medius subobiteratus from which it may be inferred that he supposes the ocelli to be three in number ; but after the most careful examination I have not been able to discover more than two. The com- pound eyes are situated immediately behind, but a little exte- riorly to the antennas : the corneas of these eyes, which are large in proportion to the size of the head, are segments of a sphere ; flattened however on the inner side so as to pre- sent a vertical plane surface to a similar plane surface in the opposite eye ; and it is remarkable that this part of the cornea, and the mere margin of the rest of it, are the only parts * Vide fig. i and 2. 213 anatomy of the mole-cricket. capable of freely transmitting light : all the remaining por- tion is covered, on the interior surface, by an opaque pulpy membrane, or pigments of a mulberry colour ; yet the por- tion obstructed by this pigment is in itself nearly as trans- parent as flint-glass : it is studded over on the interior sur- face with numerous depressions of a circular form, which, being very closely set together, give it a reticulated appear- ance. The stemmata are placed between the middle of the com- pound eyes, so as to be rather further from each other than from the eye of the same side. They are not so large as a very minute pin's head, of a lenticular form, perfectly trans- parent, but not quite colourless, resembling particles of very pale cairngorum quartz. In two instances I have found only one of the stemmata, without any trace of the other. An anomaly somewhat of the same kind has been observed by the father of my friend Dr. Ogle, of this University, in the case of a man ; on one side of whose breast the usual rudi- ments of a mamma were entirely wanting. With respect to the small quantity of light admissible through the corneas of the eyes of the mole-cricket, it is ap- parently sufficient for the purposes of an animal living almost constantly underground. The spherical form of that part of the corneas which is itself incapable of transmitting light is probably intended, as w^as suggested to me by Mr. Whessel, to whom I am indebted for the principal drawing which accompanies this paper, as a protection for the vertical transparent portion. The thorax * The form of this part is that of an irregular * Vide fig. 3 and 4. 214 Dr. Kidd on the cylinder, passing into a cone towards the anterior part : the upper portion and the sides, which are covered with a re- markably smooth down resembling the finest velvet, form a homy case of considerable thickness and strength ; which contains, or, more properly speaking, is almost entirely occu- pied by the very large and powerful muscles which move the fore-legs. It is divided longitudinally into two equal parts by an almost bony septum of a complicated form : this septum upon the whole bears an obvious resemblance, but in an inverted position, to the deep sternum, together with the furcular clavicle of birds, and is destined indeed to a similar use ; to give attachment to the powerful muscles which are to move the anterior extremities. It differs however from the corresponding part in birds in two considerable points. It differs, first, in consisting of two laminae instead of one : these lamina are parallel to, but distinctly separated from each other, so as to give passage to the esophagus, and room for the attachment of muscles which assist in moving the adja- cent parts. It differs again from the sternum of birds by having a very hard spine, which resembles a common thorn, attached to the inferior and posterior edge of the furcular bone, and passing rather obliquely downwards and back- wards. This process serves for the attachment of numerous muscles which adhere very firmly to it, and are inserted on either side of the commencement of the abdomen ; enabling the animal to bend its thorax to an angle with the abdomen, a posture which has already been described as very charac- teristic of this insect. From the under part of the thorax and near its posterior extremity arise the two fore-legs ; those singular instru- 21 5 anatomy of the mole-cricket. ments which so peculiarly characterize the mole-cricket. Compared indeed with the other legs, and with the general size of the animal, they are as if the brawny hand and arm of a robust dwarf were set on the body of a delicate infant ; and the indications of strength which their structure mani- fests, fully answer to their extraordinary size : but I shall describe them more particularly hereafter, and proceed now to the description of the abdomen. The abdomen .* In its general form and structure this part resembles the corresponding part of the hornet : but it i consists of more segments, and is much less bright in colour. There are twelve segments in the abdomen of the gryllo- talpa, of which the nearest to the thorax carries the upper pair of wings on its upper part, and the middle pair of legs on its lower part ; the next segment carries the under pair of wings on its upper part, and the hind pair of legs on its under part. These two segments which are usually de- scribed in entomological systems as belonging to the thorax, are of a horny consistence and very hard on their upper side ; while all the rest are merely membranous ; they are also covered with much long and rough hair, while all the rest, excepting the last but one, are sparingly covered with short hairs. The last segment but one is furnished on each side of its upper surface with a row of red hairs or bristles, which are curved inwards in a direction towards each other ; obviously for the purpose of preventing the folded extremi- ties of the under wings from falling off the hack on either side. The under surfaces of all the segments are of a thicker * Vide fig. 2. 216 Dr. Kidd on the x substance than the upper, and are covered entirely with a coarse down, which probably gives the animal a more firm hold while in the act of burrowing. In the last segment is situated the vent, formed by three oval flaps, two below, and one above. This segment sends out from each side of its upper surface two caudal antennae, as I have ventured to call them* of a tapering form, which differ essentially in struc- ture from those of the head, inasmuch as they are not jointed in any part of their extent, excepting at their very com- mencement : they are furnished with short hairs set compa- ratively closely about every part ; among which are inter- spersed long single hairs. These caudal antennae are evidently very sensible, and serve probably to give the animal notice of the approach of any "annoyance from behind ; they are partially hollow throughout great part of their extent, and muscles may be traced into them from the inner and adjoin- ing part of the abdomen. The legs. The anterior legs passing out from under the hind part of the thorax, advance by the side of the head in a direction parallel to each other, which is their natural posi- tion while the animal is at rest. I should deem it a servile adherence to system were I to describe the parts composing these legs by the terms strictly indicative of the order of their succession ; for, thus, that part which answers so emi- nently to the character of a hand, must be called the tibia. I * n shall beg leave therefore to state principally that the fore- leg of this insect consists of three main parts, with a lateral appendage attached to the last of them. The two first of the three parts bear some general resemblance to the claw of the crab ; being short and thick, for the purpose of affording 217 anatomy of the mole-cricket. room for powerful muscles, intended to move the last part ; which is the immediate instrument employed by the animal in burrowing. It might I think be asserted, without the fear of contra- diction, that throughout the whole range of animated na- ture, there is not a stronger instance of what may be called intentional structure, than is afforded by that part of the mole-cricket which I am now to describe.* The natural and constant position of this member is worth noticing ; the palm, as it may be called, facing outwards, and the claws ranging not in a horizontal but a vertical line, so that none of them but the lowermost, and not even this necessarily, touches the surface on which the animal is walk- ing. Accordingly the insect does not make much use of its fore-legs in walking ; and, if irritated, it advances towards you with these legs elevated, in a menacing attitude as it were ; not unlike the corresponding attitude of the insect, called the mantis. The form of the hand is that of a tri- angle ; the base of which is formed by the four claws, while the apex is situated at the joint connecting this with the pre- ceding part ; by which form and disposition, two important objects are gained ; for the joint is thus capable of a much greater extent of motion than it could have possessed, had the articulating surface been more than a mere point ; and at the same time, the greater extent of the base enables it to act with more powerful and more rapid effect than could have been otherwise produced. The four claws, which form this base, constitute the proper burrowing instrument ; and their shape and structure are beautifully adapted to the pur- * Vide fig. 5. 218 Dr. KrDD on the pose : for instead of being covered with down or hair, like all the rest of the limb, they are hard, and have a perfectly polished surface ; doubtless in order to prevent as much as possible the adhesion of the earth through which the animal is to make its way ; they have each of them sharp but strong points, which proceeding from a broad base are thus ren- dered more effectual. In each also of the claws one of the edges is sharp, while the other is comparatively blunt ; and all the cutting edges, as also the terminating points, are directed downwards. Their outer surfaces are slightly con- cave both in the longitudinal and transverse direction ; so that all together they form a scoop as it were, by which the earth that has been scraped off' by the points is moved out of the way. They are also each of them divided longitudinally on their concave side by three or four slight ridges ; so that, though highly polished, their surface is not absolutely smooth: and thus being concave and uneven, they are more apt to retain particles of the excavated earth ; which, by filling up the indentations of the claws would necessarily impede their due action. To obviate this inconvenience, an exceedingly curious instrument is attached to the upper part of the concave surface of this member : this instrument con- sists of two claws, closely resembling those already described, having by their side a small brush as it were, which termi- nates in two spines. These two claws, together with the piece bearing the spines, arise from a single piece, or handle, which is articulated in such a manner, as to move in a plane parallel to that in which the four claws are placed ; but in a direction opposite to that in which they are moved : they are also placed in such a manner that their points and cutting 219 anatomy oj the mole-cricket. edges are opposed to the points and cutting edges of the true claws ; and hence the two parts, thus opposed to each other, act like the blades of a pair of shears. When first I consi- dered this mechanism, and remembered that in the localities where I had found the animal, the earth was frequently tra- versed by fibrous vegetable roots, which must necessarily re- tard its progress, I supposed that it used this instrument as a pair of shears to cut through those fibres. It is Rosei/s opinion, however, that the instrument is intended to clear the true claws of the dirt that may from time to time collect upon and clog them ; and unless both opinions be true, Ro- sei/s appears the more probable. But I have not yet con- cluded the account of the curious mechanism of this member: for the brush which has just been described, has only such an extent of motion as enables it to clear the two uppermost claws, or at most, the three uppermost; the two lower- most however may effectually be cleared by a kind of fea- thered spur, which, arising from the further extremity of the joint answering to the femur, proceeds directly towards the lowest part of the burrowing instrument, and is easily made to sweep over the surface of the two last claws by bending the intermediate joint, the only difference in its mode of action being, that it passes over their inner instead of their outer surface. The middle pair of legs, which are the smallest of the three pairs, arises from the under part of the first segment of the abdominal division : they pass out from the body at right angles to the abdomen, and usually are seen in that direction whether the animal be in motion or at rest. They consist each of four parts ; a very short coxa, a femur and tibia mdcccxxv. G g 220 Dr. Kidd on the nearly equal in length to each other, and a tarsus, which con- sists of two long and an intermediate short joint ; the last joint terminated by two curved spines. There are several sharp, hard, straight spines near the angle made by the union of the tibia with the tarsus ; some of which being directed downwards, give the insect a firmer hold in walking. The hind legs bear a general resemblance to the middle legs ; but the coxa, femur, and tibia, the femur especially, are much larger and stronger ; the relative position of the parts with respect to each other is the same as that of the middle legs ; but their general direction, instead of being at right angles to that of the abdomen, is parallel to it. In addition to several sharp spines placed about the joint of the tibia and tarsus, and directed downwards as in the middle legs, there are four or five others placed at the back of the tibia near its lower extremity, and pointing slightly down- wards. The structure of the tarsus scarcely differs from that of the middle leg. These hind legs are evidently the great instruments of progressive or retrogressive motion. The wings. There are two pair of wings : the upper pair arising from each side of the first segment of the abdomen partially cover the lower pair, which arise from each side of the second segment. In several instances I found adher- ing to the body, in the vicinity of the roots of the wings, a minute parasytic insect of a light scarlet colour ; the number of these parasytic insects rarely exceeded eight or ten in the same mole-cricket, but in one instance I counted nearly forty.* The upper wings in the full-grown mole-cricket are not • Vide fig. 5 a. 221 anatomy of the mole-cricket. above one-fourth the size of the other pair ; they are of an oval form and convex externally ; and their nervures or wing-bones, as they are called by Dr. Leach, are remark- ably thick and hard. The under wings when expanded, measure full three inches from the outer extremity of one to the corresponding extremity of the other. They may be compared in form to a bivalve shell, contracted and elongated towards the hinge, at which point is the joint of the wing ; from hence, as many as thirty nervures, almost all of which are remarkably deli- cate, radiate in straight lines to every part of the extremity. A very thin and nearly colourless and transparent membrane forms the medium through which these nervures radiate ; and throughout the whole expanse of the wing, these ner- vures are mutually united by more delicate nervures, which cross at nearly regular intervals, and at right angles from one to the other, presenting altogether the appearance of a curiously checquered surface. These wings, though so broad when expanded, are scarcely the twelfth of an inch in breadth when folded ; and appear at first view, in this state, any thing but what they really are. They have indeed been often mistaken for a mere caudiform appendage to the other wings, from under which they emerge. When folded, and they fold themselves longitudinally like a fan, their very delicate texture is protected by the following simple contrivance. In each wing the two exterior longitudinal nervures, with their intervening membrane, are comparatively strong and thick ; and these form the lateral walls of the wings when folded. In each wing also there are two other nervures not far from the former, and circumstanced like them with respect 222 Dr. Kidd on the to strength ; which, when the wings are folded, close toge- ther so as to form a horizontal covering, or roof, of sufficient strength to protect the subjacent membrane from ordinary accidents. As the narrow case formed by the wings thus folded extends beyond the extremity of the abdomen, and might easily slip off so convex and smooth a surface, such an accident is guarded against by the contrivance already de- scribed, namely, an apparatus of hairs or bristles placed on either side of the upper surface of the last segment but one. The digestive organs * It is mentioned in the 48th Letter of White's Natural History of Selborne, on the authority of Anatomists who have examined the intestines of the mole- cricket, that “ from the number of its stomachs or maws, there seems to be good reason to suppose that it ruminates, or chews the cud like many quadrupeds." A cursory view of these parts however is enough to show, that such an opi- nion could only have been deduced from some very general points of resemblance, and the probability of its truth is entirely destroyed upon an examination of their internal structure. \ In fact, the digestive organs of this insect resemble more closely those of a granivorus bird than of any other animal, as will appear from the following description. The esophagus, which on its upper side is blended with, and forms a conti- nuation of the inner surface of the upper lip, commences on the lower surface in a loose corrugated tongue, as it were, which is attached at its base to the inner surface of the lower lip ; from hence it is continued along the under part of the head and neck, and between the bony laminae of the sternum, * Vide fig. 6. 223 anatomy of the mole-cricket. in the form of a distensible and longitudinally folded tube of a reddish brown colour ; it then passes on among the muscles of the two hind pair of legs, and at length terminates in a very large crop of an oval form. In the vicinity of the mouth it is surrounded by muscles which arise from its outer coat, and are inserted at nearly right angles into the adja- cent parts ; these muscles of course serving to open and distend it. In the crop itself two sets of muscular fibres are very easily discernible, some running in the direction of its length, others surrounding it in the opposite direction ; and it is lined by a very thin membrane having a cuticular character. The tube which passes from the crop towards the intes- tines commences so near the termination of the esophagus, that externally it appears to be a continuation of the latter ; it is very thick and strong in comparison with its diameter, and consists of a coat of muscular fibres disposed circularly, lined by a membrane which has evidently a glandular cha- racter. This tube terminates at a short distance from its commencement in a small organ, scarcely larger than a hemp-seed, which may very properly be called a gizzard ; though more complicated in its structure, and more effectual for the intended purpose than the gizzard of any bird. The form of the gizzard is nearly spherical, and it consists of a thick external muscular coat, which is lined by a glan- dular membrane of very singular construction ; the inner surface being divided longitudinally into six equal parts, separated from each other by two horny ridges of a dark brown colour ; each division is furnished with three series of serrated teeth, of the consistence of tortoise-shell, and nearly 124 Dr. Kidd on the of the same colour, running from the top to the bottom ; of which those of the middle series are twice as broad and more complicated in form than those of the lateral series. As there are fifteen teeth in each of the three series of the six divisions, the gizzard contains in the whole 270 teeth.* In separating the muscular coat of the gizzard from that 4 which lines it, which may be easily done by maceration, the exterior surface of the glandular coat in which the teeth are inserted is exposed to view. The appearance of this surface is very singular, and may be compared to a piece of fine lace- work, of which the meshes represent the intervals of the inserted teeth, the parts of the membrane in which the roots of the teeth are inserted resembling the lace- work itself. Four of the divisions above described are elongated so as to terminate in a tapering membranous appendage, consisting of a natural fold, which serves to convey onwards any fluid particles that may have been pressed out by the action of the gizzard ; and these four appendages so collapse together as to form a point, as it were, which lies immediately in contact with the commencement of the common intestines. This apparatus is only discoverable by dissection ; for it is con- tained in a large membranous cavity of the shape of a horse- shoe, the base of which passes across the lower extremity of the gizzard, while the sides form two enormous caeca, which ascend obliquely outwards on each side of the gizzard. As the muscular compression of the gizzard must neces- sarily have a tendency to force a part of any expressed fluid back into the esophagus, we may expect this organ to be so constructed as to prevent such an effect ; and it is pro- • Vide fig. 6, 7, 8. 125 anatomy of the mole-cricket . bably for this purpose, that its upper part is furnished with several projecting papillae, each terminating in a small horny particle ; which, like the sesamoid particles in the semilunar valves of the human aorta, may serve to complete the val- vular action of the papillae to which they are attached. The caeca which have been above described, are traversed longitudinally by several very broad duplicatures of their internal membrane ; and judging from their usual contents, these appendages of the intestine are destined to receive and to perfect the digestion of those particles of food from which the gizzard has pressed out the liquid contents ; and while, by means of the membranous folds already described, the expressed fluid is conveyed immediately into the mouth of the intestinal canal that passes from the general caecal cavity, the caeca themselves receive the solid compressed particles which are forced out laterally at the extremities of those two divisions of the gizzard, which, having no membranous fold attached to them, leaves thus a vacant interval for the pas- sage of the undigested mass. That this opinion is correct may be presumed, not only from the very mechanism of the parts, but from the state of the contents of the caeca, which are of a less crude character than the contents of the crop, and of a more crude character than the contents of the por- tion of intestine immediately beyond them. A strong con- firmation of the foregoing opinion is obtained from a compa- rison of this part of the anatomy of the mole-cricket, with that of the corresponding part in the ostrich ; the stomach of which bird, acting like a gizzard by means of numerous peb- bles which it takes into that organ, is aided by two enormous caeca, which, though they are not immediately in contact 226 Dr. Kidd on the with the stomach, are not far removed from it ; and like the stomach, contain numerous pebbles, which are both smaller and smoother than those of the stomach itself, as being only destined to act on food already partially digested. The ana- logy on which I have just insisted, is strengthened by the tact, that there are very large duplicatures of the internal coat of the caeca of the ostrich, as in the corresponding parts of the mole-cricket. I either therefore misunderstand, or can- not agree with M. Marcel de Serres, the author of a very interesting paper on the Intestinal Canal of Insects, published in the 76th vol. of the Journal de Physique ; who seems to attribute to the aeca above described, the office of an hepatic organ, and calls them “ Vaisseaux hepatiques superieures ’’ in contradistinction to another organ situated lower down in the intestines, and acknowledged by all to be of an hepatic character. From the common base of the two caeca a very narrow but powerfully muscular tube, which might with much pro- priety be called the jejunum, passes onwards for a very short space, and terminates in a large intestine ; this intes- tine, which is eight or ten times the diameter of the jejunum, contracts very gradually as it proceeds, till, near the extre- mity of the rectum it swells out very considerably. This large intestine is slightly convoluted in its course, and is usually more or less distended with a black pasty matter re- sembling soft clay. Among the contents of the upper part of this large intestine were almost invariably found from ten to twenty worms, of a white colour, and of a shape resemb- ling the lumbricus teres of the human intestines, but thicker in proportion to their length, and narrowing more suddenly 227 anatomy of the mole-cricket. towards their caudal extremity. In all of these worms the common intestines were distinctly visible through the inte- guments ; and in many of them were distinctly visible also from ten to fifteen ova.* * * § On opening and removing the contents of the upper por- tion of the great intestine, four rows of minute bodies of a glandular character, -f and of nearly a black colour, are brought into view ; J two of which rows originate from the very commencement of the great intestine, and pass downwards through more than half its course : exteriorly to these two rows are two others, one on each side, which are parallel to the preceding, but originate at some distance from the com- mencement of the intestine. Immediately below the termina- tion of this glandular apparatus is a small opening, very readily distinguishable on the inner surface of the intestine ; which is the orifice of a cylindrical tube of a white colour, and of about the size of a horse hair. This tube, after hav- ing been traced a short distance in a direction towards the gizzard, is lost in a mass or brush of still smaller tubes of an exceedingly bright yellow colour; these tubes, which amount probably to 150 or 200, § are partially coiled round the con- tiguous viscera so as not to be very easily disentangled. A * Vide fig. 9. f The only doubt which I entertain as to the glandular character of these bodies, arises from a reliance on the authority of Cuvier, who says, that the glands of insects are in every instance nothing more than parcels of free tubes floating in the interior of the body, and held together by the tracheae.” Journ. de Phys. Tom. 49. p. 344. | Vide fig. 9 a. § Cuvier states in the Journal de Physique, Tom. xlix, p. 346, that the num- ber of these tubes in the gryllotalpa amounts to many hundred : but I feel certain that he greatly overrates the number. H h MDCCCXXV. 228 Dr. Kidd on the similar organ is represented in Sir Everard Home's Compa- rative Anatomy, vol. 1. pi. 84, as belonging to the Cape grasshopper ; it was originally considered by Mr. Hunter, and is considered generally at present, as answering to the live!' of the higher classes of animals. Each of these tubes springs out of a common cavity in which the white tube from the intestine terminates ; but at their free extremity they are all impervious. Each tube appears partially filled with a granular pulpy substance which is almost universally of a bright yellow colour; though sometimes a particle is visible here and there of a clear light green colour, and I have seen similar green particles in the duct leading from the intestines. The following peculiarity is observable in the individual structure of these tubes : their diameter for about one-third of their course from the closed extremity is very small, and they are colourless, and apparently empty ; after which they suddenly undergo a considerable enlargement, become yel- low, and are partially filled with the contents above de- scribed. Maceration in water destroys the yellow colour in the course of a few minutes ; from whence it may be inferred, that after death the colouring matter transudes through the tubes containing it — a circumstance observable also with re- spect to the biliary vessels of the higher orders of animals ; but it seems certain that no such transudation takes place during the life of the animal ; for, upon examination of the insect soon after death, I have never found the adjacent parts coloured, as they would have been by the escape of the con- tents of the tubes. 229 anatomy of the mole-cricket. The portion of the intestine below the orifice of the hepatic duct, as it may be called, appears to be externally traversed in a longitudinal direction by several rows of small convex eminences resembling beads ; these are the outer surfaces of t so many corresponding internal sinuses, which are probably formed as the similar sinuses in the large intestines of man-, and many other animals, by a pecularity in the disposition of the fibres of the muscular coat. Near the termination of the intestine are two orifices, one on each side, communicating each with a duct which soon swells out into a vesicular bag ; these bags may probably be glands that secrete the fetid matter which the insect ejects from the anus when irritated. In one instance I found, on the site of the orifices above-mentioned, two small bodies about the size of a pin's head, of a dark colour, and to the naked eye of a spherical form ; my surprize was consider- able when upon observing them with a magnifying lens, I perceived that they exactly resembled a crystallized rosette of brown pearl-spar. Upon being removed and submitted to the requisite experiments, they proved to be of consider- -able hardness, sparry in their structure, and insoluble either in boiling water or alcohol ; but they were dissolved with rapid efferverence in diluted muriatic acid. These calculous concretions were probably the result of diseased action in the vesicular glands round the orifices of the excretory ducts of which they had been deposited. The blood. Upon wounding the animal in almost any part of the body, even in cutting off a portion of the caudal an- tenna, there oozes out a very clear thin fluid of a bright honey-yellow colour ; having sensibly alkaline properties, 230 Dr. Kidd on the and coagulating either by heat or by the addition of alcohol* A quantity of this fluid, weighing 1.85 grains, being evapo- rated under an exhausted receiver, in which was placed dry muriate of lime, left a solid residuum of a bright golden yellow colour, which weighed 0.25 grains ; this residuum was brittle, and had the general properties of solid albumen. The foregoing characters render it highly probably that the yellow fluid distributed through the body of the insect, re- sembles in its nature the serum of common blood, and there can be no doubt, arguing physiologically, that this yellow fluid is the blood or nutrient juice of the animal. I wish I could as satisfactorily show the means employed by nature to distribute this fluid through the system of this and other animals of the same class ; for, though I cannot hope to dis- cover what more experienced and skilful anatomists have sought in vain, a heart, namely, and a system of circulating vessels ; yet I cannot subscribe to their opinion, that the blood transudes through the the coats of the intestines, where of course it must be primarily formed, and thence passes, as through the pores of a sponge to every part of the body. Both Cuvier and M. Marcel de Serres completed a very elaborate set of experiments for the purpose of ascertaining whether the dorsal vessel of insects sends out any lateral branches which might serve the purpose of a circulating system, or whether any other distinct circulating system exists ; but they have entirely failed in their endeavours ; and I feel assured, that where such men have failed, others will not succeed ; and yet their consequent supposition that the blood is diffused through the general substance of the body, appears to me very highly improbable. It accords not with 231 anatomy of the mole-cricket. the general character of those means by which nature usually produces its effects ; there is too little of art and contrivance, if I may use such terms, on such an occasion, in the mode supposed to be employed. Even in the formation of mineral crystals, which are unorganized bodies, the attraction by which the component particle are aggregated is regulated by laws, the most systematically framed and observed : and whoever has viewed with any attention that wonderful mo- nument of human industry and sagacity, the Anatomical Museum of John Hunter, and has there seen the proofs of a sanguineous circulation in animals of an order so low, that they can hardly be said to have any specific form or sub- stance, will almost necessarily be disposed to expect a simi- lar provision in a class of animals, whose general structure is so elaborately and beautifully organized as that of insects. But I shall again advert to this subject after having described the tracheal system or respiratory organs of the insect under consideration. The organs of respiration. As it is very generally known that the atmospherical air, so necessary for the existence of all animated beings, is admitted into the bodies of insects by certain apertures called stigmata, and is then distributed through the system by means of tracheae or air tubes, 1 shall not dwell longer on the description of those organs in the gryllotalpa than is necessary for the elucidation of its particular history. Omitting the questionable existence of two stigmata in the upper lip, and of two others in the vicinity of the caudal antennae, there are ten stigmata very distinctly visible on each side of the body.* Hence, therefore, it is necessary to * Vide fig. 10. 232 Dr. Kidd- on the correct, though probably it has ere this been corrected by himself, a statement made by Cuvier in his Regne Animale, Tom. iii. p. 126, that in the myriapoda there are twenty stig- mata and upwards ; but in all other insects eighteen at most. He also asserts in the same place, that insects respire by two principal tracheae extending longitudinally, one on each side of the body, from which other tracheae ramify. Now cer- tainly in the gryllotalpa, and, as I have reason to believe in many other insects also, the longitudinal tracheae bear so small a proportion in their capacity to the aggregate capacity of the other tracheae, that in such instances they cannot be called principal tracheae. My own opinion is, that these longitudinal tracheae serve as connecting channels, by which the insect is enabled to direct the air to particular parts, for occasional purposes. Though not immediately bearing on the present point, 1 beg leave here to state a fact which I have not seen else- where noticed, that in the two segments of the body which carry the middle and hind pair of the true legs, in the larvae of coleopterous and lepidopterous insects, there are no stigmata, discernible at least either to the naked eye, or a common magnifying lens. But, to return to the stigmata of the gryllotalpa, the first in order beginning from the head, is situated very near the lower part of the posterior ridge of the thorax. This stigma, not to object to the term in the present instance, is apparently connected with all the tracheae both of the thorax and of the head itself. It differs remarkably in size and form from all the rest ; for instead of being a mere dot or point, it is an elongated fissure, bounded by two horny lips. The second stigma, which somewhat resembles in form, though of much 233 anatomy of the mole-cricket. less extent than the preceding, is situated immediately behind the root of the middle leg ; the third, which is still less than the second, is situated immediately behind the root of the posterior leg ; near the termination of the dorsal part of the third abdominal segment ; the fourth, fifth, and onwards to the tenth inclusive, are situated near the terminations of the corresponding dorsal segments of the abdomen. I would here notice by the way, a peculiar appearance very constantly observable on the ventral surfaces of most of the abdominal segments between the hind pair of legs and the caudal antennas. At either extremity of those segments there is a short line, not unlike that made by the stroke of a pen, passing obliquely downwards and inwards : it dees not seem easy to conjecture the use of these lines. I may state from repeated observations, that the stigmata, taken generally, are not the terminations of single tubes ; very frequently two and often more than two tracheas origi- nate from the same stigma ; and very soon after the com- mencent, one or even two of these trachea* subdivide into numerous branches, which follow as nearly as may be the direction of the original tubes. The distribution of many of the tracheas may be very satis- factorily demonstrated by drying one of the insects under an exhausted receiver, containing muriate of lime : for after hav- ing been thus dried, the tracheae become perceptible to the naked eye through the sustance of the integuments. The fore- going method of drying anatomical preparations may be suc- cessfully employed on many occasions ; it answers particularly in the case of the human eye, or the eye of any sufficiently large animal ; for, in the act of exhaustion, the air contained 234 Dr. Kidd on the in the vitreous humor of the eye becoming expanded, pre- serves the spherical form of the organ until the whole of the moisture has been evaporated ; and it is then sufficiently firm to support itself. I have traced most of the tracheae to the parts on which they are respectively distributed ; but as no adequate object, nor indeed any object of importance, would be gained by the description of a distribution which is not marked by any physiological peculiarity, I shall only insist on such points as appear to me to be either new, or hitherto not sufficiently elucidated. The tracheae of insects are generally described as tubes constructed of a spiral thread, the successive coils of which are closely in opposition with each other ; such a structure is represented in Swammerdam's plates, and I have no doubt from his acknowledged accuracy, that he represents what he observed. It has not however happened to me, with the exception of one equivocal instance, to perceive such a struc- ture in the mole-cricket, the character of the tracheae of which varies in different parts of the insect ; for sometimes they re- semble the pulmonary tracheae of the higher classes of ani- mals, in having an annulated structure ; and sometimes they appear as tubes of a perfectly uniform substance like cuticle, or some very thin and unorganized membrane. It is gene- rally understood, that the tracheae of insects penetrate each organ and every part of the body : and certainly the case is such in the instance before us. Thus, in that brush of capillary yellow tubes supposed to constitute the hepatic system, the total number of which amounts to 150 or 200, there is reason to believe that each tube is accompanied by a distinct trachea coiled round it in a long spiral. Again ; the 235 anatomy of the mole-cricket. two medullary cords which connect the several ganglions ol the nervous system, are in their natural state united together by means of the branches of a tracheal tube which runs be- tween them ; a similar tube being attached to the exterior edge of the cords ; and the surface of what may be called the brain of this insect, is as beautifully characterized by the ramifications of the tracheae which pervade it, as the surface of the pi a mater of the human brain by the blood vessels which penetrate that membrane in every direction. In meditating on the difficult problem of the sanguinous circulation of insects, it has forcibly occurred to me, that the tracheae may possibly be the instruments of such a circula- tion ; absorbing the blood or the chyle in the first instance from the internal surface of the alimentary canal, and thence conveying it to the various parts of the body ; nor is this opinion, however improbable it may appear, entirely gra- tuitous. No difficulty, I apprehend, attaches to the supposi- tion that such an an absorption may take place ; seeing that innumerable minute ramifications of the tracheae penetrate the intestinal canal in every part : nor does there seem any difficulty in admitting that the insect may, by the power of exhausting the air from individual tracheae, draw on the absorbed fluid towards those two lateral tracheal tubes, which are apparently a general medium of communication between all the other tracheae of the body. And, when once the blood has reached this supposed point of its course, it is manifest, that by whatever means the air itself is forwarded from the same point to the most distant parts of the body, by a modi- fication of the same means, the blood may be forwarded to the same part ; and the elegant proposition of Cuvier, mdcccxxv. I i 2 36 Dr. Kidd on the that “ the blood being incapable of going in search of the air, the air goes in search of it,” will still remain inviolate. If it should be argued that the tracheae are not found charged with blood after the death of the animal, it may be answered, that neither are the arteries in the higher orders of animals found charged with blood after their death. How- ever, I have actually seen some of the ramifications of those tracheae which are connected with the caeca distended with a fluid of the same colour as that found in those organs ; and though I have only witnessed this fact in two instances ; yet such a fact, even singly taken, must be allowed to be of con- siderable importance. Of one thing I am certain, that, after careful observation, I have never found the abdominal viscera, I will not say bathed, as some authors of credit have expressed themselves, in the nutrient fluid which is supposed to have transuded through the coats of the intestines ; but I have not even found them lubricated by a greater proportion of moisture than lubricates the intestines of the higher classes of ani- mals. There is another difficulty which occurs to the hypothesis of the transudation of the chyle through the coats of the in- testines ; for, if the blood be conveyed to the several parts by previous general diffusion through the interior of the body, and then by absortion into the substance of particular organs, as the hepatic tubes, the vesicular seminales and the ovaries ; how does it happen that the bile, for instance, does not transude through the coats of the same vessels, the pores of which have admitted the blood from which it has been formed ? It may be answered, that the alteration which the 237 anatomy of the mole-cricket. blood undergoes in the several organs, changes its properties to such an extent, as to render it incapable of repassing through the pores which admitted it. I cannot of course presume to say that such is not the case ; and I am aware that many entomologists will be surprised at, and perhaps disinclined to listen to the opinion here advanced with respect to a sangui- neous circulation in insects ; but I nevertheless hope that the opinion will not be rejected without some previous attention to it. With regard to the dorsal vessel of the gryllotalpa, which in this, as in other insects, has been supposed to stand in the place of an arterial heart, I have very few observations to offer. It does not agree in its form with the description commonly given of this mysterious organ ; for though it diminishes in diameter as it approaches the head, this is by no means the case towards the other extremity of it. I have not yet completely succeeded in tracing this vessel to its anterior extremity ; because as it approaches its termination in that direction, it becomes so delicate as to have hitherto broken under dissection before I arrived at the extremity of it. Towards the opposite extremity it gradually becomes larger from the centre of the body, and terminates appa- rently in a cul de sac about the last segment but two of the abdomen. The muscles. In the gryllotalpa, as in insects in general, the muscles are exceedingly numerous, and usually very distinctly defined ; but as their form and size in different parts of the body may, without difficulty, be conjectured from the form and size of the parts to which they are appropriate, I need not occupy the time of the Society by enumerating or particularly describing them. Those which move the fore 238 Dr. Kidd on the legs are remarkable for their size, and apparently fill nearly the whole of the interior of the thorax. Some muscles, as is the case with two belonging to each mandible, and with some of those that are situated within the thigh of the hind leg, have tendons attached to them of considerable extent and strength. I must not omit to mention several parallel muscular bands, which run in a longitudinal direction along the outer coat of the extremity of the great intestine, and are inserted into what may be called the sphincter of the rectum : these muscular bands may evidently assist, by their previ- ous contraction and subsequent relaxation in discharging that foetid matter, which as has been already said, the animal usually emits when irritated. For the discovery of these muscles I am indebted to Mr. Whessell, whose name I have before mentioned on a similar occasion. The nerves * In removing the integuments throughout the whole length of the lower surface of the body, we discover a series of nine ganglions, of a pale cream colour, distributed at unequal intervals from the commencement of the esophagus to the termination of the rectum ; a double medullary cord being continued from one ganglion to another throughout the whole series. The ganglions and their connecting cords lie so nearly in contact with the common integuments, that great care is requisite, lest, in removing these integuments, the nerves themselves should be removed, or at least injured. The first of these ganglions, reckoning from the anal extre- mity of the abdomen, is globular in its form ; and is situated between the intestine and the sexual organs, the latter being placed immediately under the ventral integuments. This * Vide fig. 1 1 and 12. 239 anatomy of the mole-cricket. ganglion gives off several pairs of nerves, of which by far the largest pair may be traced into the caudal antennas. The second, third, and fourth ganglions are smaller than the first, and are of an oval rather than a globular form : they each send out from two to four or five pairs of nerves. The fifth and sixth ganglions of which the former is the smallest, the latter the largest ganglion, of the whole series, are situ- ated so closely together, that it not always easy to demon- strate the connecting medullary cords. The sixth ganglion, which from its size and the number of nerves radiating from it might be called the solar ganglion, is situated between the roots of the posterior legs. The seventh and eighth gan- glions are situated respectively between the roots of the middle and the fore legs. From the eighth ganglion, which lies under the furcular bone of the sternum, two parallel medullary cords pass on to the root of the mandibles, where they unite with the ninth and last ganglion, which is situated under and in contact with the commencement of the esophagus. This ganglion, which is hollow, as perhaps all the others may be, sends off nerves to the maxilla and adjacent parts : and it sends off besides, two large and important branches which ascending on each side of the esophagus unite with two corresponding branches that descend from the brain ; which organ is situ- ated immediately in contact with the commencement of the esophagus on its upper surface : so that the esophagus is placed between the ninth ganglion on its lower surface, and the brain on its upper surface, their connecting branches completing the nervous collar which surrounds it at this part. 240 Dr. Kidd on the The brain differs in colour from the ganglions, being of a pale brownish pink, instead of a cream colour, and in size it far exceeds the largest of the ganglions. It consists of two hemispheres, separated by a fissure, from each of which pass out four processes ; the first of these processes unites as above described, with a process from the ninth ganglion, to form the nervous collar of the esophagus ; the second passes to the root of the antenna; the third, which may be called the optic nerve, passes towards the inner surface of the cornea ; and at its extremity swells out into a fringed coronet of an orange red colour ; the fourth process, the extremity of which is also of an orange red colour, proceeds to the ocellus or stemma of the corresponding side. The upper surface of the brain is covered by a mass of soft substance somewhat resembling loose fat. The sexual organs of the female .* These organs consist of two ovaries, which occupy a considerable portion of the upper part of the abdomen, and terminate by a narrow duct in a common cavity or uterus, which opens externally under the posterior edge of the last segment but one of the ventral surface of the abdomen. Behind the uterus is an oblong white body, which originating from a cul de sac, and then doubling on itself in the form of a slender tube, terminates in the uterus. The contents of this body resemble a thin white paste. The ovaries are irregularly pear-shaped, and consist of a transparent membrane irregularly convoluted, through which the ova, enveloped in a gelatinous medium, are easily distingushed. In the same ovary the ova are fre- quently of different sizes and colours ; those which are the * Vide fig. 13. 241 anatomy of the mole-cricket . largest, and which I suppose to be impregnated, are of a brownish yellow colour; they resist a considerable degree of force before they burst, and the contents when pressed out melt as it were into a soft jelly, leaving a tough mem- brane which enveloped them. The smaller ova are of various sizes and of nearly a white colour, and of a much more slender and compressed form than those which I have sup- posed to be impregnated. This difference in the degree of maturation corresponds with a fact stated by Rosel, that the mole-cricket does not deposit all the eggs of the season at one time. In a few instances I found two or three ova which had entered the narrowest part of the duct and were very near the uterus ; and from the appearance of these, which may fairly be supposed to be, if not impregnated, at least in a state fit for impregnation, I have ventured to derive the character of the impregnated ovum. The sexual organs oj the male .* I had dissected several male gryllotalpae before I was fortunate enough to meet with the sexual organs fully developed ; and while I had as yet met with only one animal bearing the character of full develope- ment, I was not certain whether I judged rightly of the natural state of those parts ; or whether their uncommon degree of enlargement were not the effect of disease the disproportion in size between the state in which they had hitherto occurred, and that to which I now allude is so enor- mous. However, subsequent dissections presenting the same phenomena, I have no scruple in considering them as indi- cating full developement. The testicles of the male are situated similarly to the * Vide fig. 14. 242 Dr. Kidd on the ovaries of the female, and are not very unlike in general appearance to the ovaries of young females ; they differ however in being divided pretty deeply into several unequal lobes, the free extremities of which look towards each other. They send out each a very fine capillary tube or duct ; which, descending towards the rectum, is in one part of its passage convoluted on itself so as to resemble the human epididymis partially unravelled. The excretory duct above described terminates at the bottom of a thick pouch, which is situated between the rec- tum and the ventral integuments, and in form is not very unlike, though larger than the uterus, opening externally, as the uterus does, under the posterior margin of the last but one of the ventral segments of the abdomen. The interior mechanism of this pouch is extremely curi- ous; for in the upper part there is contained an apparatus somewhat in the shape of a coronet, of the colour and hard- ness of tortoise-shell : and at right angles to the centre of this there is fitted a similarly hard and horny substance, ( in shape resembling a short flat club,) which descends towards the external opening of the pouch. Behind the pouch are situated one on each side, two oblong white bodies, which are twisted into three spiral coils, and then terminate by an inflected tube at the upper and back part of the pouch. These bodies evidently answer to the vesiculas seminales of insects in general : and resemble in their external character, and in their white pulpy contents, that oval body which is placed at the back of the uterus. There is also another pair of vesiculse seminales, as is fre- quently the case in insects, situated exteriorly to the former; 243 anatomy of the mole-cricket. more slender in form, also and much more convoluted, which apparently terminate near the points where the ducts of the testicles terminate. In the instances of full developement these bodies are enlarged to six times their usual size. Under the circumstances of full developement there is also found, though scarcely perceptible under imperfect deve- lopement, a large spherical mass, resembling a ball of eider down, situated immediately at the anterior edge of the pouch above described, and continued on from its substance. The examination of the mole-cricket has added, as appears from the description of the parts, another exception in the case of the female as well as the male to the general state- ment, that in insects the sexual organs pass out by the anus. Cuvier mentions, as the only exceptions to this law, the luli and libellulas.* Casting of the skin. The following are the only observa- tions I have had an opportunity of making as to this point of the history of the mole-cricket. In the process of moulting, the skin of the abdomen appears to split longitudinally down the middle of the upper part ; and the skin of the thorax separates in a similar direction ; but the skin of the head only separates partially in that direction, and then splits be- between the stemmata, in a direction towards each of the antennas ; so that the line of separation somewhat resembles the lambdoidal suture of the human skull. The corneas of the eyes are cast with the rest of the skin, as in the case of the snake ; but they lose their transparency, and become of a greyish white colour, Even the covering of the claws is cast. MDCCCXXV. * Regne Animale, Tom,, iii. p. 137. K k 244 Dr. Kidd on the The newly exposed surface of the whole body is covered with the same kind of down as that which covered the pre- ceding skin ; except in the case of the long bristly hairs of the caudal antennae, which apparently are produced after- wards. The colour of the body immediately after the cast- ing of the skin is yellowish white, and it remains of that colour for a few hours : it afterwards gradually darkens. The organ of sound. I have very little doubt that the pecu- liar sound which is charcteristic of this insect is produced by the wings ; for I have observed in several individuals in their perfect state, that, when irritated, they will separate their upper wings by a brisk motion laterally from each other ; and that upon their being suddenly brought back to their natural position, a sound is at the same moment produced, resembling that which I have heard the insect spontaneously produce during the season of summer ; but I could not fix the power of producing this sound to either sex exclusively. There is a peculiar organ, forming a part of the common integuments of the abdomen, and situated between the fourth and fifth stigma on each side ; the anterior portion of which consists of a tense membrane, like fine parchment, of a semi- lunar form ; this organ from its individual character might be supposed to contribute towards the production of the sound, but it is found in the female as well as in the male ; and its supposed use is not justified by the presence of any internal mechanism. In two or three instances I have perceived the internal and upper surface of the second abdominal segment, answering to what is generally called the third thoracic segment, fur- nished with two oblong concave laminae, terminating in free 245 anatomy of the mole-cricket. rounded edges, which are probably elastic ; but I feel by no means certain that these are exclusively characteristic of the male, though I certainly found them most distinctly deve- loped in a male individual. But my acquaintance with the interesting insect, the history of which has formed the subject of this paper, did not com- mence till towards the close of that period of the summer during which the animal is heard to produce its peculiar sound : and I propose therefore to resume the investigation of this point at a future opportunity. Oxford , Nov. 13, 1824. Dimensions of a full grown mole-cricket. Length of the body from the extremity of the lip to inches. the extremity of the vent - - 2.0 Length of the head - - - 0.165 thoracic division - - - 0.5 abdominal division - - - 1.33 Breadth of the thorax - - - - - 0.5 abdomen - - - - 0.5 Length of the antennae of the head - - 0.825 caudal antennae - - 0.666 Length of the whole alimentary canal - - 2.0 esophagus - - - 0.5 Length from the crop to the great intestine - 0.5 Length of the great intestine - 1.0 246 Dr. Kidd on the anatomy , &c. EXPLANATION OF PLATE XV. Fig. 1. Skeleton of the head, viewed from the under side. Fig. 2. A side view of the animal in its common attitude. £ - » • Fig. 3. Skeleton of the thorax. Fig. 4. Sternum, &c. with the upper part of the thorax adhering. Fig. 5. Exterior surface of the left fore leg. Fig. 5a. Parasitic insect infesting the roots of the wings; of its natural size, and also enlarged. Fig. 6. Esophagus, crop, gizzard, caeca, great intestines, hepatic organ, and anal glands. Fig. 7. Interior view of gizzard. Fig. 8. Ditto of a portion of ditto. Fig. 9. Intestinal worm of the mole-cricket ; natural size, and enlarged. Fig. 9a. Upper part of great intestine, with four rows of glands, and the orifice of the hepatic duct. Fig. 10. The stigmata of the left side ; with the organ ( situated between the fourth and fifth stigmata) described in page 224. Fig. 1 1 . The nine ganglions. Fig. 12. The brain, surrounding the esophagus. Fig. 13. The female sexual organs. Fig. 14. The male ditto. Phil. 7hms. MI D C C CXKY Plate XV. p. 246. *7? Basis* SiYi/jr*? Z 247 3 XI. Further observations on Planarice. By J. R. Johnson, M. D. F. R. S. Read March 10, 1825. About three years since I presented to the notice of the Royal Society a few observations on the genus planaria. From that period to the present having had no opportunity of extending my researches to more than two or three species in addition to those formerly described, I was unwilling to trespass upon the time of the Society by any further remarks, until I had ascertained the remaining species of this genus. A circumstance, however, attending some experiments in which I have been lately engaged, of rather a strange cha- racter, forming another interesting feature in the history of these very extraordinary animals, induces me to lay before the Society the present communication. The circumstance to which I allude, is that of the P. cornuta obtaining a second or additional head by an artificial incision, thus constituting a double headed planaria. At the period of my transmitting my former paper to the Society, I was not aware that any English author had written upon the same subject ; but was afterwards much surprised on learning that a Gentleman of Edinburgh, Mr. Dalyell, had published an account of these animals in 1814, in a work, having for its title “ Observations on some interesting Phoe- nomena in Animal Physiology, exhibited by several species of pla?iaria.” Failing to procure this work at the booksellers. 248 Dr. Johnson's further observations I was at length fortunate in obtaining it through the libera- lity of its very ingenious author, who obligingly presented me with his only remaining copy. This Gentleman, after noticing the considerable reproduc- tive powers of the planarice in general, but more particularly conspicuous in that species he terms the P. felina , and which from his description I conjecture to be the P. cornuta , ob- serves, that having occasionally seen some of these creatures deviate from their natural figure in having two tails, &c. (an event however of so rare an occurrence, that I have in no instance met with such in the many thousands submitted to my inspection) it occurred to him that monstrosities of this kind might be obtained by artificial means, founding the practicabily of this measure on what had passed under his reviews. One of these monstrosities he thus describes, “ the planaria in relation to others was of small size, its tail was bifid, and out of the cleft grew a body, separated and distinct from the main trunk of the animal, which by some strange and anomalous proceeding had been surmounted by a head, lively and well defined. In subjecting this planaria to the microscope, numerous black specks, the supposed eyes, ap- peared surrounding the larger head, and they environed the margin of the smaller head also. In the course of a week or little more the posterior head had separated by spontaneous division, and had disappeared. But soon afterwards a kind of projection occupied its place ; and it was not without amaze- ment that I beheld this projection vegetate into a new head, resembling the one which had been lost. About a month having elapsed, it was well shaped and entire. My belief being thus corroborated in the probable effect of experiment, 249 on planarice . it was reasonable to conclude, that if separating parts be- came complete animals, if a mutilated trunk regained the defective portion ; and if a head, the most important of all organs, was evolved from every inconsiderable fragment, supernumerary parts might, by some particular operation, be produced ; yet it was long before reiterated trials were re- warded with success, and I had almost determined to abandon the enquiry, conceiving that a certain nicety, of which 1 was not master, should be practised, and that it had been beyond my ability to detect the secret cause of failure/' Notwithstanding the unpromising commencement of this Gentleman’s labours he still persevered, and at length noticed, that one of the planarice upon which he had made an incision a little below the head, had, to quote his own words “ an unnatural prominence, which interrupted the general contour of the side. October 25th, nearly four weeks after the ope- ration, the superfluous reproduction was clearly recognised to be the rudiments of a new head. On the 18th of Novem- ber the operation of nature was fully accomplished ; a new and perfect body crowned by a head had grown out of the side of the parent animal, distant about two thirds of the total length from the extremity of the tail/’ The work, from which the above extracts have been copied, being now out of print, I have taken the liberty of transferring the delineation of this double-headed planaria , under a magnified form, to the drawing accompanying this paper. Vide Plate XVI. fig. 3. With the view of ascertaining whether, in my hands, these experiments would prove equally successful, I took the ear- 250 Dr. Johnson’ s further observations liest opportunity of putting them in practice, but with evi- dent mistrust as to the result (not however in the slightest degree doubting the accuracy of the above report), conceiving that no circumstance of this nature had yet occurred, in the many and repeated experiments I had performed upon these animals during the past and the preceding summer. Having a considerable number of the P. cornutce in my possession, I took at least one hundred of the most active, and made an incision on the side of the body in each, but only succeeded in one solitary instance in obtaining the wished for result. Looking over these planariae after the lapse of nearly a fortnight, I discovered that the incisions had, in by far the greater number healed, so that no evident difference existed between them and perfect unmutilated planarize. Preterna- tural excrescenses had taken place in several, and others had separated at the place of incision so as to become two animals, but only one plan aria, as before noticed, exhibited the very singular and astonishing circumstance of a double head. The additional head was in about six weeks equally perfect and well formed with the other, although it had not yet ac- quired the usual deep colour. In fig. 1. is a delineation of this double headed planaria , such as it appeared under the mi- croscope when at rest; fig. 2. as seen when in motion. In about two months after it had acquired this additional head, a fragment separated from the tail ( the most usual place of separation) and was in progress towards its entire reproduc- tion, when it was accidentally lost — a second, and ultimately a third fragment was spontaneously separated from the same 251 on planarice. animal. A delineation of these as they at present appear, (magnified) is given in fig. 4 and 5. The light portions show the parts renewed. The planar ice submitted to my experiments were, it must be confessed, from their long previous confinement, but ill adapted for the purpose ; I think it therefore more than pro- bable, that a different result would have followed, had these planarize been active or vigorous, or but recently taken from their native abode. From the number of experiments made both by Mr. Dalyell and myself, and from the very few instances in which they proved successful, it may be reasonably inferred, that the production in the same animal of a second or addi- tional head, is a circumstance of unusual and extraordinary occurrence, and as such may not be unworthy a record in the pages of the Philosophical Transactions. In addition to my former remarks on the P. cornuta and P. torva , I have to observe, that I kept a considerable number of each of these species the whole of the last and the former summer, and not having noticed, during that period, any other mode of perpetuating their kind, than that of their de- taching small fragments either from the head or tail, I am of opinion they do not, like the other planaria? — at least those I have examined, propagate by eggs ; and this may suffi- ciently account for the reproductive power being so very conspicuous in these species. The P. torva, however, does not possess this principle in so high a degree as the P. cor- nuta. In one instance, I recollect one of the latter species casting off two fragments from the tail, the very same night L 1 MDCCCXXV. 252 Dr. Johnson's further observations it was taken, which were only prevented from becoming perfect animals, by an accidental occurrence. Having found the hirudo vulgaris or common rivulet leech to produce its young in greater number when kept separate, I thought the planarice might be similarly affected. To ascer- tain this point, I took several of the P. c.ornutce and placed them singly in separate vessels, and in another vessel, by way of contrast, about an equal number together. During the first fortnight scarcely any fragments were detached from the latter, whilst the former, with but few exceptions, had each gone through this process ; some indeed throwing off' or detaching more than one fragment. This spontaneous separation occurring so soon in those planarize kept apart, led me to think it was owing to the necessity then existing of continuing their species. Hence it would also appear, that this process is at all times under command of the animal, and may be called into action upon any particular emergency. And this I think the more evident, from the circumstance of my having lately placed three lively planarize in the glass globe where the double headed planaria had been hitherto confined alone — that spontaneously divided within the short space of four days, (Dec. 24th) in the manner represented in fig. 6 , 7, 8. In regard to the planarize placed together, although at first extremely indolent, yet they ultimately threw off as many fragments as in the former case ; thus proving, that their being kept together or separate makes no further dif- ference, than that where the demand is strong upon them to perpetuate their kind, this process is sooner brought into operation. * on the pi anarice. 253 The following is the result of this experiment during the first month. No. ofPlanariae. No. of Fragments. 15 * placed together, threw off 16 10 separately - 13 25 produced - 29 These 25 planarise, now placed together, detached in the course of the second month 33 additional fragments, making a total of 6 2. Supposing therefore this operation to con- tinue in full force eight months in the year, (and I find it unchecked even in the present month of January) we should have in the whole 248 fragments, an average of about 10 to each planaria ; but if we allow these creatures to multiply in a double or treble degree when at liberty, and supplied with proper food, we may then form a tolerable estimate of the extent to which their reproductive powers might be carried. In concluding this history of the P. conmta, I may remark, that the smallest portion detached from the tail, so small in- deed as to be scarcely perceptible, is sufficient to constitute the active principle or germ of the future animal ; but in this case these animals when perfect are so extremely small, as to lead one at the first glance to believe that the parent ani- mals produced their young perfect and in a living state ; that they were in fact viviparous. I shall close this paper by a few general observations on the planaria nigra , the most common of the British planarize. 254 Dr. Johnson’s further observations P. nigra. Planaria oblonga, nigerrima, antice truncata. Long. 5 lin. Lat. 2 lin. Body, of a fine glossy velvety black, convex above, with an elevated ridge in the centre ; plain beneath, truncated before, slightly pointed behind ; two ventral foramina ; numerous eyes. This little animal, of which a front view is given of its natural size in fig. 9. is the most sluggish and inactive of all the planarice I have yet examined. It is commonly found in ditches, attached to the under part of leaves, stones, &c. ; it is often seen traversing the surface of the water in an inverted position like the glossoporce. This species, like those formerly described, is furnished with a retractile trumpet-shaped proboscis , issuing from a cir- cular aperture in the middle of the abdomen, and so capable of extension, when in search of food, as to equal in length the animal itself. A delineation of this curious apparatus, (which I shall in future take as a characteristic type of the genus I am describing) is given in a magnified view of the under part of one of these planarias in fig. 10. This singular apparatus by means, of which these animals take their food, is not the least of the many strange features in their history ; it is indeed so far removed from the com- mon mode of receiving aliment, that doubts might well be entertained as to its real office, were it not clearly pointed out by Muller, and the ingenious author of the work to which we have recently alluded. The P. nigra is oviparous ; each ovum, or more properly 255 on planarice. speaking, capsule, producing from 2 to 6 young. The period at which the young are excluded varies with the prevailing temperature ; the shortest period as seen by the following tables being 20, the longest 53 days, making a difference in this respect alone of more than a month. No. or Ova or Capsules. When deposited. No. of young. When evolved. No. of days. 5 Aug. 5 16 Sept. 25 51 1 7 5 29 53 4 14 9 30 47 5 18 51 IO 23 12 Sept. 2 48 22 20 27 capsules containing 109 young, being an average of four young to each capsule. The P. nigra , if artificially divided in two or more parts, will have the lost portion restored in about a fortnight or three weeks. One of these under a magnified form, with a renewed anterior extremity, is delineated at fig. 11, for the purpose of showing a circular range of black specks, or what are commonly called eyes, surrounding the outer margin of the head. This species does not, as far as I have been able to ascertain, separate like the P. cornuta by spontaneous divi- sion ; although, in common with the genus to which it be- longs, it is enabled to repair any mutilation to which it may have been exposed. J. R. JOHNSON, M. D. F. R. S. Bristol, Jan. ii, 1825. I 256 Dr. Johnson' s further observations, &c. EXPLANATION OF PLATE XVI. Fig. 1 and 2. P. cornuta (front view magnified) with an additional head, as seen when at rest and in motion. Fig. 3. P.felina with an additional head and body, (pro- bably the same species as the above. ) Fig. 4. A separated fragment from fig. 2. now become a perfect animal ; the lighter portion shows the part recently renewed. 5. Another fragment from the same animal, in its progress towards acquiring a new head. Fig. 6, 7, 8. Spontaneous divisions of the P. cornuta. Fig. 9. P. nigra, front view ; natural size. Fig. 10. Ditto, back view, magnified ; with the trumpet- shaped proboscis extended as in search of food. Fig. 11. Ditto, front view magnified ; showing a renewed anterior extremity, with a circular range of black specks or dots, supposed to be the eyes. mi. Trans. MD CCCXXV. Flats XVI. p. 206. Fig. 2. Ffy- 4 ■ Ftp. 7. Tip. S. I Fip. 6. I Fio. 5. , i Fiy.20. Ftp. 9. I Fu?. 77 . d*ZT “ — *7? Zfasnrr v. I C *57 3 XII. On the influence of nerves and ganglions in producing animal heat. By Sir Everard Home, Bart. V . P. R. S. presented by the Society for the Improvement of Animal Chemistry. Read March 17, 1825. X n considering this subject, I shall first mention that in the most simple animal structures endowed with life, large enough to admit of dissection, brain and nerves are met with, although many such animals possess no power of pre- serving a temperature higher than that of the atmosphere by which they are immediately surrounded. In the oyster and fresh water muscle the whole nervous system consists of two small rounded bodies ; of these one is placed upon the oesophagus, one at the opposite end of the body of the animal ; they are connected together by two lateral nerves, one on each side. The internal structure of both these rounded bodies is the same, and resembles that of the brain in other animals, which I have already shown to be composed of small glo- bules, surrounded by a transparent elastic gelatinous liquid : having this structure I shall consider them to represent the brain and the spinal marrow of the animal. The temperature of the oyster does not exceed that of the surrounding water, since a small thermometer introduced between the shells when kept open by a wedge undergoes no change. 2 58 Sir Everard Home on the influence oj In the garden snail the nervous system resembles that of the muscle, but has also numerous nervous branches going to different parts of the body. The temperature of this spe- cies of snail, when its operculum is closed, does not exceed that of the surrounding air : this is proved by making a hole in the shell and introducing a small thermometer, in which the mercury undergoes no change. It therefore appears that the existence of brain and nerves does not necessarily endow the animal with a power of pro- ducing heat. In the leech, the earth worm, and all the insect tribe, the brain and spinal marrow very closely resemble that of the garden snail ; but in all these tribes there is a pair of nerves running down from the spinal marrow the whole length of the body of the animal, which are united together at regular intervals by what are called ganglions, composed of nervous fibres, apparently entangled and agglutinated together ; and in all such animals it was proved by Mr. Hunter, in his paper on heat, that their temperature exceeds that of the atmosphere when below 56°, although in very different proportions ; the excess in the leech being only one degree, while in a hive of bees it is 2 6°. As the only difference between the nervous systems of those animals that have no power of producing heat, and those that have, consists in there being ganglions, I was led to suspect that this power was derived from the gang- lions with which the nerves are furnished. Their structure is shown in the splanchnic ganglion. To ascertain how far there were sufficient grounds for this suspicion, I began to consider, whether any parts of yierves and ganglions in producing animal heat . 259 animals possessed of an unusual temperature were devoid of nerves ; the heat of the deer's horn while inclosed in its velvet in June 1824, when only one foot long, I found to be 96°, and on the 12th of July the tip of an antler was 99-5- ; from which it was evident that these horns during their growth have a power of producing heat, independent of the direct influence of the brain or heart ; and therefore it was only necessary to ascertain whether there are nerves accom- panying their blood vessels, which Mr. Bauer not only ascer- tained to be the case, but found them equally numerous with the arteries themselves. This discovery enabled me to institute an experiment, which at once would decide in what degree animal heat was under the influence of ganglionic nerves. As I might be considered too partial an evidence respect- ing the different results arising out of such an experiment, I contented myself with superintending it, and made over the operative part to Mr. Mayo, and his associate Mr. Caesar Hawkins, teachers of Anatomy in Berwick-street. The experiment was to consist in dividing all the trunks of the nerves that supplied the velvet of one horn, while those of the other horn were left entire ; and see how far under these circumstances the horn would be liable to any diminution of its heat. The first thing required was to examine into the number of such nervous trunks, and the situations in which they were to be met with. This was done in the head of a deer with antlers, after death. The experiment was made in Richmond Park on the 21st of July, 1824, about noon, having the dissected nerves be- mdcccxxv. M m Sir Everard Home on the influence of fore us to direct the operation. These were found to be the frontal branch of the fifth pair, and the branch of the fifth belonging to the first division which ascends on the outer part of the orbit : this branch in the human body is joined by the trunk of the portio dura of the seventh pair, but in the deer it has no such connection. Each of these trunks were laid bare by Mr. Mayo in the most satisfactory manner, and a probe passed under the nerve, which was then divided just where they emerge on leaving the great ganglion, which is close to the brain. That any difference in temperature of the two horns which should occur after the experiment might be registered in the most accurate manner, a hole was bored quite through each of the horns at an equal distance from the tip, just large enough freely to receive the ball of the thermometer. An hour after the nerves were divided, which was about three o'clock of July the 21st., the temperatures were ex- amined, and so on once a day as long as there was a mate- rial difference between them. This will appear by the fol- lowing diary, only to have continued for five days. July si, Atmosphere. 66° Unnerved Horn. 72° Uninjured Horn. - 84° 22 64 - 69 - 95 23 64 - 67 84 24 64 - 7 6 84 25 67 - - 87 - 90 Forty-eight hours after the nerves were divided the tem- perature of the horn was only 30 higher than that of the atmosphere. From the time the experiment was made the deer was 26 1 nerves and ganglions in producing animal heat. kept in a small paddock with two companions. On the 26th of July it had bruised the horn so much, on which the experiment had been made, that the diary could no longer be continued, and that horn was then the hottest of the two. Upon examination after death no union had taken place between the divided trunk, but it was evident from the reco- very of its heat, that some other connection had been formed between the nerves of the horn and these of the head. This will not appear surprising when I mention that the fallow deer, before they have antlers, shed their horns in June; and immediately after, they again begin to bud, and in the middle of August are completely hardened. Those with antlers mew in April or May, according to their keep, and at the end of August are at their full growth. So that in the space of four months all the nerves that are to supply the deer’s horns of a full head have not only begun to form, and arrived at their full growth, but have ceased to exist. This rapidity of growth accounts for their recovering in five days from any check that can be given to their ready communi- cation with one another. Having gone thus far in my enquiry respecting animal heat, I was determined not to proceed till I had satisfactorily made out whether the placenta is furnished with nerves ; and upon that discovery being made by Mr. Bauer’s admi- rable microscopical observations, I found copious new mate- rials to enable me to prosecute the enquiry. The first step I took was to get my young friend, Mr. Caesar Hawkins, to examine and describe the ganglions 262 Sir Everard Home on the influence of belonging to the nerves of the uterus, those of the nerves of the oviducts in birds and of reptiles, which were found to be more numerous than those of other organs. Mr. Haw- kins's description of them has a place in my paper on the Nerves of the Placenta in the Transactions. The temperature of the human os tineas in health was 990, half a degree lower than the antler of a deer with full-head, in July ; but as I knew the nerves belonging to the uterus enlarge during pregnancy, I had no doubt that the tempe- rature of that organ would be increased at that period : in this I was confirmed by finding the oviduct of a frog ready to spawn two degrees hotter than the heart. Upon inquiring among my medical friends who practise midwifery respect- ing the heat of the pregnant uterus, I was told, that in turn- ing children, they sometimes found the heat of the cavity almost greater than the hand could bear. This information made me most anxious to have its temperature ascertained by a thermometer, as I knew that water heated to 1250 degrees is nearly as hot as the hand can well bear. Upon this occasion I applied to Dr. Granville, who has upon former occasions assisted me with his knowledge on these subjects, having shown what becomes of the remains of the corpus luteum in ovarial abortions ; and ascertained that the two ovaria are equally productive of male and female children, which had been denied ; and till Dr. Granville took up the enquiry, remained without proof. Upon this occasion Dr. Granville gave me most cordially his assistance, and ] laving been supplied with a proper thermometer sent me the following reports. nerves and ganglions in producing animal heat. 2 63 First report. In a natural labour, duration three hours. The heat of the uterus before delivery - 108° after delivery - 105 Placenta - - - - 104 The pulsations at the wrist of the mother - 70 beats in the navel string - - 140 Second report. In a labour at 7 months ; child alive. The heat of the uterus before delivery - ioo° after delivery - -99 Placenta - - - 98 The pulsations at the wrist of the mother - 60 beats in the navel string - - 110 The third report. In a labour that lasted 38 hours. The child alive, (delivered by forceps). Six hours before delivery in the intervals of the pains, the heat of the uterus - - 11 8° When the pains strong ^ - - 120 After delivery - - - 110 The placenta - - - 110 The pulsations at the wrist of the mother - 100 beats in the navel string - 120,, Sir Everard Home on the influence of The fourth report. In a labour that lasted 40 hours ; the pelvis deformed. The heat of the uterus was not accurately ascer- tained before delivery. after delivery - - 1150 When placenta expelled - - - - 118 The placenta itself - - - 112 The instant the child breathes, the pulsations in the chord begin to decrease in frequency till they become the same as at the wrist of the mother, and then cease. As the balls of some thermometers are so thin, that any pressure made upon them raises the mercury, and renders the instrument inaccurate, it is necessary to remark in this place, that the thermometer employed by Dr. Granville was not capable of having its mercury raised a single degree by the greatest pressure upon the ball that could be made without risk of breaking it. When the heart of a dog is in action, the heat in the left ventricle is 101, and is the same in the stomach, so that mus- cular action does not increase animal heat ; and the follow- ing circumstances, mentioned in Mr. Hunter's paper on this subject, in his work on the Animal CEconomy, proves that its increase or diminution of heat is independent of the action of the arteries. A gentleman while in a state of insensibility from an apoplectic fit, and lying in bed covered up with blankets, had his whole body atone instant become extremely hot, and then suddenly extremely cold, his pulse all the time undergoing no change. The glow of heat brought into the cheek in the act of 265 nerves and ganglions in producing animal heat. blushing, from whatever cause, has been generally considered to arise from the rush of blood into the smaller vessels ; it must however depend on the state of the ganglionic nerves. Although the nerves when performing their functions in health appear to have no power of producing or keeping up the heat of the animal, there is no doubt that when they are injured or diseased, heat is produced. Of this in the prac- tice of surgery the proofs are without end. 1 do not mean at present to go further into this subject, since it would lead me into discussions of some length, re- specting the real cause of the increase of temperature excited by inflammation and fever ; as however in the first the * heat never I believe exceeds the standard heat at the heart ; whereas in the second it is raised to 104° or 105°; it is reasonable to believe that the first is from affections of common nerves, the other from affections of ganglionic nerves. As the torpedo and electrical eel were among the first animals that I ever assisted to dissect, and Mr. Hunter's account of the structure of the electrical organs, and the wonderful supply of nerves with which they are furnished, was laid before the Royal Society in July 1773 ; three months after I had enlisted under his banner for the purpose of pro- secuting human and comparative anatomy, it will only be considered as natural, that I cannot conclude the present communication, without stating, that the nerves of the tor- pedo belonging to the electric organs, however numerous, not being ganglionic, do not increase the standard heat of the animal. 2 66 Sir Everard Home on the influence of As fishes have a lower standard of heat than birds, I wished for some accurate information respecting the ganglions their nerves are furnished with, to determine the proportion they bear to those in birds. I was also desirous of knowing whether there are any ganglions belonging to the nerves that supply the electrical organs of the electrical eel. Mr. Hawkins's report on both these subjects I shall give in his own words. “ My dear Sir. In the skate I find the following ganglia. “ The olfactory nerve expands into a ganglion of great size, from the lower surface of which many nerves proceed to the membrane of the nose. “ The fifth pair of nerves has a plexiform appearance, chiefly on its inferior or lower root. The lower of the two branches into which the ophthalmic nerve divides has a distinct ganglion upon it. “ The portio dura of the seventh pair of nerves forms a ganglion while passing through the cartilage of the ear. “ The eighth pair of nerves after passing through its fora- mina enlarges considerably, and that branch which passes along the oesophagus to the stomach forms a considerable plexus on the end of the cardiac portion. “ The spinal nerves originate by two roots, as in quadru- peds, and on the posterior root a ganglion is formed. “ The sympathetic nerve has several ganglia where the branches of the spinal nerves join it ; but instead of there being a ganglion at every such junction, as in the quadruped, they are only in the proportion of one to six. “ In examining the preparations of the elecric eel and torpedo in the Hunterian Collection, no ganglia are met with 26 7 nerves and ganglions in producing animal heat. in the nerves that supply the electric organs ; each of these nerves arises separately from the brain, and consists of nu- merous fasciculi. yours, &c. (LESAR HAWKINS/' From Mr. Hawkins's examination the ganglions in the skate do not amount to one-sixth part of those in the bird, and the standard heat of this fish is low in proportion ; the thermometer in the stomach being only 40°, in the rectum 38°, while the surrounding water was 36°. . EXPLANATION OF PLATE XVII. In which is exhibited the external and internal appear- ance of the great splanchnic ganglion. Fig. 1 . The ganglion in situ upon the aorta ; natural size. Fig. 2. The ganglion enclosed in its outer or dura matral covering ; magnified two diameters. Fig. 3. A longitudinal section ; magnified in the same degree. Fig. 4. A small portion from which the outer or dura matral covering has been removed, but is still inclosed in the inner or pia matral coat ; magnified six diameters. Fig. 5. A longitudinal section ; magnified in the same degree. Fig. 6. A very small portion of the internal substance of the ganglion ; magnified twenty diameters, to show that it consists of fasciculi of globular fibres from -3 Q*Q Q to part of an inch in diameter, similar to those in the brain, connected together by a transparent elastic jelly : this jelly mdcccxxv. N n 268 Sir Everard Home on the influence of the nerves , &c. is so much less readily soluble in distilled water than that met with in the brain, that after eight days maceration in it, the fasciculi are not so readily separated as those of the brain are in two. Fig. 7. A portion of a single globular fibre in its natural or contracted state, only part of an inch long. Fig. 8. The same portion of fibre extended by means of the great elasticity of the jelly which connects the globules, to more than double its former length. P/iil. 7ra/u>\ ~MJD CCCX3CV. Plate XVI I • p. z6& Jf ftasisY sculp ? C 269 ] XIII. An Essay on Egyptian Mummies ; with observations on the art of embalming among the ancient Egyptians. By A. B. Granville, M.D; F. R . S; F. L. S; F. G. S; M. R. /. one of His Royal Highness the Duke of Clarence's Physicians in Ordinary , &c. &c. Read April 14, 1825. In the year 1821, Sir Archibald Edmonstone, whose interesting work on two of the Oases of Upper Egypt has been so favourably received by the public, presented me with a mummy, which he had purchased at Gournuu, on the 24th of March, 1819, from one of the inhabitants of the sepulchral excavations on the side of the mountain, at the back of which are the celebrated tombs of the kings of Thebes. It cost about four dollars. There was no outer case to it ; and it is difficult to conceive how the beauty and per- fect condition of the surface of the single case in which the mummy was inclosed, could have been so well preserved without any external covering. It appears from Sir Archi- bald’s testimony, confirmed by my own observations, that the mummies which have a second, or an outer case, like the one bought at the same time by Sir Archibald Edmond- stone's fellow traveller, Mr. Hoghton, and now lying un- opened at his seat near Preston, in Lancashire, have been folded, externally, with greater c; re than the one about to be described ; and that the outward folds are ornamented with variegafed stripes of linen. These observations accord with those made by Jomard and Royer. 270 Dr. Granville's essay on The first, or inner case, too, of those mummies is covered with a kind of paper, on which the figures and hieroglyphics are painted with much greater brilliancy of colour. Similar remarks apply to the mummy presented to the Hunterian Museum at Glasgow, by Mr. Heywood, a Smyrna merchant, the second or inner case of which is said to be of wonderful beauty and brilliancy. The single case of the mummy which I am about to de- scribe, appears to be made of sycamore wood, two inches in thickness, consisting of two equal portions (anterior and posterior, as the case is made to stand on its feet) fastened together by pegs of the same material. It is covered, inside and out, with a kind of shell, or coat of plaster, or lime, of considerable thickness. Externally, this coat is painted with symbols and hieroglyphics running in horizontal and longi- tudinal lines laid on a deep orange ground, the whole being highly varnished. Internally, the surface is divided into hori- zontal broad stripes, except at the sides, where the stripes run in a perpendicular direction. These stripes are alter- nately white and yellow, and on both are inscribed hiero- glyphic characters an inch in length, constituting, to all appearance, one continued composition ; probably a prayer, or invocation for the dead ; or the biographical record of the individual contained within the case. The form of the case is that known to belong to most of the Egyptian mummies brought to Europe, and will be better understood by inspection of Plate XVIII. fig. 1. It mea- sures six feet five- tenths of an inch in its greatest length ; and its circumference taken at three different points, the supe- rior or shoulders, the central, and the inferior, immediately 271 Egyptian mummies. above the feet, is 5 ft. 2 in., 4ft. 11 t3q in., 3 ft. 8 in. The case is now deposited at my house. When the mummy came into my possession, it was pre- cisely in the state in which it was found when the case was first opened by Sir Archibald Edmondstone, covered with cerecloth and bandages most skilfully arranged, and applied with a neatness and precision, that would baffle even the imitative power of the most adroit surgeon of the present day. There is no species of bandage which ancient or modern sur- gery has devised, described, or employed, that did not appear to have been used in securing the surface of the mummy from external air ; and these are repeated so many times, that on weighing the whole mass of them after their removal, they were found to weigh twenty-eight pounds avoirdupois. In unravelling these complicated envelopes in the presence of two or three medical friends, and Sir Archibald himself, we could not but be struck with the precision with which the circular, the spiral, the uniting, the retaining, the ex- pellent, and the creeping roller had been applied. The neat- ness of the turns, and the judicious selection of their size, length, and forms, in order to adapt them to the different parts intended to be protected, and calculated so as to give to the whole an air of smoothness without a wrinkle, or the least appearance of slackness from the varying form of the limbs, were really surprising. We here met with the couvrechef, the scapularium, the 18-tailed bandage, the T ban- dage, as well as the linteum scissum , and capistrum. Nor were we less pleased to find the many pieces of r.eatly folded linen, placed like compresses, in all those parts of the body, 272 Dr. Granville's essay on which, presenting natural depressions, or hollows, would, unless thus filled up, have proved as many obstacles to the firm and steady application of the bandages. Each limb, nay, each finger and toe, had a separate bandage next to the skin. These observations respecting the art of bandaging among the ancient inhabitants of Egypt, as displayed in their best class of mummies, have not, as far as I recollect, been made before to the extent here alluded to, and will throw a new light on the history of that branch of practical surgery. The principal rollers appear to be made of a very compact, yet elastic linen, some of them from four to five yards in length, without any stitch or seam in any part of them. There were also some large square pieces thrown around the head, thorax and abdomen, of a less elastic texture. These pieces were found to alternate with the complete swathing of the whole body. They occurred four distinct times ; while the bandaging, with rollers and other fascia?, was repeated, at least, twenty times. The numerous bandages by which the mummy was thus enveloped, were themselves wholly covered by a roller three inches and a half wide and eleven yards long, which, after making a few turns around both feet, ascended in graceful spirals to the head, whence descending again as far as the breast, it was fixed there. The termination of this outer roller is remarkable for the loose threads hanging from it in the shape of a fringe, and for certain traces of characters im- printed on it, similar to those described and delineated by Jomard in the Description de l’ Egypte. One or two of these 273 Egyptian mummies. characters have corroded the linen, leaving the perforated traces of their form. A fac-simile of this curious fragment will be found in Plate XVIII. fig. 3. Besides this outer fascia, there was another bandage thrown over the head, brought in front of the chest, crossed there, and carried behind the back, where, being crossed also, it was again brought in front to be once more crossed and returned backward, and ultimately stretched from be- hind, before, down to the feet, where it crossed a third time in the manner delineated with great precision in Plate XVIII. fig. 2. The shape, form, and position of the limbs lay thus completely concealed, the mummy presenting a homogeneous outline resembling an elongated oval, the superior end of which was twice the width of the inferior. There was, besides, laid upon the face, above the ban- dages, a thick mass of linen, by no means neatly folded up, covered by a considerable layer of a black bituminous sub- stance, which became soft on long exposure to moisture, but which, while in that situation, most effectually concealed the features : so that in the present instance, there appears to have existed no desire in the surviving relatives to preserve the lineaments of a cherished friend, as must have been the case with regard to those mummies described by more than one author, in which the bandages applied to the head, had been so skilfully managed as to retain every feature of the face. The other remaining observations with which I shall trou- ble the Society on the subject of these bandages, have refe- rence to the materials of which they are made, and the substance with which they seem to be impregnated. 274 Dr. Granville’s essay on I have satisfied myself that both cotton and linen have been employed in the preparation of our mummy, although Herodotus mentions only cotton ( Byssus ) as the material used for the purpose. Most mummies have been described as wholly enveloped in linen cloth, and some persons are disposed to doubt the existence of cotton cloth in any, not excepting in the one now under consideration. But with respect to the last point, a simple experiment has, I think, set the question at rest. If the surface of old linen, and of old cotton cloth be rubbed briskly and for some minutes with a rounded piece of glass or ivory, after being washed and freed from all extraneous matter, the former will be found to have acquired considerable lustre ; while the latter will present no other difference than that of having the threads flattened by the operation. By means of this test I selected several pieces of cotton cloth from among the many bandages of our mummy, which I submitted to the inspection of an experienced manufacturer, who declared them to be of that material. ' Having removed, after an operation of upwards of an hour, the various envelopes of the mummy, I directed my attention to its anatomical condition and state of preservation. It was at once ascertained that the subject was a female, and that no ventral incision, as described by Herodotus, had been practised to extract the viscera. The external parts of generation, on which not a vestige of hair was found, had been brought in close contact, and notwithstanding their shrivelled condition, were readily recognised. The mammas must have been large during life, for they were found to extend as low down as the 7th 2 75 Egyptian mummies. rib, against which they are closely pressed by the arms pass- ing over them. But on lifting the latter, the breasts them- selves were raised with little exertion. Of these organs there remain, of course, little more than the integuments, which are of considerable thickness, and exhibit the nipples with their surrounding areolae in a perfectly distinct manner. The head is closely shaved ; the short hair, which is of a brown colour, can be felt on passing the hand over it ; and on close inspection, may be distinctly seen. Externally the cranium appears not to have been disturbed in any way. The eyelids were in close contact. The nose has been flat- tened down towards the right cheek, by the action of the bandages. The lips, from being retracted, allow the teeth of the upper and lower jaw to be seen, perfectly white and in a sound condition. The arms are crossed over the chest, the fore arms directed obliquely upwards, towards the extremi- ties of the shoulders. The fingers of the left hand alone were bent inwardly, the thumb remaining extended. No papyrus, or other object of interest was found within the grasp of the left hand, but a mere lump of rags which had been previ- ously dipped in the same bituminous substance observed in other portions of the envelopes. It is well known that papyri, idols, and other objects have been found placed under the arm pits of some of the mummies ; but here nothing of the sort was discovered. Only a few glass beads of a blue and green colour, and bugles in all respects similar to those which decorate the dresses of our modern ladies, and made of the same mate- rial, dropped from between some of the folds of the bandages, while we unrolled them, as if they had been thrown in gra- mdcccxxv. O o 2 76 jD r. Granville's essay on tuitously during the operation, by workmen who had been employing a large quantity of the same ornaments in pre- paring some more costly mummy, such as is described by Jomard. It will be recollected, that this gentleman found some mummies in which glass bugles and beads in profusion, disposed in a sort of trellis-work , imbedded on bituminous substance, had been fixed here and there, over the surface of the body, in obedience, no doubt, to instructions received to that effect from the opulent surviving relatives. I am the more inclined to adopt the above conjecture with regard to the presence of the few beads and bugles found in my mummy, from the circumstance of my having found, like- wise, a portion of reddish clay with characters painted on it, (either a fragment of the wall of the chamber in which the embalmers were at work, or of some case belonging to ano- ther mummy ) placed in such a manner as to act as a compress on the inside of the left leg in contact with the skin Here it served to fill up a hollow which it accurately fitted ; thus keeping the bandage, which passed over it, perfectly tight, but which would otherwise have been slack. This instance of indifference in the choice of materials to produce a parti- cular end, on the part of the embalmers, would, in my opi- nion, account also for the accidental presence of the beads; and renders it unnecessary to seek for any learned or recon- dite explanation of their object. Following up my description of the external appearances of our mummy, 1 have to remark that the inferior extremi- ties were brought together in close contact at the knees and feet, which latter were kept in that position by a contrivance similar to that which obtains to this very day in most parts Egyptian mummies. 277 of Europe, of fastening the two great toes by means of a piece of rag or tape. Numerous and deep wrinkles appeared on the integu- ments of the abdomen, denoting that before death, this part of the body must have had very considerable dimensions ; a con- jecture, the correctness of which subsequent inquiries have completely demonstrated. All these general appearances are well marked in Plate XIX. The general surface of the body is of a deep brown colour, approaching to black, and is quite dry. In parts where the larger muscles lie, as the thighs for instance, the surface feels quite soft to the touch, and the muscles yield slightly to pressure. The cuticle appears to have been removed through- out, except at the extreme points of the fingers and toes, where it can yet be seen curled up, retaining the nails, of a deep brown colour, in their situation. Some of these, how- ever, quitted their fastening when the slightest attempt was made to detach them. The dimensions of the mummy appeared to me to deserve the next consideration ; and they were taken with great accuracy. Such an opportunity as that before me, of ascer- taining the size and proportions of an Egyptian woman, who had probably lived before the building of the pyramids of Memphis, could not be allowed to escape ; especially as no admeasurement of a really perfect female mummy has been recorded in modern times. I deemed it, therefore, an object of importance in the study of the natural history of man, to have those admeasurements ascertained with precision. It is well known, that the Egyptian form has been assumed as 278 Dr. Granville’s essay on the type of a specific variety of the Ethiopian race, parti- cularly by the venerable Blumenbach, from certain supposed peculiarities of outward conformation. The consideration of what follows will enable us, as far as a solitary instance can do, to judge of the correctness of such conjectural gene- ralizations. Height of the mummy from the vertex of the Feet in. head to the inferior surface of the calcaneum 5 o.T75 Thus divided. Length of the head from the vertex to the first vertebra of the neck - - - - o 6. Length of the back bone from the first vertebra of the neck, to the articulation of the os sacrum with the os coccygis - - - - 110 Length of the thigh from the centre of the head of the femur to the centre of the knee pan - 1 5./0 Length of the leg from the centre of the knee pan to the inferior surface of the calcaneum 1 3./^ Total 5 o./o The dimensions of the upper extremities and of the foot, are these : Feet. Inch. Length of the arm - - - 1 i.T% of the fore arm - - - o 9.^ ■- of the hand from the tip of the middle finger, to the articulation at the wrist - 07 Length of the foot - - - o 7.1V These dimensions will be found accurately marked in Plate XIX. 2 6. 279 Egyptian mummies. Now we find, on comparing the principal of these dimen- A sions, with those of the Venus de Medicis, as given by Win- kelman, Camper, and others, that the difference between them is so slight, as not to deserve notice. Our mummy is that of a person rather taller. The celebrated Medicean sta- tue, which stands as the representative of a perfect beauty, is five feet in height, like our mummy, and the relative ad- measurements of the arm, fore-arm, and hand in each, are precisely similar. But in a female skeleton, it is the pelvis that presents the most striking difference in different races. Nothing, for instance, can be farther removed from the symmetrical form, and from the dimensions of the pelvis in the Caucasian or European race, than the same part in the Negro or Ethi- opian race. Of this fact, I shall be able to convince such of the Fellows of this Society, as are not conversant in these matters, by exhibiting the most perfect pelvis of a well grown Negro girl, which I prepared some years ago, in contrast with that of our mummy, which I likewise carefully dissected, and caused to be represented by the same accurate artist in Plate XX. When subjected to this comparative test, the pelvis of our female mummy will be found to come nearer to the beau ideal of the Caucasian structure, than does that of women of Europe in general, and to equal in depth, amplitude, and rotundity of outlines, the Circassian form. In illustration of this remark, I made the following mea- surements. Greatest distance or width of the pelvis from the highest point of the ridge of the ilium on one side, jn. to that of the other side - - - - n.j% 280 Dr. Granville’s essay on Distance between the two anterio-superior spinous in. processes of the ilia - - - - 10 Distance between the tuberosities of the ischium - 3-/5 Elevation of the branches of the ischium to join the descending branches of the pubis, and form the sub- pubian arch - - - - - 3 Greatest elevation of the os innominatum or haunch bone, from the tubera of the ischium to the highest point of the crest of the ilia 8 Diameter of the pelvis. Transverse, or bi-iliac diameter - - - - 5. A Anterio- posterior, or sacro-pubian diameter - - 4.^ Oblique, or sacro-ilio-cotyloid diameter - - 5. A Not only are these the most perfect dimensions which a female pelvis can have, but they are precisely in the pro- portion which the longest diameter bears to the shortest, in the Venus of the Florentine Gallery, according to Camper, namely, as 46 to 34 ; whereas in the Negro or Ethiopian race, the proportion is 39 to 27^-, or what amounts to the same thing, the longest diameter of the pelvis of the Negro girl above-mentioned is only 3.-^ inches, while the shortest is no more than 3.-^ inches. In this respect my admeasure- ments agree with those given by Soemmering. What has just been observed of the skeleton generally, and of the pelvis in particular, applies with equal force to the form and dimensions of the head. So far from having any trait of Ethiopian character in it, this part of our mummy exhibits a formation in no way differing from the European. On looking at Plate XXI. which represents with scru- pulous accuracy the contour of the head of the natural 281 Egyptian mummies. size, it is impossible not to be struck with the likeness it bears to the skull of the Georgian female represented in the “ De - cas tertia Craniorum” of Blumenbach's very instructive col- lection. In both we have the facial angle approaching nearly to a right angle : and the configuration of the vertex and occiput in each is such, as must attract attention for its ele- gance, and the indication of a something more important than mere beauty. It may be affirmed then, that Cuvier's opinion respect- ing the Caucasian origin of the Egyptians, founded on his examination of upwards of fifty heads of mummies, is corro- borated by the preceding observations ; and that the systems which were founded on the Negro form, are destroyed by almost all the recent, and certainly the most accurate inves- tigations of this interesting subject. It is a curious fact, which has been noticed by more than one traveller, that whole families are to be found in Upper Egypt, in whom the gene- ral character of the head and face strongly resembles that of the best mummies discovered in the hypogei of Thebes ; and not less so, the human figures represented in the ancient monuments of that country. Having proceeded thus far in my inquiry into the state of preservation of the mummy before me, I determined, perfect, and beautiful as it was, to make it the object of further re- search by subjecting it to the anatomical knife, and thus to sacrifice a most complete specimen of the Egyptian art of embalming, in hopes of eliciting some new facts illustrative of so curious and interesting a subject ; for it is to be observed, that the deficiency of our knowledge on the art of preparing mummies by the ancient Egyptians, both as to the mode of 282 Dr. Granville’s essay on operating, and of the degree of perfection to which that art was carried among them, has arisen from imperfect and infe- rior specimens having been generally employed for the pur- pose of investigation, the best and most perfect mummies (resembling the one I have undertaken to describe) having, invariably, been preserved intact, and, in most cases, unco- vered, as valuable objects of curiosity, in private or public Museums. A rapid glance at what has been publicly recorded on this head, will prove the correctness of my assertion. The Royal Society itself has contributed but little towards the knowledge of this interesting branch of the natural history of man. The subject of Egyptian mummies was brought before it, by two of its members, who from talent and professional avocations, were well calculated to do it justice, had their opportunities been more favourable. The first paper on this subject in the Transactions, is by Dr. Hadley, who, in 1763, examined a mummy which he had received from the Royal Society, and an account of which he presented in the following year. The paper contains a very clear statement of the successive operations for ascertaining the real condition of the mummy, but seems not to have added much to what was already known, at that time, respect- ing the mode of preparation. The mummy retained not the smallest vestige of the soft parts, except some of the tendons of the feet, to the sole of one of which a bulbous root, perhaps an onion, was discovered firmly bound by fillets and pitch ; reminding us of Juvenal’s lines : u O sanctas gentes, quibus haec nascuntur in hortis “ Numina l11 28S Egyptian mummies. The bones were all more or less brittle, and some of them separated into splinters in the progress of the examination. After an interval of thirty years, we find the subject of Egyptian mummies again before the Royal Society, in con- sequence of a letter from Professor Blumenbach, to Sir Jo- seph Banks, being read at one of the meetings in 1794, giving an account of three small mummies, and a larger one, opened by the Professor when in London. The latter, as well as one of the former, belonged to the British Museum, and the curators had allowed him to select them from among those deposited in that national collection. In addition to these, Blumenbach re-examined the mummy of a child supposed to have been six years of age, which had been inspected be- fore. The first of these proved to be nothing else than a mass of bandages, strongly impregnated with resinous sub- stance, without the smallest vestige of a human body within them, affording another instance, in addition to those noticed by other writers on the subject, of the impositions practised either by the Egyptian embalmers, or by the modern traf- fickers in mummies. The second mummy opened by Blu- menbach proved to be that of an ibis. In the third supposed mummy, only one or two fragments of a human body were discovered ; while in the fourth, the largest, indeed the only real mummy, nothing but naked bones were found within the bandages, a result not far different from that which Blumenbach subsequently obtained from the examination of two other mummies belonging to private individuals, which he had an opportunity of opening before he quitted this country. Such is the sum total of the information to be found in the Transactions of the Royal Society on the subject of mdcccxxv. P p 284 Dn Granville's essay on Egyptian mummies, and the extent of its contributions to- wards the elucidation of this interesting topic, if we except the little that Dr. Grew has said in his printed catalogue of the Museum of the Society in 1681. Nor had the inquiries of scientific men on the continent been more successful until lately. Thus Kestner, who de- scribed the mummy at Leipzig ; Hertzog who opened the one at Gotha, in which more idols, beetles, frogs and nilo- meters were found than had ever been met with under similar circumstances; Gryphius, who in the year 1662, gave an account of two mummies in the Dispensary of Crusius at Breslau ; and lastly Brunniel, who dissected the mummy at Copenhagen, found little more than fragments of bones, or whole skeletons in a dry and unsatisfactory state. Bruck- man and Storr, the one at Cassel, the other at Stuttgard, are quoted hy Blumenbach, as having written on the subject of mummies ; but I have not had the means of procuring their descriptions, which, however, to judge from Blumenbach's language, contain no better account of the state of those spe- cimens of Egyptian art, than he himself had been able to give from his own experience. Long before either Doctor Hadley or Blumenbach had directed their attention to Egyptian mummies, Rouelle, an eminent French chemist, and Caylus, an antiquarian, had treated the same subject with minute precision, although not with better results. Of two papers, which the former had promised, one only was published in the M6moires of the French Academy of Sciences. In that paper, Rouelle has given an account of several mummies he had examined, with a view to ascertain the mode in which they had been em- 285 Egyptian mummies. balmed ; and he has described several chemical operations to which he subjected them, in order to discover the nature of the ingredients employed by the Egyptian embalmers. The result of these experiments by no means settled the ques- tion they were intended to resolve. With regard to the anatomical state of the mummies examined by him, the in- formation he has given us is very deficient. All he has said reduces itself to a repetition of the common adage “ dry as a mummy." Like Dr. Hadley, Blumenbach, and many subsequent writers, he came to the conclusion, that Egyptian mummies are invariably found in a state of aridity, without the least vestige of the soft parts or viscera, and are wholly deprived of humidity, in fact, that they are mere skele- tons enveloped in “ cerecloth. ” It will be seen, that such an opinion requires considerable modification. The next information of importance we possess on the subject of Egyptian mummies, is to be found in the third and fourth volume of the Transactions of the Royal Society of Gottingen. Of two papers on the subject by Professor Heyne contained in those volumes, the first relates to the antiquity of mummies generally ; and the second gives a description of a mummy presented by the King of Denmark, to the Museum of the Royal Society of Gottingen, on which Professor Gmelin instituted various chemical experiments detailed in a separate paper, intended to throw some light on the art of embalming. Numerous as those experiments appear to have been, conducted, moreover, with great care and pre- cision, they nevertheless lead not to more satisfactory con- clusions, than the experiments of his predecessor Rouelle, between whose results and Gmelin's there exists considerable 286 Dr. Granville’s essay on discrepancy. With respect to the state of integrity of the mummy itself, it is mentioned by Professor Heyne, that not only had the viscera been removed, but that the muscles also, and every soft part, had been taken away by accurate dissection, made with some sharp instrument ; for nothing was found to intervene between the dry substance of the bones and the bandages. It is needless in this place to advert in a particular manner to the writings of older authors, who have more frequently indulged in conjectures than adhered to facts. They have treated the obscure, yet interesting subject of Egyptian mummies, with more erudition than discrimination, and have not removed the difficulties by which it is surrounded. Much curious information, however, may be collected from their works, especially from those of Kircher, Pietro della Valle, Greenhill, Pocock, Bremond, Mallet, Dr. Mid- dleton, and others. The temporary occupation of Egypt by the French army offered a wide field of observation to the antiquarians and the men of science of that nation, the fruits of whose labours have been inserted in a splendid work which must be fami- liar to the Fellows of this Society. Among the many objects of research to be found in that work, it appears that that of mummies engaged the attention of several very competent individuals, such as Denon, Jomard, Larrey and Royer. These gentlemen directed their inquiries to the number of those preparations to be found in the many excava- tions they visited, to their state of preservation, and to the probable method by which they had been embalmed. The number of mummies discovered by them was prodigious, 287 Egyptian mummies. and although they state, that the degree of preservation in which the mummies were found varied considerably, they all agree, more or less, in asserting that, as far as they had examined them, there appeared little more than the skele- tons remaining. Jomard, indeed, mentions generally, that on removing the bandages, “ on observe un corps noir et dif- forme,” and all of them are equally silent on the fact or pos- sibility of the viscera being still in existence in any mummy. Royer, who has taken a more extended view of the subject, and has described with great accuracy, the appearances in two or three distinct classes of mummies, does not mention any of the facts in reference to them, such as T shall pre- sently relate in connection with my own mummy. This omis- sion induces me to believe that the French naturalists never met with a perfect mummy, and that, therefore, the descrip- tion of a mummy in every respect much better preserved than any that has hitherto been noticed, must be a desirable object to the antiquarian, the learned commentators on ancient historians, and to men of science in general. Baron Larrey's Memoirs are chiefly intended to determine the question of the identity of the present race of Copts with the aboriginal Egyptians, whose descent he traces from the Abyssinians and Ethiopians by a comparative examination of the crania of several mummies he had collected in the desert of Saqquarah, and of those of the modern Copts found in a cemetery near Alexandria. The mummies of Saqquarah, however, are acknowledged to be very inferior to those of Upper Egypt by all travellers ; and cannot, therefore, be put in competition with the latter, in an inquiry into the art. of embalming among the ancient Egyptians. 288 Dr. Granville's essay on Independently of the information thus collected from the writings of different authors, calculated to convince me that chance had put me in possession of a better, and a differently prepared mummy from any that had hitherto been recorded’; many curious facts corroborative of that conviction, and capable of illustrating the anatomical history of mummies in general, were communicated to me by the late Dr. Baillie, by Sir E: Home, Mr. Brodie, Mr. Clift, and others. It would appear from their statements, that the inquiry into the condition of these singular preparations had, from time to time, engaged their attention ; and that if nothing very new or very interesting was discovered by those eminent anato- mists respecting them, the circumstance is to be attributed to the cause already alluded to, namely, the imperfect state of the mummies which fell under their inspection. Both the late Dr. Baillie and Mr. Wilson mentioned to me that they were present at the opening of a mummy by Mr. Hunter, who found it to consist of a mere skeleton, with the skin over it perfectly dry ; the whole presenting so confused a mass that no one particular part could be recognised. Mr. Brodie saw and examined three mummies that belonged to Lord Mount- norris, and which he found quite dry and uninteresting. Another mummy, brought to England several years ago by Colonel Leake, and at the dissection of which Mr. Brodie was also present in 1807, was not found in better condition. The same observation applies nearly to that which my friend Mr. Hamilton, the late Under Secretary of State for Foreign Affairs, sent to the College of Surgeons, and which was exa- mined by Sir E. Home, Mr. Brodie, and Mr. Clift, in the presence of Sir J. Banks, Mr. Hatchett, and others. Mr. 289 Egyptian mummies . Brodie, who took notes of the dissection, and Mr. Hatchett, have stated to me, that there were none of the viscera in the mummy in question ; that it was not in a flexible state, and that the muscles could scarcely be distinguished. Sir E. Home himself, on the other hand, cannot tax his memory as to the precise parts discovered, the dissection not having been com- pleted, in consequence of the remains of the mummy being destroyed in some of the souterrains of the College, from the effect of dampness in a newly erected building. Mr. Clift mentioned to me that the external parts of generation were perfect ; and Sir Everard recollects that the face was in a high state of preservation. If so, it is to be lamented that a circumstance, over which Sir Everard had no control, should have prevented him from prosecuting an enquiry, which no man could have rendered more instructive ; and the pub- lication of which would probably have done away with the necessity of the present communication to the Society. Sir Everard Home made some observations on another mummy brought from Thebes by the late Captain Kennet, of the Engineers, in 1806; the particulars of which he has kindly communicated to me. The mummy in this instance was that of a male ; and, as far as could be judged from ex- ternal appearances, seemed to be in good condition. No internal examination was permitted. The head had not the appearance of that of an African. The face was entirely ex- posed, as well as the chest, and the anterior part of the abdomen. The skin was entire in all these places. On the upper part of the head, as also on the chin, the hair was preserved. The teeth were perfect, and the skin was nearly quite black, a circumstance, which Sir Everard thinks, 290 Dr. Granville’s essay on must be attributed to its having been stained with some gum. The brain had been removed through one of the orbits, into which false eye-balls had been introduced. The eye-lids were entirely removed, probably from accident. Indications of mus- cles were observed on the abdomen, the scapulae, the back, and on the nates. The legs were not uncovered ; but the toes were all exposed. The arms were placed so that the hands came upon each groin, there being a middle space at the pudendum, of about two inches, between them. The male organs were so enveloped as not to be traced in any degree whatever. Sir Everard took notice of the principal dimen- sions of this mummy, which, as affording the means of com- parison between the two sexes, may properly find a place here after those of my female mummy. Length of the body, from the vertex of the Feet, inches. head to the bottom of the heel - 5 2 Breadth across the shoulders 1 3 Length of the arms, from the top of the shoulder to the end of the fingers -2 6 Breadth from trochanter to trochanter 1 o Length of the foot - - o 9 To those who are familiar with the accounts published by recent travellers in Egypt, it will be needless to repeat that Dr. Bradley on the one hand, and Dr. Richardson on the other, acknowledge that the mummies which they had an opportunity of examining appeared to consist of little more than mere dry bones. My friend, Mr. Walter Davidson, of the house of Herries and Farquhar, has also added to my store of 291 Egyptian mummies. information on the present subject. He purchased a mummy from the excavations near Thebes, at Gournon, in February, 1820, selected out of a dozen which he opened, as the best preserved. It proved to be that of a male. It was quite dry ; the hair and teeth were most perfect, the former being very long, in great profusion, and smoothly combed down. The body contained only a large quantity of gum, and there was no flesh, or very little of it, on the bones. Every part was brittle. It was enveloped in cotton bandages to a great extent, and was contained within two cases. His fellow tra- veller, T. Coates, Esquire, of Newcastle, brought from Egypt another mummy, which was presented to the Literary Society of that town, and of which an account appeared in some of the public papers of last year. This mummy was not opened. Within the last few months a highly preserved mummy, and one which, to judge from the description given in the public papers, I should be inclined to class with my own, has been dissected and exhibited before the Literary Society of Bristol. We are promised a detailed account of the appearances by a competent person ; and if these should correspond with what is detailed in this paper, an additional value will be given to my observations, which I could scarcely have hoped they would so soon receive. The facility which I deemed it my duty to afford to every individual interested in science, of witnessing the demonstra- tions of my mummy, brought to my house, among others, Mr. Wilmot Horton, Under Secretary of State for the Co- lonial Department. Pleased with what he there saw, this gentleman was kind enough to place at my disposal, the head and right arm of a male mummy, which, though not mdcccxxv. Q q $92 Dr. Granville's essay on so curious in point of preservation compared to other speci- mens, are objects of no inconsiderable interest, from the loca- lity in which they are said to have been discovered, namely, near Tripoli, on the coast of Africa. They were forwarded by the British Consul resident in that town ; but as no cir- cumstance connected with the discovery is known, it would, perhaps, be premature to come to any conclusion as to the probability of the art of preparing mummies having been exercised among the inhabitants of the north of Africa, as it had been by those of the east. These remains of a mummy are not altogether devoid of interest, in as much as they supply us with corroborative proofs of the general principles of the art of embalming, having been such as I shall describe in this paper ; and as affording additional evidence of its strong power of preser- vation. The head, in this case, was covered with a few bandages of coarse linen closely adhering, and, indeed, intimately con- nected with the integuments and muscles of the face, by a black resinous substance, which must have been applied hot, as it has burnt the soft parts to the very bone, and even some of the teeth. The hair is preserved, but it is with great diffi- culty that it can be disentangled from the hard and brittle resin. It is about two inches long, of a reddish brown, and in slight curls and tufts. Hair grew down the cheeks and on the chin, about an inch in length. I removed the bandage, and thus denuded the head and face altogether in most parts, carrying away, necessarily, the integuments and muscles. The head is not prepared in the best manner, but according to one of the least expensive processes. The brain was 293 Egyptian mummies. removed through the nostrils, and in the operation the os unguis of the right side was injured. The eyes were pre- served, but in taking away the bandages they came away with them. By immersion in hot water, I was enabled to separate the external coat of the eye ball, which became as soft and globular as in a recent specimen, though discoloured. There is a very remarkable feature in the skull, and that is the extreme depth of the orbits, which amounts to in- ches, tapering inwardly, so as to present the appearance of a perfect cone. Whether this head bears marks of being that of an African, in the full sense of the word, or not, I am not able to decide. The contour of the head, the maxillary bones and jaws, and the appearance of the hair, incline me to that opinion ; but the Members of the Society will have an opportunity of judging for themselves, by inspecting the head after the meeting. Certain am I, that it is not the head of a Negro. The arm, sent with the head from Tripoli, is uncovered. The muscles are preserved, but they are harder than in my other perfect mummy. The hand is stretched. There is only a portion of the humerus, which seems to have been fractured off', not cut regularly, from the appearance of its splintery extremity. The length of what remains is 8 inches. That of the fore arm is inches, and the hand, from the wrist to the tip of the middle finger, is 7y inches long. This specimen also will be submitted to the inspection of the Members after the meeting. Having thus brought within narrow limits the literary history of Egyptian mummies in general, I shall proceed to 294 Dr. Granville's essay on the conclusion of my account of the dissection of the one I have described, by which I trust the Society will be enabled to form an opinion of the degree of importance that belongs to the present communication. An incision having been made into the parietes of the ab- domen, just below the ribs, and continued down to the hip bone, on both sides, and carried along the margin of the pubis, the whole of the integuments and muscles were re- moved, so as to expose that cavity completely to view. The objects which then presented themselves were a portion of the stomach adhering to the diaphragm, the spleen much reduced in size and flattened, attached to the super-renal cap- sule of the left kidney, and the left kidney itself, imbedded in, but not adhering to the latter, and retaining its ureter, which descended into the bladder. This, as well as the uterus and its appendages, were observed in situ, exhibiting strong marks of having been in a diseased state for some time previously to the death of the individual. Fragments only of the intestinal tube could be found, some of them of considerable dimensions, and among them part of the coecum, with its vermiform appendix, and portions of the ilium. Several large pieces of the peritoneal membrane were like- wise observed. (See Plate XXII. fig. 1, 2, 3.) There were also several lumps of a particular species of brittle resin, two or three small pieces of myrrh in their simplest and natural state, and a few larger lumps, of an irre- gular shape, of some compound of a bituminous and resinous nature, mixed up with an argillaceous earth. These seemed to have been forced up to fill the cavity of the abdomen, after the removal of the largest portions of the intestines, and of 295 Egyptian mummies. as much more of the contents of that cavity as the embalmers could get at, by the very clumsy process which appears to have been employed in this case, for the extraction of those parts through the anus. This orifice was cut in various direc- tions, probably with the intention of enlarging it ; but, more likely, in consequence of the forcible introduction of the in- strument employed in extracting some of the viscera. No traces of the right kidney could be found, nor of the liver or minor glands of the abdomen ; although, among the many fragments of membranes and other soft parts which lay in confusion, and were removed for better inspection, the late Dr. Baillie, who was present at one of the demonstrations, detected the gall-bladder slightly lacerated, but in other respects perfect, retaining a small portion of the peritoneal covering of the liver attached to it, as well as considerable remains of its own ducts. The cavity of the abdomen being emptied of all its con- tents, I continued the circular incision back to the spine, which I divided at the first lumbar vertebra. I next sawed off the thighs a few inches from the hip, and dissected carefully all the soft parts from the pelvis, so as to ascertain the condition and dimensions of this important part of the female skeleton. In performing this last operation, which occupied me two hours a day for nearly a week, (some medical or scientific friends being present at each sitting), we could not help be- ing struck with the remarkable degree of preservation of the muscles, such as had never before been noticed in Egyptian mummies, and such as to admit of their being separated from one another, as readily as in the dissection of a recent subject. Nor was the perfect condition of the articulatory 296 Dr. Granville’s essay on membranes and ligaments less surprising, which allowed us to impart to the great articulation of the thigh with the ilium, its various movements, a circumstance seldom ob- served, even in modern preparations of the pelvis. Some of the dissected muscles, as well as the denuded pelvis itself, will be submitted to the inspection of the Fellows after the Meeting of the Society.* The cavity of the thorax was next examined, and this I effected without disturbing the anterior portions of the ribs or breast bone, by simply detaching the diaphragm all round, and bringing it away. It was found that the pericardium, which adhered partially to the diaphragm, came away with it, and that a laceration had taken place at the same time in that sac. This circumstance denoting that the heart was present, I introduced my hand to remove it, when it was found sus- pended, in situ, by its large blood vessels, in a very con- tracted state, attached to the lungs by its natural connections with them. The latter organs adhered throughout their posterior surface to the ribs, and were brought away alto- gether in as perfect a state as could be effected. All these various parts are accurately represented in Plate XXIII. fig. 1, 2.f The last cavity examined was that of the cranium ; for this purpose it was sawed in two, horizontally, and when * Among the detached muscles exhibited in the most distinct manner, there were the triceps femoris, the sartorius, portion of the vastus externus, and the principal abdominal muscles. f All the parts represented in Plate XXII. and XXIII, were exhibited after the meeting, to the Fellows and Visitors present, on three successive Thursdays. Egyptian mummies. 297 thus opened, it was ascertained that the brain had been removed through the nostrils ; the plates of the inner nasal bones having been destroyed in the operation by the instrument employed, as evidenced by the state of those parts. It is a matter of no little surprise how, under circumstances of so much difficulty, the operators could have contrived to remove every vestige of the membranes investing the brain, one of which is known to adhere firmly in most subjects to the inner surface of the superior cranial bones. There can scarcely be a doubt but that some injection had been thrown into the cavity in question, to clear it out in so perfect a manner ; for no instrument could have effected such a pur- pose. A black resinous substance, but in a small quantity, was found adhering to the inner surface of the occipital bone, which must have been thrown in quite hot, as it had pene- trated through, and burnt partially, the superior part of the lambdoidal suture through which the liquid escaped, so as to be now seen extravasated under the scalp. But how this liquid resin was thrown in, and for what purpose, it is not easy to conjecture. It could only have been made to pene- trate through the opening which had previously been made in the ethmoid bone, to extract the brain ; and if so, it is dif- ficult to conceive in what manner it was made to reach the spot it now occupies without having adhered to any other intermediate portion of the cranium. It was remarked, at the time of opening the head, that its inner surface was studded with small crystals of what appeared to be an animal sub-' stance, resembling steatine. The last observation I have to make on the structural condition of this mummy, refers to the state of the eyes. 298 Dr. Granville’s essay on which appear not to have been disturbed ; and to the state of the mouth, which was as carefully examined as circumstances would admit, without destroying the contour and general appearance of the face. The tongue is preserved, and neither above nor below it was there found any coin or piece of metal, as recorded of some of the mummies, but a lump of rags dipped in pitch. The teeth, as I before remarked, are perfectly white and intact ; nor did I observe that peculiar cylindrical form of the incisores which has been assumed by some naturalists, as one of the characters of the head in the Ethiopian race. In order to complete the present essay on Egyptian mum- mies, I must now trouble the Society with the farther details of my observations on the age of the female under our con- sideration, and on the disease of which I conceive her to have died, as deduced from the examination of the parts. When we reflect for a moment, that the individual in question, according to the more generally received opinion respecting the antiquity of mummies found in the hypogei of Thebes, had probably lived upwards of three thousand years ago,* it will bespeak a very extraordinary power of preserva- tion in the mode of embalming then practised, in some cases at least, to be able to say, that the female of which we are speaking, died at an age between fifty and fifty-five years ; that she had borne children ; and that the disease which appears to have destroyed her was ovarian dropsy attended with structural derangement of the uterine system generally. * Consult Mons. Jomard’s Memoir on the antiquity of the hypogei at Thebes, Mons. Royer on the art of embalming, and the recent publications of Monsieur Champoluon. 299 Egyptian mummies. That such are the facts, I appeal to the state of the bones of the ilium, and of the uterus with its appendages, for proof. * The first exhibit that peculiar degree of thinning in the cen- tre of their osseous plates which has been noticed in women by Professor Chaussier and others, in the course of a great number of observations, as an indication of their having borne children, and of their having passed the fortieth year. This thinning of the bones, in the particular part just mentioned, has never been observed under forty years of age, and be- comes gradually greater until fifty-five, when it has reached its maximum, however longer the woman may continue to live. In my mummy it will be seen, on looking at the pel- vis, or at Plate XX. that the thinning of the iliac bones seems to have reached its maximum ; and as there are no characters of decrepitude in the individual, it appears to me, that from fifty to fifty-five was about the number of years the individual had lived. The thinning of the bones in question has not been observed in women who have not borne chil- dren, nor am I aware that it has been noticed in the male sex, except in the shoulder blades of porters, long used to carry heavy weights on their back. In confirmation of this I have to state, that in more than one pelvis in my collection, with the history of which I am perfectly acquainted, I find the above law to hold good. The thinning of the central portions of the ilium in this mummy is so complete, that small frag- ments have come away in consequence of their being fre- quently touched by the numerous persons who saw the pelvis at my house, and were incredulous as to its real texture without touching it. With regard to the disease, the effects of which I detected, mdcccxxv. R r 300 Dr. Granville’s essay on I have to state, in support of my assertion, that the womb is of larger dimensions than it is known to have at the age in question : that the ovarium and broad ligament of the right side are enveloped in a mass of diseased structure, while the Fallopian tube of the same side is perfectly sound and beau- tifully preserved ; and lastly, that the contracted parietes of what (to judge from the dimensions of the remains) must have been a large sac connected with the left ovarium, leave no room to doubt of the correctness of the opinion I have ventured to express. This opinion, I have the satisfaction to add, has not been disputed by a single individual out of the many very competent judges to whom I submitted the parts, among whom I may mention the late Dr. Baillie, and Mr. Wilson, Mr. Carpue, Mr. Brooks, and others. The whole of the uterine system, as now described, forming the most ancient pathological preparation of its kind, is now in my possession, and will be exhibited to the Members after the meeting, and may be compared with its accurate delineation as given in Plate XXII. fig. 1.* * Another mark, denoting the previous existence of disease, I detected on the scalp, namely, the remains of that peculiar cutaneous affection of the head, which has been denominated Porrigo decalvans, from its effect of destroying the hair as well as of preventing its growth. Was it for this, that the head of this mummy had been shaved, as I have already stated, so as to admit a readier application of remedies to the morbid part, as practised at the present day ? or was it for any other particular reason ? No mention is made, in any author, of females having their head shaved, though the cutting off of the hair in men is frequently alluded to. Again, with what sort of instrument has the operation been executed? It certainly could not have been performed with scissors, however skilfully constructed, as the hair could not have been cut so close, nor of such uniform length with them. If with any instrument approaching to our razors in structure, of what material was it made ? These are highly curious inquiries, which naturally spring from the ex- amination of the condition of this mummy. Egyptian mummies. 301 The next points of inquiry to which I directed my attention were, First, to discover, if possible, the method by which this perfect specimen of Egyptian mummies had been pre- served. Secondly, to ascertain how far the description given by ancient writers of the art of embalming among the Egyp- tians, applied to the present specimen. And lastly, to deter- mine the nature of the substances employed for the purpose. In pursuing this investigation, I flattered myself that the Royal Society would consider it as something more than a mere object of useless curiosity. In order to carry on my inquiry respecting the three points above-mentioned with that precision which alone could lead to a satisfactory conclusion, I proceeded to note down all the principal facts resulting from a close examination of the mummy, as detailed in this paper ; next to ask myself how those facts could be explained ; and lastly, if explained, whe- ther the facts themselves could be reproduced by following the method which the explanation might point out. I shall leave it to the Society to determine, whether I have been successful in my attempt. The first fact to be noticed, in regard to the preparation of the mummy, is the chestnut brown tint of all the bandages, denoting the presence of some colouring matter in them, the nature of which it was important to ascertain, in order to judge of the intention of those who employed it. For this purpose I made a few experiments with .portions of the ban- dages taken from different parts of the body, when it was found that they had all been steeped in some vegetable solu- tion, which, when treated with gelatine, exhibited the pre- sence of tannin in considerable quantity, a circumstance far- SOS Dr. Granville's essay on ther corroborated by the peculiar taste of the infusion. Now, as every particle of the bandages had been equally died with this vegetable solution ; and as it appears evident, from other circumstances, that such a process had not been adopted for the sake of giving to the envelopes of the mummy the par- ticular colour in question, may we not infer that the Egyp- tian embalmers were acquainted with the antiseptic power of astringent and slightly bitter vegetable infusions, a power which modern discoveries have attributed to the presence of the peculiar principle already mentioned ? This inference is confirmed by the second fact to be noticed, namely, the appearance and condition of the integuments, which, besides being of a dark brown colour, differ in no respect from prepared leather, particularly those of the abdo- men, the thighs, and the mammae. The Society will have an opportunity of examining several portions of these integu- ments, and will be struck with the similarity alluded to. Indeed they might be taken for prepared leather at first sight, and the knowledge which I obtained, by a second series of experiments, that a solution of some vegetable astringent, similar to that used for the bandages, but much stronger, had been employed to produce that appearance, must prove con- clusive on this point. A question then will naturally arise, was it the bark of the acacia, so plentiful in Egypt, that was employed for the purpose ; or did the Egyptians import oak bark from the coast of Syria, where that tree grows in abundance * * It is not improbable, that a gum, not unlike kino, may have been the sub- stance used for the purpose of tanning the integuments, as I found, among the vari- ous lumps of resincontained in the abdomen, several portions of such a substance. Egyptian mummies. 303 The two preliminary and curious facts just detailed, con- nected with the art of embalming among the Egyptians, have never been noticed before. Neither Herodotus, nor Diodorus Siculus, mention them, and all the more modern writers are silent on the subject. The next fact worthy of notice, is the appearance of minute saline crystals, found in great abundance in almost every part of the external, but more particularly of the internal surface of the body. These, at first, had escaped notice ; but upon the various portions of the dissected mummy being exposed to the open air, in one of the rooms on the ground • floor in my house for some weeks, where a fire was kept, the appearance of the saline particles became strikingly visible. This saline efflorescence I gently swept off the sur- face with a new brush, and subjected to various analytical experiments, from which it results, that it consists of nitrate of potash, carbonate, sulphate, and muriate of soda, and traces of lime. Now, as as none of these salts have ever been ob- served to form spontaneously, either within or upon the sur- face of preserved human bodies, particularly where the con- tact of external air has been so studiously excluded as in the present case, it follows, that in the preparation of mum- mies, the embalmers must have had recourse to the immersion of the body into a saline solution of a mixed kind. Hero- dotus, indeed, states that the body was covered with natron for the space of seventy days ; but it is more probable, that the water of the celebrated natron lakes, which lay so con- veniently at hand, rendered more active by previous evapo- specimens of which I exhibited to the Society, and which gave to distilled water a deep brown colour, from which a precipitate is obtained by gelatine. 304 Dr. Granville’s essay on ration, was used for the purpose. The presence of lime may he accounted for by supposing, that in a preliminary opera- tion, the cuticle, which, as I before stated, could not be detected in any part of the body, except the head and the extremity of the toes, and has been found invariably wanting in all other mummies, was removed by means of that alka- line substance. This circumstance again goes far to show that the Egyptian embalmers were acquainted with an important physiological truth, namely, that in order to pro- mote the absorption of liquid substances, particularly of the tanning liquor and saline solution, applied to the external surface of the body, the cuticle must first be removed. The presence of saline substances in mummies has been noticed by more than one modern writer, especially by Mons. Royer, already mentioned in the course of this essay ; but the conjecture as to the origin of the salts themselves, has not been hinted at before. A fourth fact, deserving of our attention, is the presence of a resino-bituminous substance between some of the folds of the remaining portions of the peritoneal membrane. On col- lecting this substance, and instituting some experiments upon it, I ascertained that the bitumen was mixed with a greater proportion of wax, so as to have rendered the mixture per- fectly plastic. To have penetrated thus far, and to have lodged between closely adhering membraneous folds, this mix- ture must either have been injected quite warm into the cavity of the abdomen, or the body itself must have been plunged into a vessel containing a liquefied mixture of wax and bitumen, and there kept for some hours or days, over a gentle fire. The latter operation, not noticed by the older historians, has Egyptian mummies. 305 indeed been surmised by some of the modern writers on the subject ; but in none of them have I been able to find a cor- roborating proof of the correctness of such a surmise. 1 he examination of my mummy has afforded me that proof, in the shape of a fifth fact, namely, the thoroughly impregna- ted state of the bones, membranes, and muscles, in every part of the body, by the same waxy and bituminous substance. The inspection of the bones of the pelvis, of those of the thighs, and of the vertebrae, as well as of some of the mus- cles, and membranes, to be submitted to the Society, will shew this abundantly. Now such a condition of the parts could not have been produced, but by maceration or immer- sion, for a length of time, of the whole body, into a liquefied mixture of those two ingredients ; accordingly we must conclude that such a process was actually followed by the embalmers ; unless we feel disposed to believe that they in- jected the body through the blood-vessels ; an operation of which there is not the most distant evidence in the mummy before us. The adoption of my view on this point, is farther authorized by the soft and pliant condition of the capsular membranes, of the cellular texture, and above all, of the two coverings of the spinal marrow, than which nothing can be more beauti- ful or striking ; whether we admire their perfect preservation, or reflect on the number of centuries through which these delicate tissues have travelled. I have already noticed to the Society the flexibility of the joints, a circumstance which is entirely due to the process here explained ; and now I have to add that this process is made out beyond contradiction, by my having been able to separate the wax by means of 306 Dr. Granville's essay on combustion and ebullition, from the soft parts, particularly the muscles, the singularly distinct fibres of which, beau- tifully arranged and displayed, the Society will not omit remarking. In examining the dissected parts of the mummy, which I have carefully displayed for public inspection after the meet- ing, the Members will not fail being struck with the differ- ence that exists between the two nates detached from the body. The one has been left in the state in which it was handed down to us by the Egyptian embalmers, dark, tanned, contracted, and impregnated with the mummifying ingre- dients ; the other, on the contrary, has been deprived, in toto, by my process, of those ingredients, (the principal of which is bees wax, as will be seen from the quantity which I collected) ; so as to appear like the same part in a recent subject, soft, elastic, of a yellowish white, with the cutaneous pores very distinct, and with its muscles, adipose substance, and blood vessels perfectly striking. The sixth , and last fact to be noticed, is the presence of several moderately sized lumps of an earthy matter, mixed with pieces of resin, found loose in the cavity of the abdomen. That these were thrown into that cavity for the double pur- pose of filling up the space left in it by the abstraction of some of the viscera, and of adding, at the same time, to the anti- septic power of the process employed in embalming, are conjectures that will perhaps be readily admitted. The ex- periments made to ascertain the nature of the earthy substance in question, tend to prove the latter part of these conjectural propositions. It was found to consist of the same saline com- pounds, noticed on the surface of the mummy, mixed with 30? Egyptian mummies. argillaceous earth. Now, if the embalmers used the water from the natron lakes, as I have laid down good grounds for believing, nothing is more probable, than that they also made use of the earthy sediment of that water which con- tains the salt in question, and which could be procured in abundance at the margin of those lakes, where it has been observed by the naturalists who accompanied the French ex- pedition into Egypt. As to the nature of the resin and bitumen used as ingre- dients in the embalming process, it is a question of com- paratively little interest. Nor does it matter much, whether aromatic vegetable substances were employed or not. In the mummy before us, two or three small pieces of myrrh in a loose state were found, and evidence is not wanting of both resin and bitumen, though not in their purest form, having been had recourse to. But their presence seems by no means necessary for the completion of that admirable method of embalming, devised and followed by the ancient Egyp- tians, which my inquiries have been directed to ascertain, and which may be summed up in a few words by saying : that it consisted in impregnating the body with bees wax. The various circumstances detailed in this essay furnish us with sufficient reasons for believing, that in the most per- fect, and, I would call them, the primitive specimens of the art of embalming, the progressive stages of the Egyptian method must have been as follows : A. Immediately after death the body was committed to the care of the embalmers, when, in the majority of cases, the viscera of the abdomen, either wholly, or partially, were forth- with removed ; in some cases through an incision on the one MDCCCXXV. S S 308 Dr. Granville's essay on side of the abdomen, as stated by Herodotus, and as proved by some of the mummies examined ; and in others through the anus, in which latter case, the extremity of the rectum was previously disengaged from its attachments all round by the knife, and the intestines imperfectly extracted. The cavity of the thorax in the most perfect specimens was not disturbed. B. The head was emptied, in all instances, of its contents, either through the nostrils, by breaking through the supe- rior nasal bones, as in the instance under our consideration, as well as in that of the head from Tripoli, already mentioned, or through one of the orbits, the eyes being previously taken out, and artificial ones -substituted in their place, after the operation, as in the instances of the mummies examined by Sir E. Home and Mr. Brodie. The cavity of the cranium was repeatedly washed out by injections with some fluid, which had the power of not only bringing away every vestige of the substance of the brain, but even of the enveloping mem- branes of it. Yet the liquid could not have been of a corro- sive nature, else the tentorium, or that membranous floor which supports the brain must have disappeared with the meninges ; whereas it is still in existence, and does not appear to have been in the least injured. A small quantity of hot liquid rosin was then injected into the cranium. C. The next step taken in the embalming process, was to cover the body with quick lime for a few hours, and after to rub the surface of it with a blunt knife, or some such instru- ment as would most effectually assist in removing the cuticle. The scalp, however, does not appear to have been touched ; and care was taken also not to expose the root of the nails Egyptian mummies . 309 to the action of the alkali, as it was intended that these should remain in all cases. In the mummy I have described, this point has been so much attended to by the embalmers, that the nail of the principal toe of the right foot having been detached, it was replaced and retained in its position by three or four turns of thread passed around it ; and in this state it must have continued for the last thirty centuries. D. The operation of removing the cuticle being accom- plished, the body was immersed into a capacious vessel, con- taining a liquefied mixture of wax and resin, the former predominating ; and some sort of bituminous substance being added, not however essential to the process. In this situation the body was suffered to remain a certain number of days over a gentle fire, with the avowed intention of allowing the liquefied mixture to penetrate the innermost and minutest structure ; nor can there exist any doubt, but that on this part of the embalming process depended not only its great preservative power, but also its various degrees of perfection. Thus, when the process was properly managed and watched, mummies, such as the one under consideration, would be produced; whereas when neglected or slovenly conducted, the mummy resulting from it, would present those appear- ances of dryness, blackness, and brittleness, together with the carbon ifi cation of the muscles and intimate adherence of the integuments to the bones, which have been noticed by Dr. Hadley, Professor Gmelin, Blumenbach, Hunter, Dr. Baillie, Mr. Brodie, Jomard and others, when they examined imperfect or inferior mummies. The fraudulent subtraction of the allotted quantity of wax required for the principal and important part of the embalming process we are now con- S10 Dr. Granville's essay on sidering, or the neglecting to regulate the fire in using the wax and bitumen, would necessarily give rise to the latter results, which the covering bandages were sure to hide from the eye of the surviving relatives to whom the body was to be returned. It is also fair to presume, that inability or un- willingness on the part of friends and relatives to pay for the ingredients or for the labour necessary to carry on the operations just described, have, on many occasions, been the cause of mummies being prepared in that imperfect manner which has been noticed in so many instances. E. When the body was taken out of the warm liquid mix- ture, every part of it must have been in a very soft and sup- ple condition, wholly unsusceptible of putrefaction. The next steps therefore to be taken, with a view to convert it into a perfect mummy, must have been those, which, had they been taken before that part of the process that has been just described, would have exposed the body to inevitable putrefaction, in a climate like that of Egypt. I allude to the tanning of the integuments, and the exposing of their sur- face to the additional influence of those salts, the presence of which, as well as that of tannin, I have most clearly de- monstrated. Whether an infusion of the vegetable astringent employed for tanning the integuments was had recourse to in the first instance, and the immersion of the body into the con- centrated water of the natron lakes followed, or whether the tanning liquid was itself made by infusing the vegetable as- tringents themselves in the water of the natron lakes, and the body then immersed into it, are questions, which it is neither possible, nor important to decide ; the body was unquestion- 311 Egyptian mummies. ably submitted to the operation of both those means, but in what order, it is difficult to ascertain ; and when the em- balmers judged by the condition of the integuments, that they were sufficiently impregnated with the active principles employed, the body was allowed to dry for a few hours, and then the bandages previously prepared with a solution of tannin also, as proved by my experiments, were applied to the different parts, beginning with each separate limb. While the operation of bandaging took place, the mummy must have been in a very supple state, else the numerous deep longitudinal wrinkles observed in all those parts where the integuments are generally looser, as in the upper part of the thighs and arms, as well as over the abdomen, and at the breasts, could not have existed. These wrinkles, so well marked in Plate XIX. must have been produced by the ban- dages at the time of their application. It appears also, that with a view of rendering the bandages more supple in particular places, where such a condition was required, and of obviating the inconvenience of slackness in some of the turns, they were daubed over in a few places with two different substances, the one consisting of wax and resin, the other of resin alone, both applied warm ; so that, while the first served to give pliancy to some of the linen employed, the second caused the slack and loose edges of the bandages to adhere together, by which process the whole was rendered compact and firm, without producing hardness. The lumps of myrrh, resin, and bituminous earth, noticed in the abdomen, were pushed up through the enlarged aper- ture of the anus, immediately before the application of the bandages, for the purposes already detailed. 312 Dr. Granville's essay on The preceding explanatory description of what appears, from the unquestionable facts collected in the course of my inquiry, to have been the best, and, in my opinion, the pri- mitive mode of preparing mummies by the ancient Egyp- tians, differs from that found in Herodotus, as well as from those accounts which we read in other writers who came after him. It does not however appear that the eminent historian just mentioned had ever been present at the em- balming of a mummy, or that he ever had an opportunity of examining one of them. He must, therefore, like many other travellers, have noted down what he had collected from hearsay, in which, amidst much that was surmised, there was something approaching to the truth. It is in evidence that the art was kept a profound mystery among those who professed it, so that the different modes of em- balming described with such orderly minuteness of details by Herodotus, could only have been conjectural. It is a curious fact, that, with the exception of the lateral incision, and immersion into a saline solution mentioned by that histo- rian, we find no confirmatory evidence of the other steps of the supposed processes of embalming detailed by him in any of the various mummies that have hitherto been examined. And in the one now submitted to the inspection of the So- ciety, by far the most perfect that has yet been publicly described, we have none of the characteristic features of the three several modes of embalming which we are told were fol- lowed by the ancient Egyptians ; while, on the other hand, some of the lesser features of each process are strikingly apparent. We have, in fact, the presence of that which Herodotus asserted was invariably removed in the better 313 Egyptian mummies. prepared mummies, and some of those parts are absent, on the other hand, which he stated never to have been touched in the inferior class of those singular preparations. These facts will be duly valued by the scholar, and the commen- tators of that historian ; and the explanation now given of the real mode of mummifying, will enable the lexicographer to advance with confidence, that the name mummy was given to such preparations from the circumstance of wax ( mum in the Cophtic language), being the really preservative ingre- dient employed in their preparation. I have had occasion in the course of this paper to observe, that as by carefully taking into consideration the various facts which presented themselves during the examination of our mummy, it was natural to suppose, that the mode in which it had been prepared would be discovered ; so would that discovery be confirmed if, by acting on those facts, some- thing resembling a mummy could be produced ; and in the specimens which will be submitted to the members after the meeting, the different steps will be seen, by which I was led to what may be considered as an imitation of the Egyptian mummies.* * There were exhibited after the meeting four different specimens of imitative mummies, each of them illustrative of one or two of the successive stages of the process of embalming detailed in this essay ; the last being intended to illustrate all the stages together, and exhibiting a close resemblance to the Egyptian mummy itself. A still born child had been employed for the purpose, and this modern mummy has now been in existence upwards of three years, without bandage or covering of any kind, exposed to all sorts of temperature and rough usage without betraying the slightest vestige of decay or putrefaction. It is rather darker than the Egyptian mummy from the circumstance of a too concentrated solution of tannin having been employed in preparing it. 314 Dr. Granville's essay on I purposely omit speaking of the various modes of em- balming adopted by different nations, or of those which may have prevailed at different epochs in Egypt ; although in the course of my investigation I collected ample materials for entering into such a subject. The art of embalming, with a view to the preservation of the human body, for an indefinite series of years, as strictly illustrated by the mummies of ancient Egypt, does not appear to have been practised with success by any other nation. We find no remains of such high antiquity in any other part of the world ; and the mum- mies of Mexico, those of the Atlantic islanders, the dried bodies found in the catacombs of some of the states bor- dering on the Mediterranean, are but of yesterday, compared to the age of the mummy which I have had the honour of bringing under the notice of the Society. Indeed the art soon began to decline among the Egyptians themselves, and the mummies found in the hypogei which bear evidence of having been more recently erected, as well as those of the plain of Saqquarah, are, in every respect, inferior to the primi- tive mummies. Whether this arose from the growing igno- rance of the real process, the directions respecting which could only have been handed down traditionally ; or from carelessness in the operation ; or from indifference on the part of the people toward such an object ; or from all these causes united, it is not easy now to determine. Certain it is, that the genuine process of embalming, among the Egyptians under the dynasty of the Pharaohs described in this paper, appears to have been progressively disregarded, and forgot- ten among them, until at last it was lost altogether. Nor does it appear ever to have been known by other nations. 315 Egyptian mummies. In order to appreciate properly the durability of the bodies prepared by the Egyptian process, it is essential to observe, that the mummy I have described with so much minuteness, after having resisted putrefaction for above three thousand years, covered by bandages, inclosed in a thick wooden case, and placed in recesses, far from the external influence of atmospheric vicissitudes, has since withstood the inclemency and variations of an English climate, without any of those protecting circumstances ; nay, exposed purposely, but ineffectually, for four years, to the various causes that are known to favour putrefaction.* The deep feelings of interest that have of late been excited respecting the Egyptians, have induced me to extend my present inquiry to a greater length, than I should have done under less inviting circumstances. It was impossible not to feel extremely interested in the subject ; and when I beheld before me the heart of an Egyptian female, whom imagina- tion, aided by historical records, may fancy to have been cotemporary with the great Sesostris, I could not help ex- periencing a degree of enthusiasm, a portion of which, me- thought, I could impart to others. I recollect with pleasure the sensation which the demon- * A singular contrast this, with what has since happened to one of the nates alluded to in a previous note. Being divested of the protecting and embalming ingredient, by the process I there alluded to, this part has partially run into putre- faction, and emits the peculiar smell of animal substances, placed under similar cir- cumstances. Nay, in the case of one of the large muscles of the thigh, and a large portion of the integument, which I similarly deprived of their protecting ingredi- ents, such has been the rapidity with which putrefaction has followed, that although well covered, the vessels containing those parts emitted the most insufferable smell> and the parts themselves were found infested with myriads of large maggots. Tt MDCCCXXV. 316 Dr. Granville’s essay on Egyptian mummies. stration of the various parts of this mummy, at the time it was first opened, excited amongst upwards of an hundred sci- entific and literary characters, who in the course of six weeks honoured me with their presence at my house to witness the dissection, and by whom I was encouraged to follow up the investigation, and to communicate the result to the public. It is in obedience to their suggestion, and more especially to the recommendation of the President of the Royal Society, that I have taken a comprehensive view of the whole subject, instead of limiting myself to the dry description of a solitary specimen. Phil. Trans. MD CCCZTV. Plate XVm.p ■ t fivin • {‘rrn, ■ del T Tf .Rtt.tirr 77 20 inches Jfcctrv Perry del? Phi/. Trans. Ml ) C C CJCTV. J'/a/r X XT. p.gti. , Verr v Sen TfBasir • % '‘W%\ JVM.Zrans.'MllCCCXZV. flat? 2QflI .p .3/0- — " if Phil. Trans. MD C C CXXV. Plate XXUl . p .316. 'enrvPerrr (tel T 7f Pasi/Y sculpt C 117 ] \ XIV. On the temporary magnetic effect induced in iron bodies by rotation. In a Letter to J. F. W. Herschel, Esq. Sec. R. S. by Peter Barlow, F. R. S. Communicated April 14 th, 1825- Read May 5, 1825. Dear Sir, Xt is more than two years since, in a conversation I had with you on subjects connected with magnetism, you enquired what effect I thought might result from giving to an iron ball a rapid rotation ? The subject however dropped, and it did not occur to me again, till in some speculative views in which I was lately engaged, as to the cause of the rotation of the earth's magnetic poles, the apparent irregularity of the terrestrial directive powers, &c. I was led to consider that, probably, rotation might have a certain influence. We know that iron is rendered magnetic by various processes, as dril- ling, hammering, &c. and it was possible also by rotation ; your query now occurred to my mind ; and knowing at the same time that Mr. Christie had found a permanent change in the magnetic state of an iron plate by a mere change of position on its axis, it seemed highly probable this change, due only to a simple inversion, would be increased by a rapid rotation. In t iis respect, however, I was deceived ; for I found afterwards, that all the effect that was produced was merely temporary ; and if any permanent change did take place, it was too small in my cast iron shell to be observed with the small compass I employed in these expe- riments. 318 Mr. Barlow on the temporary magnetic effect Being however thus urged to the inquiry, as well by my own speculative views as by your query, and encouraged by Mr. Christie's results, I resolved to put the idea to the test of experiment, and to attempt it at once upon a scale that should decide the question in the first instance. As soon as I had determined upon the experiment, I found an excellent opportunity of making the first trial, through the kindness of Generals Cuppage and Millar, of the Royal Artillery, who gave me permission to have a 13 inch mortar shell fixed to the mandrel of one of the powerful turning lathes worked by the steam engine in the Royal Arsenal. This having been done, and the compass properly placed near the shell, I turned the shell slowly round, in order to ascertain whether in this case, as in Mr. Christie's, there were any effects depending on a change of position ; but if there were any, it was so small in the cast iron shell as not to have been rendered sensible with the small compass I employed. The wheel being now put in geer, the shell commenced its revo- lutions at the rate of 640 per minute, and the needle wqs deflected out several degrees, at which it remained perfectly stationary while the ball was in motion : but it returned imme- diately to its original bearing as soon as the motion ceased. I now inverted the motion of the shell, and the needle was deflected about the same quantity the contrary way, observ- ing a similar steady direction as in the former case ; but as before, it returned to its original bearing the moment the motion was discontinued. These experiments were repeated several times before some scientific officers of the artillery and engineers, always with the same results. I induced in iron bodies by rotation. 319 I afterwards found, that the needle being placed in diffe- rent situations, its motion was reversed, although the direc- tion of motion in the shell was the same ; the amount of the whole deflection also differed very considerably according to the situation of the compass, its direction in some cases having been wholly reversed, while in others no perceptible motion was produced, although the rotation of the shell remained the same both in direction and in speed. I was therefore desirous of undertaking a regular set of experiments, in order to reduce the several apparently ano- malous results to some certain law of action ; and as the shell in question was rather too heavy for us to feel a perfect security, as to personal safety, when it was in rapid rotation, and moreover, as its effects were larger than seemed neces- sary for the purpose, I now selected a Shrapnel shell of 8 inches in diameter, which weighed only 30 lbs. and chose another lathe, whose axis was nearly north and south, that in the former instance having been east and west. I had also a table made with a circular hole in it, which I could place at any height above, below, or about the centre of the ball ; I could also set my compass on any azimuth on the same, and observe the effects of the direct and reversed mo- tion ; but after several days observations, I found the results so complicated, and the needle so much influenced by the iron work of the lathe and other machinery, that it would be useless to proceed, unless I could contrive to produce the rotation out of the way of any disturbing cause of the kind above mentioned. This also, through the kindness of Colonel Sir Alexander Dickson, and the officers above named, I was enabled to 320 Mr. Barlow on the temporary magnetic effect accomplish ; and having got the machine erected on my own premises, I was soon enabled to clear up the difficulties which had hitherto so much embarrassed my proceedings, although even here, in the first instance, I found some results very difficult to explain. The machine I now employed is shown in the annexed drawing. Plate XXIV. A B C D is a strong wooden frame, resembling that of a common electrical machine, the shell S being hung in the same manner as the cylinder ; the axis is made in two parts of gun metal, and very strong ; s s are two strong screw bolts and nuts, which were used for fixing the frame firmly to the top of the table, the bolt passing through from below. EGF is a substantial table with its feet sunk into the ground, and the floor of the room cut away where they passed through, in order to prevent any effect of shaking on the stand carry- ing the compass. The stand consisted of an upright pedestal filled with sand, to render it steady, and to this was fixed the table ML, with a semicircular hole cut in it, so that it might be placed near the shell. This table might be elevated or depressed at plea- sure, and it was divided into the points, quarter points, &c. of the compass. By means of different holes bored in the top of the table, the machine might be placed N and S, E and W, &c. at pleasure, and the motion of the shell be inverted by turning the handle to the right or left. The large wheel is six times the diameter of the small one ; and as it might easily be turned twice in a second, the number of revolutions of the shell were gradually about 720 per minute. The little apparatus I induced in iron bodies by rotation. 321 seen above the shell, is a small stand and sliding wire, car- rying a common lamp glass, in which a very small dipping needle was suspended by silk ; and when the lamp glass was out of the ring, the latter served for setting the hori- zontal needle on, so as to bring it over any required point of the shell. It should be observed that the pedestal was moveable, and might therefore be placed on either side of the machine. The stand and upright figure 2, is one of two large magnets ultimately employed for neutralizing the needle. The machine being thus prepared, I screwed it down ; first with its axis in the magnetic meridian, and then placed the compass successively at the several points on the table all round, and registered the deviation produced at each, with the motion of the shell direct and reversed. I then removed it, and placed the axis east and west, and again registered in the same manner ; but the results were very irregular with respect to quantity. Although I obtained some uniformity regarding direction only , viz. in both cases I found four points of change at about 30° from each extremity of the axis, or four points of non action. For example, when the axis was in the meridian from N 30° E to N 30° W, the motion of the needle arising from the rotation was made to the right. From N 30° W to S 30° W to the left. From S 3 o° W to S 30° E to the right. From S 3o°E to N 30°E to the left; the direc- tion of motion in the shell being the same ; with the direc- tion of motion reversed, the deviation was reversed also. While at these four points themselves, the needle had no motion. I tried also a variety of other positions, but I could obtain no such results as to lead to a concise expression of 322 Mr. Barlow on the temporary magnetic effect the effect, and for this reason I shall not trouble you with the detail of them. It at length occurred to me, that the reason of my failure arose from the compound influence under which the needle was placed, viz. that of the iron ball and of the earth ; I there- fore now neutralized it from the effect of both, by means of magnets properly disposed, adjusting it always before the rotation to a direction tangential to the ball, so that what- ever effect was produced at each point, might at least’ become decided as to its direction. I now immediately arrived at that kind of general law I had been in search of ; for I found when things were thus arranged, that whatever might be the direction of the axis of rotation, if the motion of the ball were made towards the needle, the north end of the latter was attracted ; and if from the needle, the north end was repelled by the iron, the points immediately in the axiis * ( when of course the motion of the shell was parallel to the needle) being neutral, or those at which the change of direction took place ; in other words, if the motion of the shell continue the same, and the compass be successively placed all round the ball, in that semi-circle (from one axis to the other) in which the motion is towards the needle, the north end approaches the ball, and in the other semicircle it recedes, or the south end approaches ; the points of non action being in the two extremities of the axis, and those of maximum effect in two opposite points at right angles to the axis ; in which two latter the needle, when properly neutra- tralized, points directly to the centre of the ball. This will be perhaps better understood by reference to fig- 3, where S is the shell, ab its axis, and ns , ns, &c. the induced in iron bodies by rotation. 323 needle in its various positions prior to the motion, and ri s', n’ s\ &c. its direction as resulting from the motion ; the rotation of the shell being from c towards d . . of course with the rotation reversed, the effect will be reversed also. Now this effect you will, I think, find to be perfectly con- sistent with the view you have taken of the subject, in your letter of Jan. 13th, where you say in reference to your for- mer query, and to the views I then entertained, “ I should rather have expected a diminution of the magnetic polarity, commensurate to the rapidity of rotation and a change in the direction of the magnetic axis of the globe, from parallelism to that of the earth, to a position somewhere intermediate between that and the axis of rotation, but approaching nearer the latter as the velocity increased, &c." The fact is, that the needle in my experiments being under no influence prior to the rotation from either the iron or the earth, the direction which it takes up in consequence of the motion, enables us to discover the precise direction of the new forces thus impressed upon the shell, and it will be seen immediately to indicate a polarization of the latter in the direction c d\ that is, in a direction perpendicular to the axis of motion, and to the plane passing through that axis and the actual poles of the ball. You will of course understand that I do not mean that such a polarization actually takes place ; I mean merely that the cohesive power of the iron is such, as to resist in a cer- tain degree the inductive powers of the earth, whereby the magnetic forces are changed, as you have suggested, from their original direction, parallel to the magnetic axis of the ball into a position oblique to it, which oblique forces mdcccxxv. U u 1 324 Mr. Barlow on the temporary magnetic effect being resolved into two, the one parallel to the original axis, and the other perpendicular to it, and the former being nearly neutralized by the magnets used for the purpose in the first instance, the perpendicular forces will act upon the needle in the same manner as if the ball were really polarized in the direction above alluded to. Having got this view of the subject, I soon found that many of my former results, which appeared to have scarcely any conformity among themselves, were perfectly consist- ent with this hypothesis : of these the experiments given above, before the needle was neutralized, may be mentioned. In these I found the point of change to be at about 30° on each side of the axis, so that the arcs in which similar effects were produced were divided into the unequal portions of 6o°, 120°, 6o°, and 120°, which appeared to be anomalous; but according to the view now taken of the subject, this is per- fectly consistent ; it is precisely what ought to happen ac- cording to the law tan. dip. = 2 tan. mag. lat. and which actually takes place on the earth. That is in passing from the magnetic equator 30° towards the pole, the dipping needle has actually described a quadrant, as referred to its position at the equator ; and it would describe a quadrant, in an oppo- site direction in going 30° towards the other pole ; so that in passing through 6o° the needle is actually inverted ; but if we start from mag. lat. 30° through the pole, we must pass through an arc of 120° before the direction of the needle is inverted, and the same in the other half of the meridian ; and in like manner by referring the motion of my needle as in- duced by the rotation of the shell to its original magnetic direction, it is obvious that I ought to have found, as I actually induced in iron bodies in rotation . 325 did before I was aware of the cause, a point of change at 30° distance on each side of the meridian passing through the axis ; which meridian, as respects the induced power, is actually the equator of the new magnetic sphere. To render this more obvious, let us refer to fig. 4, in which AB represents the axis of rotation of the shell, the black lines the needle in its natural direction, and the dotted lines the direction the needle has a tendency to assume ac- cording to the law above named, in consequence of the mag- netism impressed by the rotation in the line n s. Beginning at the point A, if we say the motion is from left to right, that is from n to n' , it will be from right to left at 6o°, 750, 90°, &c. till we arrive again at 30® ; at this point as at the former the new power is exerted in the actual direction of the needle, and if it were greater than its natural directive power, it would wholly invert it ; in this case it would pass to either hand ; but as the new power cannot invert it, it has no tendency to deflect it, and it therefore remains stationary. Thus one of the results which was at first the most perplex- ing, serves to confirm the law we have established. On similar principles, if we conceive a circle passing ver- tically from 90° to 90°, and if the needle be perfectly neu- tralized at different positions in this circle, and rendered parallel to the axis at each, then in every case the needle will have a tendency to take up a position directly at right angles to the axis of the shell, and it will point in opposite directions at certain parts of this circle: thus, if to fix the idea we conceive the axis to be in the meridian, and the motion of the shell from west to east, then at the east point of the horizon the needle will point to the west, and it will do the 326 Mr. Barlow on the temporary magnetic effect same at all points between the horizon and an altitude of 6o° ; beyond this, the north end will point to the east till we have passed the zenith 30° on the west side ; and then again from this point to the west horizon the north end will again point to the west; and similar changes will take place below the ball. This, which is a necessary consequence of our hypothesis, is completely verified by experiment. It will of course be understood, that the supposition of the axis being in the meridian is merely to fix the idea ; for a similar motion takes place whatever direction the axis of the shell may have. It is presumed, that what has now been stated is sufficient, without referring to any further experiments, to establish the principal fact adverted to in this letter, viz. that when any iron body is put in rapid rotation on any line not coinciding with its magnetic axis, a temporary derangement takes place in its magnetic powers, which in its effects is equivalent to a new axis of polarization perpendicular to the plane passing through its axis of polarization and rotation. I have stated in the beginning of this letter the motives which led me to undertake these experiments; but notwith- standing I have certainly found a stronger effect produced by the rotation than I anticipated, yet it does not appear to be of a kind to throw any new light upon the difficult sub- ject of terrestrial magnetism. I think there are strong rea- sons for assuming, that the magnetism of the earth is of that kind which we call induced magnetism ; but at present we have no knowledge of the inductive principle, and are therefore unable to judge, how far the earth's rotation may be influential in producing those discrepancies from the gene- f induced in iron bodies in rotation. 3*7 ral laws which are known to exist. The formula, which we owe to Mr. Biot and to Mr. Kraft, expressing the law of the dips in different latitudes, viz. tan. dip. — 2 tang. mag. lat. certainly agrees with observation in many cases, but the variation computed on the same principles, and which neces- sarily ought also to coincide with observation, is widely in error. It seems therefore very obvious that some disturb- ing cause exists, but whether any part of it can be attributed to the rotation of the earth is, notwithstanding the preceding results, very doubtful ; at the same time I may perhaps be allowed to observe, that one of the essential conditions for the production of such an effect has place in the earth, viz. that it does not revolve about its polarized axis ; and if the inductive principle through which it receives its magnetism be exterior to itself, then it would follow almost of necessity that some such an effect should take place. I beg however to be understood as advancing nothing in this letter, beyond the mere experimental fact above stated, which, even if it should find no useful application, may perhaps be thought sufficiently curious to be recorded in the Transactions of the Royal Society. PETER BARLOW. C 828 2 XV. Further researches on the preservation of metals by electro- chemical means. By Sir Humphry Davy, Bart. Pres. R. S. Read June 9, 1825. In two papers read before the Royal Society, I have de- scribed the effects of small quantities of electro-positive metals in preventing the corrosion or chemical changes of copper exposed to sea water, and I have stated that the results appear to be of the same kind, whether the experiments are made upon a minute scale, and in confined portions of water, or on large masses, and in the ocean. The first and preliminary experiments proved, that the copper sheeting of ships might be preserved by this method ; but another and a no less important circumstance was to be attended to, how far the cleanness of the bottom, or its free- dom from the adhesion of weeds or shell fish, would be influenced by this preservation. The use of the copper sheathing on the bottom of ships is two fold : First, to protect the wood from destruction by worms : And secondly, to prevent the adhesion of weeds, barnacles, and other shell fish. No worms can penetrate the wood as long as the surface of the copper remains perfect ; but when copper has been applied to the bottom of a ship for a certain time, a green coating or rust, consisting of oxide, submuriate Sir Humphry Davy’s further researches , &c. 32$ and carbonate of copper and carbonate of magnesia forms upon it, to which weeds and shell fish adhere. As long as the whole surface of the copper changes or $ corrodes, no such adhesions can occur ; but when this green rust has partially formed, the copper below is protected by i , and there is an unequal action produced, the electrical effect of the oxide, submuriate, and carbonate of copper formed, be- ing to produce a more rapid corrosion of the parts still exposed to sea water ; so that the sheets are often found perforated with holes in one part, after being used five or six years, and comparatively sound in other parts. There is nothing in the poisonous nature of the metal which prevents these adhesions. It is the solution by which they ar e prevented — the wear of surface. Weeds and shell fish readily adhere to the poisonous salts of lead which form upon the lead protecting the fore part of the keel ; and t to the copper, in any chemical combination in which it is insoluble. In general in ships in the navy the first effect of the adhe- sion of weeds is perceived upon the heads of the mixed metal nails, which consist of copper alloyed by a small quantity of tin. The oxides of tin and copper which form upon the 9 head of the nail and in the space round it, defend the metal from the action of sea water ; and being negative with respect to it, a stronger corroding effect is produced in its immediate vicinity, so that the copper is often worn into deep and irre- gular cavities in these parts. When copper is unequally worn, likewise in harbours or seas where the water is loaded with mud or mechanical de- posits, this mud or these deposits rest in the rough parts or 330 Sir Humphry Davy's further researches on depressions in the copper, and in the parts where the diffe- rent sheets join, and afford a soil or bed in which sea weeds can fix their roots, and to which zoophytes and shell fish can adhere. As far as my experiments have gone, small quantities of other metals, such as iron, tin, zinc, or arsenic, in alloy in copper, have appeared to promote the formation of an inso- luble compound on the surface ; and consequently there is much reason to believe must be favourable to the adhesion of weeds and insects. I have referred in my last paper to the circumstance of the carbonate of lime and magnesia forming upon sheets of cop- per, protected by a quantity of iron above parts, when these sheets were in harbour and at rest. The various experiments that I have caused to be made at Portsmouth, show all the circumstances of this kind of action, and I have likewise elucidated them by experiments made on a smaller scale, and in limited quantities of water. It appears from these experiments, that sheets of copper at rest in sea water, always increase in weight from the depo- sition of the alkaline and earthy substances, when defended by a quantity of cast iron under of their surface, and if in a limited or confined quantity of water, when the propor- tion of the defending metal is under 4-Q^. With quantities below these respectively proportional for the sea, and limited quantities of water, the copper corrodes ; at first it slightly increases in weight, and then slowly loses weight. Thus a sheet of copper 4 feet long, 14 inches wide, and weighing 9 lb. 6 oz., protected by of its surface of cast iron, gained in ten weeks and five days, 12 drachms, and was coated the preservation of metals by electro-chemical means . 331 over with carbonate of lime and magnesia : a sheet of copper of the same size protected by -—3, gained only 1 drachm in the same time, and a part of it was green from the adher- ing salts of copper ; whilst an unprotected sheet of the same class, both as to size and weight, and exposed for the same time, and as nearly as possible under the same circumstances, had lost 14 drachms ; but experiments of this kind, though they agree when carried on under precisely similar circum- stances, must of necessity be very irregular in their results, when made in different seas and situations, being influenced by the degree of saltness, and the nature of the impregna- tions of the water, the strength of tide and of the waves, the temperature, &c. In examining sheets which had been defended by small quantities of iron in proportions under ~~ and above T Qx5-d, whether they were exposed alone, or on the sides of boats, there seemed to me no adhesions of confervas, except in cases where the oxide of iron covered the copper immediately round the protectors ; and even in these instances such adhe- sions were extremely trifling, and might be considered rather as the vegetations caught by the rough surface of the oxide of iron, than as actually growing upon it. Till the month of July 1824 all the experiments had been tried in harbour, and in comparatively still water ; and though it could hardly be doubted, that the same principles would prevail in cases where ships were in motion, and on the ocean ; yet still it was desirable to determine this by direct experi- ment ; and I took the opportunity of an expedition intended to ascertain some points of longitude in the north seas, and which afforded me the use of a steam boat, to make these MDCCCXXV . X X 332 Sir Humphry Davy's jurther researches on researches. Sheets of copper carefully weighed, and with different quanties of protecting metal, and some unprotected, were exposed upon canvass so as to be electrically insulated upon the bow of the steam boat ; and were weighed and ex- amined at different periods, after being exposed in the north seas to the action of the water during the most rapid motion of the vessel. Very rough weather interfered with some of these experiments, and many of the sheets were lost, and the protectors of others were washed away ; but the general results were as satisfactory as if the whole series of the arrange- ments had been compleat. It was found that undefended sheets of copper of a foot square lost about 6.55 grains in passing at a rate averaging that of eight miles an hour in twelve hours ; but a sheet, having the same surface, de- fended by rather less than lost 5.5 grains ; and that like sheets defended by and of malleable iron were similarly worn, and underwent nearly the same loss, that of two grains, in passing through the same space of water. These experiments (the results of which were confirmed by those of others made during the whole of a voyage to and from Heligoland, but in which during the return the protectors were lost) shows that motion does not affect the nature of the limits and quantity of the protecting metal ; and likewise prove, that independently of the chemical, there is a mechanical wear of the copper in sailing, and which on the most exposed part of the ship, and in the most rapid course, bears a relation to it of nearly 2 to 4.55. I used the very delicate balance belonging to the Royal Society in these experiments ; the sheets of copper weighed between 7 and 8000 grains ; and I was fully enabled to ascer- the preservation of metals by electro-chemical means. 333 tain by means of this balance, a diminution of weight upon so large a quantity, equal to iss of a grain. It was evident from a very minute inspection of the sheet with the largest quan- tity of protecting metal, that there was not any adhesion of alkaline or earthy substances to its surface. Having observed in examining the results of some of the experiments on the effects of single masses of protecting metal on the sheeting of ships, that there was in some cases in which sheets with old fastening had been used, tarnish or corrosion, which seemed to increase with the distance from the protecting metal, it became necessary to investigate this circumstance, and to ascertain the extent of the diminution of electrical action in instances of imperfect or irregular con- ducting surfaces. With single sheets or wires of copper, and in small confined quantities of sea water, there seemed to be no indications of diminution of conducting power, or of the preservative effects of zinc or iron, however divided or diffused the surface of the copper, provided there was a perfect metallic connection through the mass. Thus, a small piece of copper containing about 32 square inches, was perfectly protected by a quantity of zinc which was less than 1 part of the whole surface ; and a copper wire of several feet in length was prevented from tarnishing by a piece of zinc wire which was less than i*\nr part of its length. In these cases the protecting metal cor- roded with great rapidity, and in a few hours was entirely destroyed ; but when applied in the form of wire and covered, except at its transverse surface, with cement, its protecting influence upon the same minute scale was exhibited for many days. A part of these results depend upon the absorption 334 Sir Humphry Davy's further researches on of the oxygen dissolved in the water when its quantity is limited, by the oxidable metal, and of course the propor- tion of this metal must be much larger when the water is constantly changing ; but the experiments seem to show that any diminution of protecting effect at a distance, does not depend upon the nature of the metallic, but of the imperfect or fluid conductor. This indeed is shown by many other results. A piece of zinc and a piece of copper in the same vessel of sea water, but not in contact, were connected by different lengths of fine silver wire of different thickness. It was found that whatever lengths of wire of j— of an inch were used, there was no dimunition of the protecting effect of the zinc ; and the experiment was carried so far as to employ the whole of a quantity of extremely fine wire, amounting to upwards of forty feet in length, and of a diameter equal only to of an inch, when the results were precisely the same as if the zinc and copper had been in immediate contact. Pieces of charcoal, which is the worst amongst the more perfect conductors, were connected by being tied together, and made the medium of communication between zinc and copper, upon the same principles, and with the same views as those just described, and with precisely the same consequences. In my first experiments upon the effects of increasing the length or diminishing the mass of the imperfect or fluid con- ducting surface in interfering with the preserving effects of metals, I used long narrow tubes ; but I found them very in- convenient ; and I had recourse to the more simple method of employing cotton or tow for this purpose. Several feet of copper wire in a spiral form were connected the prevention of metals by electro-chemical means. 335 with a small piece of zinc wire of about half an inch in length. The zinc and a portion of the copper were intro- duced into one glass, and the coils of copper wire were intro- duced into other glasses, so as to form a series of six or seven glasses, which were filled with sea water, and made part of the same voltaic arrangement, by being connected with pieces of tow moistened in sea water. It was found in these experiments, that when the pieces of tow connecting the glasses were half an inch in thickness, the preserving effect of the zinc in the first glass was no where diminished, but extended apparently equally through the whole series. When the pieces of tow were about the fifth of an inch in thickness, a diminution of the preserving effects of the zinc was perceived in the fourth glass, in which there was a slight solution of copper ; in the fifth glass this result was still more distinct, and so on till in the seventh glass there was a con- siderable corrosion of the copper. When the tow was only the tenth of an inch in thickness, the preserving effect of the zinc extended only to the third glass ; and in each glass more remote, the effect of corrosion was more distinct, till in the seventh glass it was nearly the same as if there had been no protecting metal. All the che- mical changes dependent upon negative electricity were suc- cessively and elegantly exhibited in this experiment. In the first glass containing the zinc, there was a considerable and hasty deposition of earthy and alkaline matter, and crystals of carbonate of soda adhered to the copper at the surface where it was clean and bright ; but in the lower part it was coated with revived metallic zinc. In the second glass the 336 Sir Humphry Davy’s further researches on wire was covered over with fine crystals of carbonate of lime ; and the same phaenomenon of the separation of carbonate of soda occurred, but in a less degree. In the third glass the wire was clean, but without depositions ; and the presence of alkaline matter could only be distinguished by chemical tests. In the fourth glass the copper was bright, evidently in consequence of a slight but general cor- rosion, but with a scarcely sensible deposit ; in the fifth, the deposit was very visible ; and in the seventh the wire was covered with green rust. These results, which showed that a very small quantity only of the imperfect or fluid conductor was sufficient to transmit the electrical power, or to compleat the chain, in- duced me to try if copper nailed upon wood, and protected merely by zinc or iron on the under surface, or that next the wood, would not be defended from corrosion. For this pur- pose I covered a piece of wood with small sheets of copper, a nail of zinc of about the part of the surface of the cop- per being previously driven into the wood : the apparatus was plunged in a large jar of sea water : it remained per- fectly bright for many weeks, and when examined, it was found that the zinc had only suffered partial corrosion ; that the wood was moist, and that on the interior of the copper there was a considerable portion of revived zinc, so that the negative electricity, by its operation, provided materials for its future and constant excitement. In several trials of the same kind, iron was used with the same results ; and in all these experiments there appeared to be this peculiarity in the appearance of the copper, that unless the protecting metal below was in very large mass, there were no depositions of the preservation of metals by electro-chemical means. 337 calcareous or magnesian earths upon the metal ; it was clean and bright, but never coated. The copper in these experi- ments was nailed sometimes upon paper, sometimes upon the mere wood, and sometimes upon linen ; and the communica- tion was partially interrupted between the external surface and the internal surface by cement ; but even one side or junction of a sheet seemed to allow sufficient communication between the moisture on the under surface and the sea water without, to produce the electrical effect of preservation. These results upon perfect and imperfect conductors led to another enquiry, important as it relates to the practical appli- cation of the principle ; namely, as to the extent and nature of the contact or relation between the copper and the pre- serving metal. I could not produce any protecting action of zinc or iron upon copper through the thinnest stratum of air, or the finest leaf of mica, or of dry paper ; but the action of the metals did not seem to be much impaired by the ordi- nary coating of oxide or rust ; nor was it destroyed when the finest bibulous or silver paper, as it is commonly called, was between them, being moistened with sea water. I made an experiment with different folds of this paper. Pieces of cop- per were covered with one, two, three, four, five and six folds ; and over them were placed pieces of zinc, which were fastened closely to them by thread ; each piece of copper so protected was exposed in a vessel of sea water, so that the the folds of paper were all moist. It was found in the case in which a single leaf of paper was between the zinc and the copper, there was no corrosion of the copper ; in the case in which there were two leaves, there was a very slight effect ; with three, the corrosion was dis- 338 Sir Humphry Davy's further researches on tinct : and it increased, till with the six folds the protecting power appeared to be lost : and in the case of the single leaf, there was this difference from the result of immediate contact, that there was no deposition of earthy matter. Showing that there was no absolute minute contact of the metals through the moist paper; which was likewise proved by other experiments : for a thin plate of mica, as I have just mentioned, entirely destroyed the protecting effect of zinc : and yet when a hole was made in it, so as to admit a very thin layer of moisture between the zinc and copper, the cor- rosion of the copper, though not destroyed, was considerably diminished. The rapid corrosion of iron and zinc, particularly when used to protect metals, only in very small quantities, in- duced me to try some experiments as to their electro-che- mical powers in menstrua out of the contact, or to a certain extent removed from the contact of air, such as might be used for moistening paper under the copper sheathing of ships : the results of these experiments I shall now detail. A small piece of iron was placed in one glass filled with a saturated solution of brine, which contains little or no air ; copper, attached by a wire to the iron, was placed in a vessel containing sea water, which was connected with the brine by moistened tow. The copper did not corrode, and yet the iron was scarcely sensibly acted upon, and that only at the surface of the brine ; and a much less effect was produced upon it in many weeks than would have been occasioned by sea water in as many days. With zinc and brine in the same kind of connection there was a similar result : but the solution of the zinc was com- the preservation of metals by electro-chemical means. 339 paratively more rapid than that of the iron, and the copper was rendered more highly negative, as was shown by a slight deposition of earthy matter upon it. A solution of potassa, or of alkaline substances possessing the electro-positive energy, has nearly the same effect on saline solutions as if they were deprived of air; and when mixed with sea water impedes the action of metals upon them ; but if used in quantity in combinations such as these I have just described, in which iron is the protecting metal, it destroys the result, and renders the iron negative. Thus, if iron and copper in contact, or fastened to each other by wires, be in two vessels of sea water connected by moist cotton or asbestos, all the various circumstances of protec- tion of the two metals by each other may be exhibited by means of solution of potassa. By adding a few drops of solution of potassa to the water in the glass containing the iron, the negative powers of the copper in the other glass are diminished ; so that the deposition of the calcareous and magnesian earths upon it is considerably lessened ; by a little more solution of potassa the deposition is destroyed, but still the copper remains clean. The corrosion of the iron, which before was rapid, is now almost at an end ; and a few drops more of the solution of potassa produces a perfect equilibrium : so that neither of the metals undergoes any change, and the whole system is in a state of perfect repose. By making the fluid in the glass containing the iron still more alkaline, it no longer corrodes ; and the green tint of the sea water shows that the copper is now the positively electrified metal ; and when the solution in the glass containing the iron is strongly alkaline, the copper in the other glass corrodes with mdcccxxv. Y y 340 Sir Humphry Davy's further researches on great rapidity, and the iron remains in the electro-negative and indestructible state. I began this paper by some observations upon the nature of the processes by which copper sheeting is destroyed by sea water, and on the causes by which it is preserved clean, or rendered foul by adhesions of marine vegetables or animals ; I shall conclude it by some further remarks on the same subject, and with some practical inferences and some theoretical elucidations, which naturally arise from the results detailed in the foregoing pages. The very first experiment that I made on harbour-boats at Portsmouth, proved that a single mass of iron protected fully and entirely many sheets of copper, whether in waves, tides, or currents, so as to make them negatively electrical, and in such a degree as to occasion the deposition of earthy matter upon them ; but observations on the effects of the single contact of iron upon a number of sheets of copper, where the junctions and nails were covered with rust, and that had been in a ship for some years, showed that the action was weakened in the case of imperfect connexions by distance, and that the sheets near the protector were more defended than those remote from it. Upon this idea I pro- posed, that when ships, of which the copper sheathing was old and worn, were to be protected, a greater proportion of iron should be used, and that if possible it should be more distributed. The first experiment of this kind was tried on the Sammarang, of 28 guns, in March, 1824, and which had been coppered three years before in India. Cast iron, equal in surface to about — ^ of that of the copper was applied in four masses, two near the stern, two on the bows. She the preseivation of metals by electro-chemical means. 341 made a voyage to Nova Scotia, and returned in January 1825. A false and entirely unfounded statement respecting this vessel was published in most of the newspapers, that the bottom was covered with weeds and barnacles. I was present at Ports- mouth soon after she was brought into dock : there was not the smallest weed or shell-fish upon the whole of the bottom from a few feet round the stern protectors to the lead on her bow. Round the stern protectors there was a slight adhesion of rust of iron, and upon this there were some zoophytes of the capillary kind, of an inch and a half or two inches in length, and a number of minute barnacles, both Lepas anatifera and Balanus tintinnabulum. For a con- siderable space round the protectors, both on the stern and bow, the copper was bright ; but the colour became green towards the central parts of the ship ; yet even here the rust or verdigrease was a light powder, and only small in quan- tity, and did not adhere, or come off' in scales, and there had been evidently little copper lost in the voyage. That the protectors had not been the cause of the trifling and per- fectly insignificant adhesions by any electrical effect, or by occasioning any deposition of earthy matter upon the copper, was evident from this — that the lead on the bow, the part of the ship most exposed to the friction of the water, con- tained these adhesions in a much more accumulated state than that in which they existed near the stern ; and there were none at all on the clean copper round the protectors in the bow ; and the slight coating of oxide of iron seems to have been the cause of their appearance. I had seen this ship come into dock in the spring of 1824, before she was protected, covered with thick green carbonate 342 Sir Humphry Davy 's further researches on and submuriate of copper, and with a number of long weeds, principally fuci, and a quantity of zoophytes, adhering to different parts of the bottom ; so that this first experiment was highly satisfactory, though made under very unfavour- able circumstances. The only two instances of vessels which have been recently coppered, and which have made voyages furnished with protectors, that I have had an opportunity of examining, are the Elizabeth yacht, belonging to the Earl of Darnley, and the Carnebrea Castle, an Indiaman, belonging to Messrs. Wigram. The yacht was protected by about T~ part of malleable iron placed in two masses in the stern. She had been occasionally employed in sailing, and had been some- times in harbour, during six months. When I saw her in November she was perfectly clean, and the copper appa- rently untouched. Lord Darnley informed me that there never had been the slightest adhesion of either weed or shell-fish to her copper, but that a few small barnacles had once appeared on the loose oxide of iron in the neighbour- hood of the protectors, which however were immediately and easily washed off. The Carnebrea Castle, a large vessel of upwards of 650 tons, was furnished with four protectors, two on the stern, and two on the bow, equal together to about -I~: of the surface of the copper. She had been pro- tected more than twelve months, and had made the voyage to Calcutta and back. She came into the river perfectly bright; and when examined in the dry dock was found entirely free from any adhesion, and offered a beautiful and almost polished surface ; and there seemed to be no greater wear of copper than could be accounted for from mechanical causes. the preservation of metals by electro-chemical means . 343 Had these vessels been at rest, I have no doubt there would have been adhesions, at least in Portsmouth or Sheer- ness harbours, where the water is constantly muddy, and where the smallest irregularity or roughness of surface, from either wear, or the deposition of calcareous matter, or the formation of oxides or carbonates, enable the solid matter floating in the water to rest. There is a ship, the Howe, one of the largest in the Navy, now lying at Sheerness, which was protected by a quantity of cast iron judged sufficient to save all her copper, nearly fifteen months ago. She has not been examined ; but I expect and hope that the bottom will be covered with adhesions, which must be the case if her copper is not corroded ; but notwithstanding this, when- ever she is wanted for sea, it will only be necessary to put her into dock for a day or two, scrape her copper, and wash it with a small quantity of acidulous water, and she will be in the same state as if newly coppered. At Liverpool, as I am informed, several ships have been protected, and have returned after voyages to the West Indies, and even to the East Indies. The proportion of pro- tecting metal in all of them has been beyond what I have recommended, ~ to ^ ; yet two of them have been found perfectly clean, and with the copper untouched after voyages to Demarara ; and another nearly in the same state, after two voyages to the same place. Two others have had their bottoms more or less covered with barnacles ; but the pre- servation of the copper has been in all cases judged complete. The iron has been placed along the keel on both sides ; and the barnacles, in cases where they have existed, have been generally upon the flat of the bottom ; from which it may 344 Sir Humphry Davy's further researches on be concluded, that they adhered either to the oxide of iron, or the calcareous deposits occasioned by the excess of nega- tive electricity. In the navy the proportion adopted has been only of cast iron, at least for vessels in actual service, and when the object is more cleanness than the preservation of the copper. It is very difficult to point out the circumstances which have rendered results, such as these mentioned with respect to Liverpool traders, so different under apparently the same circumstances, i. e. why ships should exhibit no adhesions or barnacles after two voyages, whilst on another ship, with the same quantity of protection, they should be found after a single voyage.* This may probably depend upon one ship having remained at rest in harbour longer than another, or having been becalmed for a short time in shallow seas, where ova of shell fish, or young shell fish existed ; or upon oxide of iron being formed, and not washed off, in consequence of calm weather, and which consolidating, was not afterwards separated in the voyage. From what I can learn, however, the chance of a certain degree of foulness, in consequence of the application of the full proportion of protecting metal, will not prevent ship owners from employing this proportion, as the saving of copper is a very great object ; and as long as the copper is sound, no danger is to be apprehended from worms. It ought to be kept in mind that the larger a ship, the more the experiment is influenced by the imperfect conduct- ing power of the sea water, and consequently the proportion of protecting metal may be larger without being in excess. * The quality of the copper may be another cause. the preservation of metals by electro-chemical means . 345 I have mentioned these circumstances because they apply to ships already coppered, and because I have heard that a Liverpool ship, of which it was doubtful whether the copper was in a state such as would enable her to make another voyage to India with security, has, by the application of protectors of T^, made this voyage,* without apparently any wear of her sheeting ; and that she is now preparing with the same protectors to make another voyage. In cases when ships are to be newly sheathed, the experi- ments which have been detailed in the preceding pages render it likely, that the most advantageous way of applying protection will be under, and not over the copper : the elec- trical circuit being made in the sea water passing through the places of junction in the sheets ; and in this way every sheet of copper may be provided with nails of iron or zinc, for protecting them to any extent required. By driving the nail into the wood through paper wetted with brine above the tarred paper, or felt, or any other substance that may be employed, the incipient action will be diminished ; and there is this great advantage, that a considerable part of the metal will, if the protectors are placed in the centre of the sheet, be deposited and re-dissolved : so there is reason to believe that small masses of metal will act for a great length of time. Zinc, in consequence of its forming little or no insoluble compound in brine or sea water, will be preferable to iron for this purpose ; and whether this metal or iron be used, the waste will be much less than if the metal was exposed on the outside : and all difficulties with respect to a proper situation in this last case are avoided. * The Dorpthy. 346 Sir Humphry Davy’s further researches , &c. The copper used for sheathing should be the purest that can be obtained ; and in being applied to the ship, its surface should be preserved as smooth and equable as possible : and the nails used for fastening should likewise be of pure copper ; and a little difference in their thickness and shape wilt easily compensate for their want of hardness. In vessels employed for steam navigation the protecting metal can scarcely be in excess ;* as the rapid motion of these ships prevents the chance of any adhesions ; and the wear of the copper by proper protection is diminished more than two- thirds. * * I have mentioned in the two last communications on this subject some appli- cation of the principle ; many others will occur. In submarine constructions — to protect wood, as in piles, from the action of worms, sheathing of copper defended by iron in excess may be used ; when the calcareous matter deposited will gradu- ally form a coating of the character and firmness of hard stone. I 347 3 XVI. On the Magnetism of Iron arising from its rotation . By Samuel Hunter Christie, Esq. M. A. of Trinity College , Cambridge ; Fellow of the Cambridge Philosophical Society ; of the Royal Military Academy . Communicated April 20, 1825, by J. F. W. Herschel, Esq. Sec. R. S. Read May 12, 1825. A s the principles on which phaenomena depend can only be discovered by a careful investigation of the circumstances attending every new fact which presents itself, its import- ance must not, in the first instance, be estimated by the magnitude of the effects produced, but by their peculiarity. However minute may be the effects, an inquiry into the laws which govern them, if unattended by any other, will have this advantage, that these laws will serve as an additional test of the correctness of the principles advanced for the ex- planation of the more striking phaenomena, firmly establish- ing their truth, if the consequences of those principles, or being incompatible with them, pointing out their fallacy. Thus the severest test that the principle of gravitation has been subjected to, is the explanation of the minute irregula- rities in the planetary motions ; and the coincidence of the observed irregularities with those deduced from the applica- tion of this principle would have established its truth beyond dispute, had any doubt previously remained. In the expe- riments which I am about to detail, the effects produced are of this minute character ; but as they point out a species of mdcccxxv. Z z 348 Mr. Christie on the magnetism of action not hitherto observed, they will not, I trust, be consi- dered unimportant. It has been stated that different effects will be produced on iron, as regards its polarity, when struck, twisted, filed, or scoured in different positions, with respect to the magnetic axis or line of the dip ; but I am not aware that it has ever been suspected that the simple rotation of iron, in different direc- tions, would have any effect on the manner in which the iron influenced a magnetic needle. This I have discovered to be the case ; and that the laws which govern this peculiar action on the needle are so general and uniform, that I have no doubt their causes are as steady in their operation, as those to which the more striking phenomena of magnetism owe their origin. On observing these magnetical phenomena arising purely from rotation, it appeared to me that they might possibly indicate the cause of the earth's magnetism ; and this was a further inducement to me thoroughly to investigate the circumstances connected with them. Before giving the particulars of these phenomena, it is necessary that I should mention how I was first led to observe them. For some time previous I had been engaged in making several series of experiments, with a view to discover the precise manner in which unmagnetised iron acts upon a mag- netic needle. For this purpose I had made use of an iron ball 13 inches in diameter, and likewise of a shell 18 inches in diameter, and observed their effects on the needle in vari- ous positions, as referred to certain planes passing through its centre. The shell and the needle were placed in the re- lative positions which I wished to give them, by determining a radius and an angle on an horizontal plane, and a vertical 34.9 iron arising from its rotation. ordinate. The requisite computations being necessarily tedious, when I wished to pursue the subject further, I found them, from their number, so laborious, that I resolved, if possible, to supersede the necessity of them by the construc- tion of an instrument, by which I could adjust the iron and the needle in their proper relative positions, without any previous computation. In this I succeeded ; but as the iron was to be supported on an arm of brass, it became necessary to make use of a plate of iron instead of the heavy shell of nearly 500 lbs. weight ; and in consequence of this, when I expected that I had overcome the principal difficulties, I found they had only commenced. It is well known that almost every mass of iron, but especially sheet iron, pos- sesses polarity in a slight degree, and of a very variable nature in some parts of it, whatever care may have been taken in its manufacture ; and I soon found, to my no small vexation, that the effects apparently produced by it in that which I made use of were so various, that they would for a long time baffle me in my investigations, if they did not ulti- mately frustrate all my attempts at drawing any conclusions from the experiments. The instrument which I have mentioned is represented in Plate XXV. fig. 1. The principal part consists of two strong limbs of brass : one, SON, a semicircle, 18 inches in diameter, 2.15 inches broad and .3 inch thick: the other consists of two semicircles joined together ; S JE N, 1.2 inches broad and .22 thick, and its outer diameter 18 inches ; s cen .9 inch broad, .22 thick, and its inner diameter 9.2 inches S JE N n ce s and S Q N are attached to each other by strong brass pins passing from S to .v and N to n ; so that s /E n will 350 Mr. Christie on the magnetism of > revolve about the axis S s n N, while S Q N is fixed. S JE N and S Q N are graduated from R E and Q towards S and N, as is likewise s cen from ce towards s and n. The semicircle S Q N passes freely through an opening in the support G I, but may be clamped firmly in any position by means of two strong screws, working into the parts G,G7 from the back of the instrument. On the chamfered edge of the opening g , in the face of G G, is an index showing the inclination of the axis S N to the horizon ; and on the part K k at the foot of the pillar, and attached to it, is an index pointing out on the graduated circle L /, fixed on the table T t , the situation of the fixed limb SON with respect to the magnetic meridian. R r is another graduated circle, fixed to the moveable limb S ; which, by the index at x on the fixed limb S Q N, shows the angle described by S N from the plane of S Q N. A very strong brass pin, soldered to the foot of the pillar, passes through the table T t and a thick circle of wood, to which the legs are attached, and has below a clamping screw, to fix the whole firmly together in any position. The com- pass box N7 S7 is fitted on to a stand fixed to the support F /, which consists of two parts ; f fitted to G, and F sliding on a tube attached to/; so that the compass may be elevated or depressed. An arm A B, to carry the circular plate of iron C c, is connected with the moveable limb S^N. The part A a consists of two flat pieces, having the limb of the instrument between them, so that the arm may be moved into any position on it, and be fixed in that situation by means of a strong screw working into the face A a. On the cylin- drical part B 6, a short hollow cylinder slides freely, having a circular rim raised .6 inch from it, to support the iron plate 351 iron arising from its rotation. C c at right angles to the axis of the cylinder. Over the plate of iron is a wooden washer D d , which is pressed on it by the screw h working on the short cylinder. The cylinder with the plate is fixed in any position on the arm by the clamp M m. In the part A a of the arm are two openings o, o', on the chamfered edges of which are indexes in a line with the axis of the cylinder B b, so that when each points to the same arc on the semicircles S JE N, s cen, the axis of the cylinder B b is directed towards their centre, and every point in the edge of the plate is at the same distance from that centre. As the weight of the plate was a considerable strain on the instrument, a scale to contain a counter-weight, was suspended from the ceiling of the room, and the line from it passed through a moveable pulley, attached to the arm B b , so that the weight might easily be adjusted to relieve nearly altogether the strain of the plate on the arm in any position. The arm was also occasionally supported, and kept steady in its position, by a sliding rod resting on the table T t. The compass consists of a circular box, containing a circle 6 inches in diameter, very accurately divided into degrees, and again into thirds of a degree ; and a very light needle, having an agate in its centre, and its point of suspension only .07 inch above the surface of the needle. The extremities of the needle are brought to very fine points ; so that by a little practice, with the assistance of a convex lens, I could read off the deviations very correctly to two minutes, being the tenth of the divisions on the circle. To this compass I have ano- ther needle, which has a vernier at each end ; but this being much larger and heavier, and consequently not so sensible, I greatly prefer the other for all delicate experiments. In the 352 Mr. Christie on the magnetism of experiments which I had previously made, and in those which I proposed making with this apparatus, I conceived a sphere to be described about the centre of the needle, referring the situation of the iron to a plane, in which, according to the hypothesis I had adopted, it should equally affect the north and south ends of the needle. The line in which the needle would place itself, if freely suspended by its centre of gravity, I considered as the magnetic axis ; the points where this axis cuts the sphere, the poles, the upper being the south, and the lower the north pole ; and the great circle at right angles to the axis, the equator, being the plane above mentioned. The position of the iron was thus determined by its latitude and longitude ; the longitude being always measured from the eastern intersection of the equator with the horizon. The angle which the axis makes with the horizon I considered to be, according to the most accurate observations, very nearly 70° so'.* As I shall have frequently to refer to different adjustments * In 1818 Captains Kater and Sabine found the dip to be 7 o° 34 in the Regent’s Park; and in 1819, in the same place. Captain Sabine found it to be 70° 3 3'. 27. Since making the greater part of these experiments, I have had oppor- tunities of observing the dip at this place. With a very good instrument, by T. Jones of Charing Cross, having a 7-inch needle, consisting of two circular arcs, on Captain Kater’s construction, the mean of 40 observations, 10 with the face of the instrument east, 10 with the face west, and the same with the poles reversed, gave the dip 70° 15.25 on the 23d December, 1821, between the hours of 1 and 4 P. M. the observations being made in my garden. With another instrument, also by T. Jones, having an 8-inch rectangular needle, the mean of 40 observations made in my garden, (about a mile from the former place of observation) near noon on the 5th and 6th May, 1824, gave 70°o6.5 for the dip. With the same instru- ment, but using a needle on Meyer’s construction, the mean of 40 observations near noon on the 8th May, 1824, gave the dip on the same spot 700 io'.5. 353 iron arising from its rotation. of the instrument, I will here briefly notice their effects. The angle which the axis SN, fig. 1. makes with the horizon H O, being 70° 30', if S ON is in the magnetic meridian, and the compass is adjusted, so as to have its centre in the centre of the instrument, SN will be the magnetic axis, and the centre of the plate, as there represented, would, by the rota- tion of the limb S/EN, describe a parallel of latitude, its longitude being indicated on the circle R r : and if the in- dexes at 0, o' be brought to coincide with JE, the centre of the plate would then describe the equator. If the limb SQN be slided through G G' until the index there coincide with 19° 30', from O towards S, and the indexes 0, o' be made to coincide with /E as represented in Fig. 2, the centre of the plate, by the revolution of the limb, would describe a secon- dary both to the meridian and equator, and its latitude would be indicated on the circle R r. If the point Q, Fig. 1, or zero on the limb S Q N, be brought to coincide with the index at g, and the instrument make a quarter of a revolution about G I , so that the index at K may point to 90°, the centre of the plate would describe the meridian when the indexes at 0, o' coincide with JE, ce ; and the latitude would be deter- mined from the degrees indicated on R r. This is repre- sented Fig. 3, where the contrary side of the instrument to that seen in Fig. 1, 2, is placed in front, in order 'to show the situations of the screws, which clamp the arm A B and the limb SQN in their respective situations. Thus, by a proper adjustment of the indexes at KJ(g, 0, o', the centre of the plate may be made to describe any circle of the sphere. After making a very few sets of experiments with this instrument, I found that it was necessary to attend very par- 354 Mr. Christie on the magnetism of ticularly to the situation of certain points on the iron plate with respect to the limb, since, with one point coinciding with it, the deviation of the needle, when the centre of the plate was on the meridian, would be easterly, and with another point coinciding, westerly ; whereas had the iron possessed no partial magnetism, which was the case I wished to investigate, there would have been no deviation when its centre was on the meridian. My first object was to find what points on the plate must coincide with the limb, in order that the plate, when its centre was on the meridian, should cause no deviation in the needle ; and it was in my attempts to effect this, which at first sight appears sufficiently easy, that I discovered the leading feature in all the phe- nomena which I am about to describe. General description of the phcenomena arising from the rotation of an iron plate. In order to find the points which I have mentioned, 1 adjusted the instrument so that the plane of the fixed limb was exactly in the magnetic meridian, and then brought the other limb into the same plane : the centre of the plate was then on the magnetic meridian, and its plane perpendicular to that plane, as represented in Fig. 1. I now made the plate revolve in its own plane about the axis B b , and noted very carefully its effect on the needle. In doing this I found that if I placed the plate on the arm, so that a certain point, c for instance, coincided with the plane of the limb, the deviation was different when the same point, by the revolu- tion of the plate, coincided with the limb again. As it ap- peared by this that the revolution of the plate had an effect ThibJTrans. MDCCCXXV^W. Phil Trans. MDC C G XX-V. Plate JOCV1 . p ■ 35P ■ JT. Christie del * •Pf Posit e scalp* ♦ 3 55 iron arising from its rotation. upon the needle, independent of the partial magnetism of particular points, I considered that if the plate were made to revolve the contrary way, the deviation ought to be on the opposite side, and this I found to he the case. I will illustrate this by the observations made when I first noticed the effect. The plate was divided at every 300 of its circumference (Fig. 4.) by lines drawn through the centre, and being placed on the arm, so that o° coincided with the upper part of the limb, the north end of the needle pointed io' east ; but when this point again coincided with the limb, by the upper edge of the plate revolving from west to east , the needle pointed 30' east : making the plate revolve the contrary way, that is, its upper edge from east to west , when o° coincided with the limb, the north end of the needle pointed 28' west: so that there was a difference of 58', when every point of the plate had the same position with respect to the needle, according as the plate was brought into that position by revolving from west to east , or from east to west. As this appeared extra- ordinary, I made repeated observations at the time, to ascer- tain that the effect was independent of any accidental circumstances, and found that the results always accorded with the first, the difference caused by the rotation of the plate being however greater or less according to the position of the plate. Having fully satisfied myself that, in whatever manner the rotation of the plate might cause this difference, such was really the effect, l next endeavoured to ascertain the nature and degree of the difference, according to the different situa- tions of the centre of the plate. For this purpose I made a great variety of experiments, of which I shall not however MDCCCXXV. 3 A 356 Mr. Christie on the magnetism of here give the details, as I afterwards repeated them in a more convenient manner, and with greater precision; but shall merely point out the nature of them in general, and the con- clusions which I at the time drew from them. The instru- ment being adjusted, and the arm fixed so that the centre of the plate was in the position which I required, I made the plate revolve so that its upper edge moved from west to east, and noted the greatest and least deviation of the north end of the needle ; I then made the corresponding observations when the plate revolved in the contrary direction : a mean of the differences between the two greatest and between the two least I considered as the effect produced on the needle by the rotation of the plate in opposite directions. Repeating these in a variety of positions, I found that when the centre of the plate was in the magnetic meridian, its plane being always a tangent to the sphere circumscribed about the centre of the needle, the deviation of the needle caused by the rotation of the plate in its plane was the greatest when the centre of the plate was in the equator, and that it de- creased from there towards the poles, where it was nothing ; * that when its centre was on the equator, this deviation was the greatest when the centre of the plate was on the me- ridian, or in longitude 900, and decreased to nothing in the east and west points, or when the longitude of the plate was o° or 180°; and that when the centre of the plate was in the * I should here mention, that, from the nature of my instrument, I could not make observations at the north pole ; but as the results, as far as I could observe, were of the same nature on this side of the equator as on the south side, I think I am warranted in concluding, that at the north pole the results would likewise be of the same nature as at the south pole. iron arising from its rotation. 357 secondary both to the equator and meridian, the rotation of the plate, whatever might be its latitude, caused no deviation of the needle. In these experiments, the plate which I made use of was a circular one 17.88 inches in diameter, and .0 99 inch in thickness, weighing 1 1 2 oz. The further I had pursued this inquiry, the more I was disposed to attribute the effects I have mentioned to a general magnetic action, arising in a peculiar manner from the rotation of the iron ; and my next experiments were with the view of ascertaining how far this idea was correct. As similar results might not be obtained with any other plate, I next made use of a plate 12.13 inches in diameter and .075 inch in thickness, weighing 38.75 oz., and with it obtained results precisely of the same nature, though considerably less in quantity. Another objection which occurred to me was this — that the iron being evidently slightly polarised in particular points, the effect might be supposed to arise from an impulse given to the needle by the motion of these points in a particular direction, and that the directive power of the needle not immediately over- coming the slight friction on the pivot, a deviation might thus arise from the rotation of the plate. Had this, however, been the cause of the deviations, I should have expected that, when the centre of the plate was in the meridian, the greatest effect would be produced with the plate parallel to the horizon, and its centre vertical to that of the needle ; but I had seen that the greatest deviation took place when the centre of the plate was in the equator, its plane being per- pendicular to it ; and the deviation arising from the rotation , when the plate was parallel to the horizon, was not a fifth of the deviation when the plate was perpendicular to that 358 Mr. Christie on the magnetism of plane. Besides it was manifest that if this were the cause, any other impulse would have a similar effect. I therefore made the needle revolve first in one direction and then in that opposite, by means of a small bar magnet, and invariably found that it settled at the same point, in whichever direction the impulse was first given, and the results obtained by the rotation of the plate were in these cases of the same nature as before. It was also evident, that if the deviations I have mentioned arose from this circumstance, the needle being agitated after any particular point of the plate was brought to the limb of the instrument, it ought to settle in the same direction, whether that point were brought into this position by revolving from east to west or from west to east ; but this, except in the cases I have mentioned, where the rotation pro- duced no deviation, was not found to take place. In order wholly to obviate this objection, in all my future experi- ments, after any point had been brought to the limb of the instrument, I agitated the needle, and let it settle before I noted the deviation. Description of particular experiments. As I had found in my first experiments that I could obtain the nature of the deviation caused by the rotation by noting the greatest and least deviations when the plate was made to revolve in contrary directions, but that the quantity of that deviation could not by this means be determined with any degree of precision, I resolved to make my future ob- servations differently. The method I adopted, when the change in the deviation from one point of the plate to another was considerable, was this : the plate being placed in any 359 iron arising from its rotation. required position, I made it revolve once, for example, the upper edge from east to west , without noting the deviations, bringing the point marked o° to coincide with the line indi- cating the position for observation ; from hence I continued the revolution of the plate until the point marked 30° coincided with the same line, and, after slightly agitating the needle, noted the deviation ; and in the same manner were the points 6o°, 90°, 120°, 150°, 180°, 2100, 2400, 270°, 300°, 330°, 360° or o° brought successively to coincide, and the deviations noted. I now made the plate revolve once from west to east , without noting the deviations, bringing o° or 360° to coincide with the same line, and then brought in succession 330°, 300°, 270°, 240°, 210°, 180°, 1500, 120°, 90°, 6o°, 30°, o° to coincide, noting the deviations as before. The sum of the first set divided by 12, I considered as the mean deviation, when the plate revolved from east to west; and the sum of the others divided by 12, as the mean deviation, when the plate revolved from west to east : their difference was the mean effect of the rotation in contrary directions. This I call the Deviation due to Rotation ; and to distinguish it from the deviation caused simply by the position of the iron, I call this last the Absolute Deviation. When the change in the deviation from one point of the plate to another was not so considerable, I made the observations only for the points o°, 90°, 180°, 270° on the plate. I now proceed to the detail of the experiments, and the conclusions I draw from them. In those which I shall first describe, the centre of the plate was always in the magnetic meridian ; its plane was perpendicular to the meridian, and a tangent to the sphere, whose centre was the centre of the 26o Mr. Christie on the magnetism oj needle; and the plate revolved, as in all other cases, in its own plane: they are a repetition of those by which I first discovered several of the facts I have mentioned, but made for the purpose of determining more precisely the deviation caused by the rotation. In making these, the in- strument was adjusted so that the index at g, fig. 1, pointed to o°, that at K to 90°, and those at o, o' to Zero ; so that S N was horizontal and pointed east and west, as represented in fig. 3. In the following table, the numbers in the first column indicate the points of the plate which coincided with the plane of the meridian nearest the south, or upper pole of the sphere, when the several directions of the north end of the needle in the same lines with them were observed ; the latitudes and longitudes are those of the centre of the plate as referred to the centre of the needle, the longitudes being measured from east through north ; the letters at the tops of the columns indicate the direction in which the edge of the plate, nearest the south pole of the sphere, moved ; the mean deviation of the needle, when the plate revolved in this direction, is placed in the line below the other deviations ; the direction in which the deviation due to rotation took place, in the following line ; and the whole deviation, arising from making the plate revolve in opposite directions, below this : the deviations observed always refer to the north end of the needle. The distance of the centre of the plate from that of the needle was 9.75 inches ; the diameter of the plate, 17.88 inches; thickness, .099 inch; weight, 112 oz. : so that its specific gravity appeared to be 7826. This plate I call No. I. iron arising from its rotation. $6 1 c* b+ CO 2 W w £ £ w • w C) w £ w W Hl(4 W 0 :£ ■MS S| O CO 0 0 0 •M CIS -5 •£2 £ - 0 0 NO O b* 'b to O NO N O 0 N O X u cS c 0 0 CO . 0 0 ^ G 4-1 O rt 4-» ^°° v CO 0 <-> N i-« O 4* N 0 ■b 'b O NO N O 4-J Z 00 CO 2£ ■5 0 CO « 0 0 £ 00 O £ » -r\ O w 00 N O O N O *£ vi -M CO 0 O 0 4-J w W N ' N O O N CO *«H £ N b+ ■b CO O hJN iri O £ 0 4-J O '-CD ^ •Hi CO CO 2 w « & * w £ w 0 CO o* 0 O m N N 0 C 4J 0 CJ H-l £ w w £ to °o m ^°o bi)^ G O C3 V-l ^ N O O NO O -*b Tb 0 NO cn O N O 4-J Mlrt 'r^. 0 4-> w -8 0 *■< 00 »-H 0 N O O O O bb, NO N O O 4-» z >- 0 cd *>o N ntn O 4J w ».» O w N N O 00 0 0 NO >■* £ 0 0 4-J Z z . "0 © 0 0 0 w 0 4-t H3 n 'b S-H 0 O N -b O w NO CO 0 w CO 0 H4 w ON M O m 0 4- Z vO ur> G •O | ■ s ho 3§ s • ^ *> * G +-> O rt .-1 *1 w 0 4-i £ 0 0 w N bH m 00 ■4- 0 NO N O w NO ►-« 0 w 0 4-» £ O O ^ On • CO bo G 4-1 O rt *-1 J 0 4-J w £ — b " Tb 0 O O m £ NO O W N M O rx CO O £ 0 4-J z O O csi oj •'Ha £ Oj'cd w 0 4-J w v'O LO Q_P O & N O w 00 0 w HlrJ NO 0 0 ‘ w 0 4-J fc "on °oZ w 0 4-* W '8 O ^ 00 O £ NO N O « O W *-iW On O O w 0 4-J hW- V NO ^ a. | .42 3 ~ Q n3 cj S :S -r s .« cd iC2 bo^ G .iJ O rt ^ h-J 0 -M w W 0 0 0 ^h* vy-\ >— < »-H w 0 0 W|N M V O O 4-1 O O C\o bS)^- G 4^ 0 rt ^-1 0 4-J W X ^ M O O £ NO rh £ NO *-* w 0 N O tx. CO 0 £ O 4-J 55 0 O * CO °o 0 y mi ~°Os 0 4-J w £ ^ O 0 0 ■■* W ^b O O NO l-N N rj- Mlr» 00 NO O £ O ■M £ 'HJCt m z, °' *Q g.® N =On O 4-J w £ 'Bn O O w NO 0 00 0 vO CO HH H]<4 ON ■b O £ 0 4-J z H|f4 NO CO *N 2 £ s s :g 0 hO’-C •3 :« 1° • 5. § O W 0 4-i 55 til ” G 4J O C3 w 0 4-» w 0 0 W w 0 CO 0 O O O w ' 0 w 0 4-J 55 O cd . '0 O CO w 0 4J w ^ Tf- 0 0 N ro O W Tb «JO 0 w 0 CO M w ON CO 0 W 0 4-1 H|rt ro *.'o O MO w 0 4-* w O O N N O W 0 NO O w 0 bb W cn C K ^ s e s HD 0 ’ 0 ON . H3 0 w O ^ V" rn O W •b O O W 0 N M W 00 r^i O w 0 4-1 'Z, mx b. o" O N O b0° C 4-J O rt *1 0 4-J w ^ 0 0 0 N N N O DO N O *— £ 0 £ O 4-J z Ml(4 is ^ s K 0s- cd S > • *1 bb° S ~ O cc ^ 3\ O •M w w . N O O O £ O N O ►H O N O N O * 0 4-< '4m 0 *-« CxS O 4-J £ ^ N • O w NO N M nf" N 1— w NO CO O w J-!rt OO •b O H 0 4-* £ On 0 G 0 •a c c 5.9 QJ H- S 1 QJ 2 • O c c .2.0 0 Q QJ 3 c “ 0 a 5 2 2 G O « ■- '> O u ** Q O O On 0 00 O IS 1 rs ► 1 QJ -o C c 5.2 QJ *-• t QJ T3 O * C C .2 0 g.s .b > Q QJ 3 -a c 0 c ’z; O *5 0 2 u- *> 0 QJ ~ a * In these positions the plane of the plate was vertical, and its centre in the same horizontal line as that of the needle. + In this position the plane of the plate was horizontal, and its centre vertical to that of the needle. I Here the deviations are those corresponding to the coincidence of the points on the plate with the southern meridian- 36 2 Mr. Christie on the magnetism of From these observations it appears, that when the centre of the plate was in the pole of the magnetic sphere, its plane being parallel to the equator, the position of the needle, for any situation of the several points of the plate, was the same whether they were brought into that situation by the plate revolving from east through south to west, or from west through south to east ; that is, that the deviation due to rotation was nothing : That the deviation due to rotation increased from this point towards the equator, where it was the greatest : And that the horizontal needle was affected by the rotation of the plate, not according to the situation of the centre of the plate as regarded the poles and equator of the horizontal needle, but as regarded the poles and equator of an ima- ginary dipping needle passing through the centre of the horizontal needle. This last is not so evident, from the circumstance of the deviation being nothing when the centre of the plate was in the pole of the dipping needle, and a maximum when in the equator, as from its being very nearly equal at equal distances on each side of the pole, and also of the equator, that is, at very unequal distances from the axis of the horizontal needle ; and from the deviations at equal distances from the axis of the horizontal needle being very unequal. For if we compare the deviation due to rotation in lat. 70° 30' S, long. 90°, with that in lat. 7o°3o'S, long. 270°, the difference is only l' ; in the first case, the centre of the plate was at the dis- tance of 90° from the axis of the horizontal needle, and its plane parallel to it ; and in the other at the distance of 510, and its plane making an angle of 39° with this axis. Again, 3 6$ iron arising from its rotation. in the four corresponding situations of lat. 190 30', the mean deviation due to rotation is i° 32', and none of the deviations differ from this by more than 5', although in two cases the centre of the plate was in the axis of the horizontal needle, and its plane perpendicular to it, and in the two others the centre of the plate was at the distance of 390 from this axis, and its plane made an angle of 510 with it. The mean of the deviations due to rotation in the three* corresponding situa- tions of lat. 450 is 49', from which none of the deviations differ by 3', notwithstanding the difference in the situations of the centre and plane of the plate, in these cases, with re- spect to the axis of the horizontal needle. In long. 900 lat. 45° S, the centre of the plate was 64° 30' above the horizontal axis, and its plane made an angle of 250 30' with it ; in long. 90° lat. 450 N, it made an angle of 64° 30' at 250 30' below it ; and in long. 270° lat. 45° S, it was in a position above it similar to the last. Any doubt, however, on the subject will be removed, if we compare the deviation in long. 90° lat. 390 N with that in long. 270° lat. o ; the one deviation being nearly double of the other, although the centre of the plate was at the distance of 1 90 30' from the axis of the horizontal needle, and its plane made an angle of 70° 30' with it in both cases. The difference is even more striking, if we compare the deviation in lat. 70° 30' S, long. 270°, with that in lat. 310 30'S, long. 90°, the centre of the plate being in each case at the distance of 510 from the axis of the hori- zontal needle, and its plane making an angle of 390 with it. * The nature of the instrument would not admit of obserrations being made so near to the north pole in long. 270° as lat. 450, or so near as lat. 70° 30' on the other side of the support G I. 3 B MDCCCXXV. 364 Mr. Christie on the magnetism of The differences which we have noticed in the deviations ob- served at the same distance from the equator, is not more than I have found to arise from a slight change in the adjust- ment of the centre of the needle to the centre of the instru- ment, the plate remaining in the same position. These errors of adjustment I found it almost impossible to avoid, owing probably in a great measure to the magnetic centre of the needle not being in the centre of suspension ; and it was to counteract their effects, that I generally made observa- tions on contrary sides of the centre. With respect to the direction in which the deviation due to rotation took place, it appears, that the rotation of the plate always caused the north end of the needle to move in the same direction as the edge of the plate nearest the south pole of the magnetic sphere : so that the deviation of the north end of the needle was in the direction in which the south edge of the plate moved, and that of the south end of the needle in the direction in which the north edge moved, referring the edges to the poles of the sphere. Having ascertained, that when the centre of the plate was in the pole, and its plane parallel to the equator, the deviation due to rotation was nothing ; and some of the first experiments which I had made having indicated that this was also the case when the centre of the plate was in the secondary to the equator and meridian, and its plane, as before, a tangent to the sphere, I wished to ascertain whether such were really the fact. The experiments, the results of which are given in the following table, left no doubt in my mind on the sub- ject. In making them, the instrument was adjusted, so that the index at K (Fig. 1 ) pointed to zero, that at G to 190 30' 365 iron arising from its rotation. from O towards S, and those at o, o' to zero on the limb S^N, as in Fig. 2. The deviations for the several points of the plate are those observed when these points coincided with the southern or upper part of the secondary to the equator and meridian ; and the direction of rotation is, as before, that of the edge of the plate nearest to the south pole of the sphere. II. Table of the deviations of a magnetic needle caused by the rotation of a circular plate of iron , when its centre was in the secondary to the equator and meridian , and its plane a tangent to the sphere : the distance as before 9.75 inches. Plate No. I. — — Points on the Plate. Long. o°. Lat. o°. Long. 1800. Lat. o°. Long. o°. Lat. 4.50 S. Long. 180°. Lat. 450 S. Long. o°. Lat. 450 N. Long. 1800. Lat. 450 N. S to N N to S N toS S to N S toN N toS N to S S to N StoN N to S N to S S to N 0 0 06 E A / 0 06 E 0 0 26 W 0 / 0 24W 0 / 7 24W 01 ^° / 7 22W 6 48 E 0 / 6 48 E 0 / 7 08 E 0 , 7 10 E lo , 7 3 2 W 0 , 7 3 2 W 90 0 14 E 0 14E 0 40 W 0 40W 7 40 00 t-O VQ O 6 56 7 18 7 20 8 00 7 58 180 0 04 E 0 04 E 0 32 W 0 32W 6 52 6 54 5 58 6 00 6 26 6 26 j6 52 6 52 270 0 04 w 0 04W 0 20 W 0 20W 6 28 6 28 5 48 5 48 6 08 6 08 |6 30 6 28 Mean Deviations 0 5 E 0 05 E 0 29 1 W 0 29W 7 06W 7 06W 6 23 E 6 23 E 1 6 45 E 6 46 E 7 13 l W 7 I2*W Deviation due to rotation o° oo' o° oo' | o° 00' 0° oo' o° oi' o° 01' From these observations, combined with the preceding, we may infer, that if the centre of the plate were made to de- scribe any parallel of latitude, the deviation due to rotation would be nothing when the longitude was o° or 180°, and a maximum when the longitude was 90° or 270°, which is precisely the reverse of the absolute deviations that would be produced by the plate describing the parallel of latitude. 366 Mr. Christie on the magnetism of The next experiments which I made, were with the view of determining whether the rotation of the plate would pro- duce any deviation, when its plane coincided with the equator. For this purpose an axis was fixed perpendicularly on the arm of the instrument in such a manner, that, when the plate revolved on it, its plane was parallel to the limb. This is represented in fig. 5 : AB is the arm, on the cylindrical part of which, B 6, is fixed perpendicularly to it the axis V v, on which the plate of iron, C c, here seen edgewise, revolves. A, a , are the two flat pieces, having an opening between them for the limb of the instrument ; Z is the clamping screw, and Y y the circular rim to support the iron plate, which are not seen in fig. 1. In order to make these observations, it was necessary to adjust the whole instrument twice ; since the deviations for the longitudes 90° and 270° could not be observed with the same adjustment as those for the longitudes o° and 180°. For the longitudes 90° and 270°, the axis of the instrument was horizontal and pointed east and west, as in fig. 3, and the moveable limb E AW revolved on the axis until its plane, and therefore also that of the iron plate, made an angle of 90° 30' with the horizon, rising towards the north ; so that the compass being elevated until the centre of the needle was in the plane of the plate, the plate was then in the equator. For the other longitudes, the axis of the instrument was inclined to the horizon at an angle of 190 30', and in the plane of the meridian, as in fig. 2, and the moveable limb adjusted at right angles to the fixed one: the compass was then elevated to coincide with the plane of the plate. In these experiments the distance of the centre of the iron iron arising from its rotation. 3 67 from the centre of the needle was 13.2 inches; but as its edge was only 4*26 inches distant, the differences between the deviations corresponding to the several points on the plate were greatly increased ; and therefore, to obviate any inaccuracies that might arise, from the points not being brought into precisely the same situation when the plate revolved in the opposite directions, I increased the number of observations, making twenty-four for each position, namely, twelve points on the plate, as I have before de- scribed, the deviation for any point being observed when that point coincided with the line joining the centre of the plate and needle. The letters at the tops of the columns indicate the direction of rotation of the inner edge of the plate, or that nearest the centre of the needle. III. lable gJ the deviations of a magnetic needle, caused hy the rotation of a circular plate of iron, when its centre was in the equator 9 and its plane in the plane of the equator. Plate No. I. 36 8 Mr. Christie on the magnetism of 3 69 iron arising from its rotation. These observations show very clearly, that when the centre of the plate is in the equator, and its plane also coincides with the plane of the equator, the deviation due to rotation is always nothing, since the small differences to be observed here in the revolutions in opposite directions are only such as may justly be attributed to slight errors in the adjustments of the centre of the needle or of the plane of the plate, which are almost unavoidable. With regard to the several deviations in the different columns, I should notice, that they are not those actually observed, but derived from them by subtract- ing the same number from all the deviations observed in two corresponding columns, so that they indicate the same dif- ference of deviations in the two revolutions as those actually observed, and therefore give the same deviation due to rotation. The necessity of this reduction arose from the circumstance of my having to adjust the compass to the proper height, so that its centre might be in the plane of the plate, while it was under the influence of the partial magnetism of particular points in the plate ; and having done this, when zero of the compass was brought to coincide with the point of the needle it was not necessarily in the magnetic meridian, since the needle was under the influence of this partial magnetism ; and as I wished the deviations to be those from the meridian, I reduced the observed deviations as I have mentioned. Being convinced that the rotation of the plate in the plane of the equator caused no deviation of the needle, I proceeded to determine the effects produced by its rotation in other planes. In the first set of observations which made, the centre of the plate was in the meridian, and its p ane perpen- dicular to the plane of the meridian and passing through the 370 Mr. Christie on the magnetism of centre of the needle. Before however making these, to avoid the necessity of moving the compass as in the last, I made a slight alteration in the instrument. Instead of having the axis on which the plate revolved perpendicular to the arm, and the plate consequently parallel to the limb, this axis was inclined in such a manner that the plane of the plate passed through the axis of the instrument, as represented fig. 6 ; so that the axis of the instrument being horizontal, and passing through the centre of the needle perpendicularly to the meridian, as in fig. 3, when the arm of the instrument was adjusted to zero on the limb, the revolution of the limb caused the centre of the plate to describe the magnetic meridian, and at the same time the plane of the plate always passed through the centre of the needle. The distance be- tween the centre of the plate and that of the needle was as in the last 13.2 inches. The observations are given in the fol- lowing table, where the letters above the columns indicate the direction of rotation of the plate's inner edge. Long. o°. Lat. o°. Long. o°. Lat. io°S. Long. 0°. Lat. 20° S. Long. o°. Lat. 30°S. Long. 0°. Lat. 40°S. Long. o°. Lat. 45° S. Long. o°. Lat. 50“ S. Long. o°. Lat. 6o° S. Long. o°. Lat. 70° S. Long. o°. Lat. 8o° S. Lat. 900 S. Upper Edge. E to W W to E E to W | W to E E to VI MW to I :j e to Vi WtoE EtoW WtoE EtoW W to E E to W W to E EtoW W to E E. to W W to E E toW WtoE E to W W to E Inner Edge. S to N N to S S to IS N to S to b N to £ S to b N toS S toN N to S S to N N to S S to N N to S S to N N to S S to N N to S S to b N toS 0 ° / 2 10 E 0 1 1 24 w O / l O / 5 24W| 8 46V O / / J3 OO \ V 16 10V Vi 1 9 16V V 21 30V O / V 21 50W 23 08V 0 1 T 21 44W O ' / 22 30W O 1 21 52W O '22 16 w 18 18W O . 1 8 00W O . , 13 22 W 12 22W O 1 8 20W 6 58 W 1 46 W 0 18 W 3° 1 54 1 5° 5 4° 9 28 13 IO 16 44 19 22 21 50 21 54 23 20 21 50 22 40 21 50 22 io 18 30 l8 12 13 TO 12 20 8 18 6 58 1 48 0 24 60 > 46 ‘ 58 6 34 9 44 13 16 1 6 50 1 1 9 22 21 54 21 56 23 20 21 48 22 40 21 30 21 50 l8 24 l8 04 13 20 12 18 8 14 6 j4 1 46 0 iS ( 9° 0 54 2 38 7 20 n 06 j’ 4 *4 17 24 1*0 40 23 06 23 18 24 38 23 20 23 58 22 40 22 56 19 16 18 58 14 00 12 50 9 00 7 36 2 18 0 48 1 120 O OO 3 4° 8 30 ! I 2 20 |»5 12 18 32 21 20 23 38 23 4° 24 56 z3 38 24 16 22 44 [22 S8 ■9 H 18 JO 14 00 12 50 8 50 7 26 1 56 O 22 150 0 30 W 14 20 9 34 >3 08 ij 52 19 10 (21 54 24 22 24 l6 25 26 23 S8 24 36 23 20 j23 4° 19 22 18 58 14 06 12 52 8 56 7 32 1 58 0 28 180 0 30 |+ 40 9 36 13 34 15 50 1 9 3° 21 46 24 3° 24 04 25 24 24 OO 24 38 00 ~nT 04 04 OO 19 18 18 56 14 00 12 52 8 52 7 36 1 42 O 20 210 |o 08 '4 30 9 10 !3 20 IS 32 1 1 9 02 21 36 24 3° 23 38 25 08 23 36 24 26 22 56 23 16 1 8 46 18 30 ■3 42 12 46 8 24 7 08 i 24 O OO 24O 0 30 E 3 38 8 00 1 1 38 14 06 17 44 20 04 22 28 22 44 24 04 22 20 23 10 22 08 !22 30 l8 OO 17 42 13 10 12 18 7 5° 6 38 o 54 0 38 E 27O 1 46 1 54 6 16 1 g 48 12 26 1 1 6 04 18 20 20 46 20 58 22 24 ' 20 56 21 46 21 20 '21 42 17 10 l6 50 12 56 n 48 7 36 6 10 O 5O 0 44 30° 2 44 j I 20 4 46 8 28 1 1 48 15 18 17 50 20 20 20 22 21 40 20 36 21 20 21 06 21 26 16 54 >6 38 12 56 11 46 7 38 6 12 O 5O O 4O 33° 2 38 jt 20 4 5° j 8 28 j 1 2 06 15 20 18 16 20 26 20 58 22 08 20 48 21 26 21 10 21 26 17 18 l6 52 13 10 I I 50 7 44 6 18 1 28 0 18 Mean Deviations. 0 56 £E 2 46 w 7 1° 49. '3 52 | 17 19 >9 58l 22 26 1 22 28i 23 48 22 224 23 06 1 22 09 i j22 I9 18 22 -i 18 02 J ‘3 3° i 12 241 8 18 f 6 57i 1 32 fW ° °3{W Direction of Deviation by rotation. S to W S to E S to W S to E S to W S to E S to W S to E S to W S to E S to W S to E S to W S to E S to E S to W S to E S to W S to E S to W S to E S to W Deviation due to rotation. 3° 42' T 3° 4°'t 3" 26' Jj 2° 27'i 1° 19' i °° 43' 4 0° l9'i — o° 20' .— 1° 06' — 10 21 i 29'£ Long. 1800. Lat. o°. Long. 1800. Lat. io°S. Long. 1800. Lat. 20° S. Long. 1800. Lat. 30° S. Long. 1800. Lat. 40' S. Long. 1800. Lat. 450 S. Long. 1800. Lat. 50° S. Long. 1800. Lat. 6o° S. Long. 1800. Lat. 70°S. Long. 180°. Lat. 8o° S. Upper Edge. E to W W to E E to W W toE E to W W toE E to W WtoE E to W W toE E to W W to E EtoW W to E E to W W to E E to W W toE E toW W to E inner Edge. N toS S to N N to S S toN N to S S to N N to S S to N N to S S to N N to S S to N N toS S to N N to S S to N N to S S toN N to S S to N O 0 / I 30W 04 W 6 48 E 3 36 E 0 / 14 06 E O / 10 50 E O / 19 50 E o i, 17 24 E O , 21 44 E 0 / 20 10 E ° 21 36 E O / 20 50 E 20 58 E 20 38 E 17° 26 E O / 17 48 E O / n 42 E O / 12 48 E O f 5 34 E O , 6 52 E 3° 0 32 1 '8 7 38 4 3° >4 52 I I 5O 20 42 18 18 22 IO 20 40 21 46 21 OO 21 OO 20 40 17 26 17 46 II 4]2 12 48 5 36 6 50 60 0 38 E z 52 8 42 5 20 15 44 12 42 20 OO [9 34 22 38 ZI 30 22 IO 21 22 21 10 20 52 17 36 18 00 12 OO 12 56 5 38 6 56 9° 2 14 20 9 46 6 18 16 48 13 38 23 00 20 22 22 42 21 40 22 12 21 30 21 00 20 42 17 22 17 48 11 32 12 34 5 08 5 2» 120 3 16 3 22 10 48 7 32 18 00 15 OO Z4 20 21 44 24 02 22 58 23 40 23 OO 22 18 22 02 18 16 18 40 12 08 13 10 5 34 6 58 •5° 3 12 3 26 10 40 7 12 8 00 15 OO 24 IO 21 34 24 08 22 50 z3 54 23 10 22 24 22 08 18 16 18 40 12 04 13 08 5 3° 6 50 180 12 26 10 46 7 16 7 58 14 58 24 20 21 36 24 34 23 16 24 30 23 48 22 50 22 32 18 38 19 04 12 22 I3 20 3 44 7 00 210 40 12 11 30 7 58 9 20 5 54 25 OO 22 14 25 24 !3 56 25 26 24 34 23 40 23 20 I9 12 19 36 12 50 13 58 6 08 7 20 240 38 IO 1 1 48 8 16 9 22 15 58 24 50 22 08 25 54 !4 38 25 52 Z5 10 24 12 23 52 -9 46 20 08 13 20 14 22 6 40 8 00 27O 24 12 10 40 7 06 7 48 4 4° ’-3 °° 20 28 25 08 -3 38 25 04 24 20 23 4Z 23 22 19 22 19 50 13 12 14 18 6 38 8 00 300 42 52 9 10 5 4° 6 52 3 26 I 42 ‘9 34 24 06 2 36 Z4 OO 23 18 23 10 22 48 19 OO 19 26 12 50 14 06 6 30 7 52 33° 50W 4 28 w 7 4° 4 >4 5 18 1 40 O 22 8 02 22 56 1 18 22 40 21 56 12 OO 21 38 18 IS 8 40 12 28 13 36 5 14 7 34 Mean Deviations. 45 iE 1 58 jw 9 39 T 6 14I 7 00 1 3 48 2 46 ^ .0 144 -3 47 i 2 25 4 23 34rr 22 49 4 22 22 22 02 1 18 *3\ ■8 47 i 12 20 J ■3 25 i 54 i °8-j* r )irection of Deviation by rotatiou. S to W S to E S to W S to E S to W S to E S toW S to E S toW S to E S to W S to E S to W S to E S to E S to W S to E S to W S toE to W E eviation due to rotation. 3° 43' i 3° 24' 1 3° 12' | 2° 31' J i° 21' 4 °° 44' i °° 19' i — o° 24' — i°°4f -»°i3$ • In adjusting the compass for the observations in long. 0°, lat. io° and lat. o°, the north end of the needle pointed 50' W of zero in the box, and consequently 50' should be subtracted from the westerly, and added to the easterly deviations. A similar error of 30' W was made in the adjustment for lat. 8o°, long. i8o°and long. o°, and lat. go°. These will not affect the deviations due to rotation; but the absolute deviations must be increased when-east, and diminished when west. , -S . . * - . . -n - ~ . 371 iron arising from its rotation. Here we find, directly contrary to what took place when the plane of the plate was a tangent to the sphere, that the devi- ation due to rotation increases from the equator to the pole where it is a maximum. In this case, however, as in the other, the deviations are very nearly equal at equal distances on each side of the equator ; so that, as before, it appears that the horizontal needle was affected by the rotation of the plate, not according to the situation of the centre of the plate with respect to the poles and equator of the horizontal needle, but with respect to the poles and equator of an ima- ginary dipping needle passing through the centre of the horizontal needle. , * With regard to the direction of the deviation due to rota- tion, it appears, that when the centre of the plate had north latitude, the north end of the needle deviated in the direction of the motion of the plate’s inner edge ; and when it had south latitude, the north end deviated in a contrary direction to that of the inner edge of the plate, and therefore the south end devi- ated i?i the direction of the inner edge : so that, the end of the needle of the same name as the latitude, always deviated in the direction of the motion of the plate's inner edge. Let us compare this with the inference we have drawn from the observations in Table I. viz. that when the centre of the plate is in the meridian, and its plane a tangent to the sphere, the north end of the needle, by the rotation of the plate, deviates in the direction of the motion of the south edge, and the south end in the direction of the north edge of the plate ; that is, either end of the needle deviates in a direc- tion contrary to that of the motion of the edge of the plate nearest to the pole of the sphere of the same name as that MDCCCXXV. 3 C 372 Mr. Christie on the magnetism oj end. Now, if from the position which the plate had in the last experiments, namely, its plane passing through the cen- tre of the needle, it be conceived to revolve about its dia- meter, which is perpendicular to the plane of the meridian, until its plane be a tangent to the sphere, the direction of the revolution about this diameter being of the inner edge towards the pole of the same name as the latitude of the plate's centre, the inner edge will become the edge of the same name as the end of the needle, which, in its first position, according to our inference from the last observations, deviated in the direction of its rotation ; but according to the inference drawn from Table I. the end of the needle of the same name as this edge will, in the new position, deviate in a direction contrary to that of its rotation ; so that the rotation of the plate being in the same direction in both positions, the deviations by rota- tion will be in contrary directions in the two cases : and con- sequently, between the two positions, the plane of the plate must have passed through one in which the rotation would produce no deviation. If we conceive the plate to come into the position of the tangent plane by revolving about its dia- meter in the opposite direction, that is, by the inner edge moving towards the pole of a contrary name to the latitude, the inner edge will become the edge of the contrary name to the end of the needle, which in the first position, deviated in the direction of its rotation ; and therefore that end of the needle will still continue to deviate in the same direction ; that is, the direction of the rotation being the same in the two positions, the deviation by rotation will be in the same direction in both cases ; and consequently, between the two positions, either there is no position of the plane of the plate 373 iron arising from its rotation. in which the rotation will produce no deviation, or there are two, or some even number of such positions. I have not been able to determine in all cases experimen- tally the situation of the plane in which the deviation due to rotation vanishes, or whether there may be more than one plane in which this takes place; but all the observations which I have made, confirm me in the opinion which I formed on comparing the preceding results, that when the centre of the plate is in the meridian, there is only one plane between the tangent plane and the plane passing through the centre of the needle in which the deviation due to rotation vanishes, and that that plane is parallel to the equator. Another conclusion which we may draw from these expe- riments compared with those in Table I. is this, that when the centre of the plate is in the meridian, and its plane per- pendicular both to the meridian and equator, then, supposing the plate always to revolve in the same direction, the devi- ation will always be . in one direction, in whatever point of the meridian the centre of the plate may be ; for when the centre of the plate is in longitude 90°, latitude o, Table I. the plane of the plate has this position, and also when in lati- tude 90° S. and 90° N. Table IV. and with the same direc- tion of rotation, the deviation will be in one direction in these two cases. As I had already found, that, when the centre of the plate was in the secondary to the equator and meridian, and its plane a tangent to the sphere, the rotation caused no devi- ation of the horizontal needle ; it appeared to me, that there ought to be no deviation due to rotation when the plane of the plate was in any other plane perpendicular to this secondary. 374 Mr. Christie on the magnetism of To ascertain how far my views were correct, or otherwise, I adjusted the plate on the arm as in fig. 6. the same as in the last experiments, and the instrument as in fig. 2 : so that the axis y£Q being in the plane of the meridian and inclined to the horizon at an angle of 190 so', the centre and plane of the plate were, during the revolution of the limb, always in the position I required. The distance between the centres of the needle and plate was as before 13.2 inches. The follow- ing Table exhibits the observations which I made ; the letters at the tops of the columns indicate the direction of rotation of the plate's inner edge ; and the numbers in the first column, the points on the plate which coincided with the plane of the secondary, when the several directions of the north end of the needle in the same lines with them were observed. The observations were made at every io° of latitude, as in some cases there was an indication of deviation due to rotation. To fact pagt 374. V. Table of the deviations of a magnetic needle caused by the rotation of a circulur plate o) iron when its centre was in the secondary to the equator and meridian , and its plane perpendicular to this secondary, and passing through the centre of the needle. Plate No. 1 Long. o° Lat. o° Long. o° Lat. io° S. Long, o'5 Lat. 200 S. Long. o° Lat. 30° S Long. o° Lat. 40° S Long. 0® Lat. 450 S Long. o° Lat. 50° S Long. o° Lat. 6o° S. Long. o° Lat. 700 S. Long. o° Lat. 8o°S Lat. 90° S S toN N toS S to N N to S S to N N to S StoN N to S StoN N to S S to N N to S S to N N to S S to N N to S S to N N to S S to N N toS S to N N to S 0 1 16 E °i 16 E 6 58 W 3 56 W i°i 10 W 1 1 10W 16 12W 16 14W 17 36 W 0 • 17 30W 17 5°W 17 50W i°6 56W 16 58W !°3 40W i°3 38 W i°o 08W 10 02W 1 S 08 W 5 08W 0 / 0 x 2 E 0 1 0 22 E 30 1 24 E 1 22E S 3° 5 3° 10 24 10 24 1 5 16 15 10 16 52 16 50 17 02 17 00 16 20 16 20 13 32 13 26 10 00 9 54 S 06 5 °4 0 20 0 20 60 1 18E 1 20 E 3 44 3 42 9 22 9 24 13 32 13 32 15 42 15 38 IS 56 15 5 2 15 24 15 22 12 58 12 52 9 3* 9 26 4 5° 4 5° 0 24 0 22 90 0 s+E 0 52E 3 CO 2 58 9 26 9 2 4- 13 14 13 10 15 40 ij 40 •5 44 •S 4° 1 S *4 15 08 12 S2 12 48 9 24 9 20 4 50 4 S° 0 20 0 22 120 0 20 E 0 18E 2 56 2 52 9 32 9 32 13 18 13 20 IS 48 ■ s 48 16 00 IS 58 1$ 20 15 20 12 56 12 54 9 32 9 3° 4 5° 4 48 0 18 O 22 I50 0 18W 0 22 W 3 38 3 4° 10 22 10 24 14 10 14 16 16 18 16 20 26 38 16 38 15 s 2 IS 50 13 04 13 02 9 46 9 42 4 5° 4 48 0 20 O 24 l8o i 00 W 1 04 W 4 56 4 5Z 1 1 26 1 1 22 >5 3° 15 30 17 18 17 22 17 36 17 40 16 40 16 40 13 24 13 24 IO 08 10 10 4 5* 4 54 0 24 O 28 210 1 44 W 1 42 W 6 24 6 24 12 30 12 30 17 10 17 10 18 18 l8 20 18 46 18 42 17 36 17 36 14 00 13 56 IO 32 10 30 5 °» 5 °4 0 22 O 26 24O . 54 W . s+w 7 44 7 42 13 04 13 00 18 08 18 06 18 56 18 54 19 24 19 20 18 16 iS 12 14 18 14 12 IO 46 10 40 5 08 5 08 0 26 O 24 27O i 04 w I 02 W 8 04 8 04 12 40 12 34 18 00 i7 58 18 38 l8 36 19 16 19 12 18 02 18 20 14 06 14 00 IO 36 10 36 5 10 5 *° 0 24 O 24 300 0 04 w O 02 W 8 06 8 06 2 00 1 1 56 17 40 17 38 18 24 l8 20 19 02 19 02 17 S2 ■7 5* 14 00 13 58 IO 32 10 30 5 *° 5 *° 0 22 O 22 33° 0 38 E 0 42 E 7 44 7 44 11 34 11 32 16 52 16 52 17 50 17 48 18 26 l8 22 17 20 17 l6 >3 42 •3 42 IO l8 10 16 5 08 5 08 0 20 O 20 Mean Deviations. 0 01 1 W ooijW S 434 S 4*1 ■I 07 i 1 1 06 ■S 45 i >5 44l 17 17 ■7 *5 1 17 387 17 36 16 444 16 4* r «3 32 7 ■3 *94 10 06^ 10 03 5 °° 1 5 00 i 0 21 f 0 23 Deviations due to rotation. 0 oof' o° 014' o° oi|' o° 00J' o° OI o° oi|' o° 01 o° 03V °° °3l' o° ooj' o° 01^' ... ' • . * 375 iron arising from its rotation. Although the deviations due to rotation are here in some cases greater than might perhaps on a first view be expected, if in the position in which I have supposed the plate, its rotation would really produce no deviation, yet the differ- ences are not in any case more than may, I consider, be fairly attributed to errors in the adjustments. That the deviations, when the plate revolved from south to north, had a tendency most generally to be greater than when it re- volved in a contrary direction, as is evident by referring to the Table, appears at first sight more unfavourable to my opinion than the magnitude of the difference ; but on further consideration, I think that this will be allowed rather to point out the source of the errors in the results, than the incorrect- ness of my views, and that these errors arose from the plane of the plate not being in those cases perpendicular to the plane of the secondary to the equator and meridian. The proximity of the edge of the iron to the ends of the needle, varying from 5.16 inches to 4.27 inches at the south end, and from 5.16 inches to 5.92 inches at the north end, I con- sidered to be another source of error ; the inequalities arising from the effects of particular points near the edges of the iron on the ends of the needle being the more sensible when the distances are small. All my observations were made as near to the centre of the needle as the instrument would admit, in order that the effects of the rotation, since they were in many cases extremely small, might be the more sensible ; and by this means I discovered the nature of the effects produced on the needle by the rotation of the plate ; but I am fully convinced, that for the purpose of comparing the results of observation with the conclusions from theory, 376 Mr. Christie on the magnetism of it is always desirable, that the observations should be made when the iron is at such a distance from the centre of the needle, that the effects of particular points, near its edges, on the ends of the needle are nearly insensible. Taking these circumstances into consideration, I was quite satisfied from these experiments, that, if the centre of the plate be in the secondary to the equator and meridian, and its plane per- pendicular to the plane of that circle, the rotation of the plate will produce no effect on the absolute deviations caused by the mass. In order to determine what effects would be produced by the rotation of the plate when its centre was in the secondary to the equator and meridian, and its plane in the plane of this circle, the instrument was adjusted as in fig. 1. the index at g pointing to 70° 30'; the limb S^TN was then placed at right angles to SQN, and the arm AB attached to it with the iron plate on the axis as in fig. 5 ; and that the centre of the needle might be in the plane of the plate, the compass box was moved in the direction of the meridian. Some of my first observations were made with the centre of the plate in the equator, and I immediately found, that the deviation due to rotation , instead of being o, as in the cases when the plate revolved in the planes at right angles to its present position, was here considerable ; and also that, that of the south end of the needle was in the direction of the upper, or south edge of the plate, contrary to what had been observed in the same plane at the pole (Table IV. lat. 90°). This in- dicated that there must be, at least, one point in this circle on each side of the pole, where the deviation due to rotation was o ; and to determine nearly the latitude of this point, I 377 iron arising from its rotation. made observations at every io° degrees of latitude on each side of the south pole. Before, however, giving these obser- vations, it is necessary that I should state the kind of reliance I place on them as forming a complete set. In order to make the observations near the pole, it was necessary to adjust the instrument as in iig. 3. and after having made the complete set, I suspected that, in the change from the one adjustment to the other, the centre of the plate had been nearer to that of the needle in making the observations near the equator, than those near the pole ; and that consequently, the deviations due to rotation in the former case, were proportionally too great. I was confirmed in this suspicion on comparing these observations with those which I had, in the first instance, made in lat oc and in lat. 900; and still further on comparing them with others, which I subsequently made at the several distances 15, 17, 19, 20 inches; in the corresponding situ- ations. For example, in my first observations, the deviations due to rotation in lat. o°, long. o°, and in lat. o° long. 180° were 30 10', and 30 14', giving a mean 30 12' in lat o ; and in lat. 90 S, i° 31'; when the centres of the plate and needle had been carefully adjusted to the same distance 13.2 inches, in the two cases ; whereas the corresponding deviations in the table are 3° 43' and i° 29^' ; and, by subsequent obser- vations, I found the sum of the deviations at the distances 15, 17, 19 and 20 inches to be in these two cases, 70 20' and 3° 32', to which 30 12' and i° 31' are very nearly propor- tional. As however these differences do not in the least affect the conclusions which I at the time drew from this set of observation, and they were all made immediately follow- each other, I prefer giving them as a complete set for the 378 Mr. Christie on the magnetism of purpose of illustration ; they are contained in the following Table. The numbers in the first column indicate the points on the plate which coincided with the line joining the centres of the plate and needle, when the several observations of the directions of the north end of the needle were made. Of the letters at the tops of the columns, the upper ones indicate the direction of rotation of the south ; or upper edge of the plate, with respect to the points in the horizon ; and the lower ones, the direction of the inner edge , or that nearest the axis, with regard to the poles of the sphere ; the letters at the bottoms of the columns indicate the direction of the devi- ation of the south end of the needle due to rotation , To /act page 378 VI. Table of the deviation s of a magnetic needle, caused by the rotation of a circular plate of iron, when its centre was in the secondary to the equator and meridian, and its plane in the plane of this secondary. Plate No. I. Long. o°. Lat. o°. Long. o°. Lat. io°S. Long. cp. Lat. 200 S. Long. ce. Lat. 3Q°S. Long. ce. Lat. 40°S. Long. o°. Lat. 450 S. Long. o°. Lat. 5o°S. Long. 0*. Lat. 6o° S. Long. o*. Lat. 70° S. Long. o“. Lai. 8o* S. Lat. 90* S. Upper Edge. E to W | W to E Eto W | WtoE E 10 W IW to E E to W W toE E to W WtoE Eto W W to E E to W W to E Eto W W to E E to W W to E E toW W to E E to W W to E Inner Edge. S toN J N toS S toN I N toS IS to N j N to S S to N N toS | S to N | N toS S to N N toS S to N N toS S toN N to S S to N N to S S to N N to S O 2 10 E L . Ii 24 w 5 Mv L , |. , 1. . 1. . 8 46Wji3 00W 16 10W 19 16W 21 30W Li 50WI23 08W 21 44 W 22 30 W 21 52 W 0,0, 22 16W18 18W 18 00W >”3 22W 12 22W 8 z'oW 6 58 W °i 46 W 0 i*8 W 30 1 54 ji 50 5 40 9 28 13 10 1 1 6 44 |*9 22 21 50 I*1 54 |*3 20 21 50 22 40 21 50 22 IO 18 30 18 12 13 »o 12 20 8 18 6 58 1 48 0 24 60 1 46 ■ 58 6 34 9 44 1 1 3 16 1 1 6 50 ‘ *9 22 21 54 j2* s« 23 20 21 48 22 40 21 30 ^21 50 l8 24 is 04 13 20 ,2 .8 8 14 6 54 1 46 0 iS 90 0 54 2 38 7 20 1 1 06 |*4 >4 |*7 24 20 40 23 06 |23 >8 24 38 23 20 23 58 22 4° |22 56 *9 16 18 58 14 00 12 50 9 00 7 36 2 18 0 48 120 0 00 3 4° 8 30 12 20 J 1 5 12 1 1 8 32 21 20 23 38 23 4° 24 5« 23 38 24 l6 22 44 *22 58 19 I4 18 50 14 00 12 JO 8 30 7 26 1 S6 0 22 | 150 0 30 W I4 20 9 34 ‘3 |'S 5* |*9 IO 1** 54 24 22 Jz4 *6 25 26 j23 58 24 36 23 20 [23 40 *9 22 .8 58 14 06 12 S2 8 36 7 32 1 58 0 28 180 |° 3° ]4 4° 9 36 ‘3 34 |'S 5° |*9 3° 21 46 24 30 24 04 25 24 24 OO 24 38 23 18 23 38 19 18 l8 36 14 00 12 52 8 52 7 36 1 42 0 20 210 |o 08 J4 30 9 10 13 20 (15 32 j 1 9 02 2 I 36 24 30 |23 38 25 08 |23 36 24 20 22 36 23 l6 18 46 l8 3O •3 42 12 46 8 24 7 08 1 24 0 00 24O [0 30 E |3 38 8 00 1 1 38 j 1 4 06 Ji 7 44 20 04 22 28 22 44 24 04 122 20 23 IO 22 08 22 30 |i8 00 >7 42 13 10 12 l8 7 5° 6 38 O 54 0 38 E | 270 1 46 ji 54 6 16 9 48 ,12 26 |i6 04 l8 20 20 46 20 58 22 24 20 56 21 46 21 20 21 42 |'7 >o 16 50 12 56 1 1 48 7 36 6 10 O 5O 0 44 | I 3°° 2 44 |l 20 4 46 1 8 28 J 1 1 48 Ji 5 18 17 50 20 20 20 22 21 40 20 36 21 20 21 06 21 26 16 54 if. 38 1 2 56 I 1 46 7 38 6 12 O 5O O 4O 33° 2 38 1 20 4 50 | 8 28 1 1 2 06 15 20 18 l6 20 26 20 58 22 08 20 48 21 26 21 IO 21 26 17 18 16 52 1 3 10 I I 50 7 44 6 18 1 28 O l8 Mean Deviations. ° sn e 2 46 w 7 084 10 49* 13 52 17 I9 '9 58 T 22 26 £ 22 28£ 23 48 22 22* 23 06 7 2 2 09 i 22 10 18 22 1 18 02 J *3 3° * 12 24* 8 18 £ 6 S7 $ ■ 32 7 W 0 °3 i W Direction of Deviation by rotation. S to W S to E S to W S to E S to W S to E S to W S to E S to W S to E S to W S to E S to W S to E S to E S to W S to E S to W S to E S to W S to E S to W Deviation due to rotation. 3° 4 2'i 3° 4°'t 3" *6' 4 2" 27'* t” 19'* °° 43' T o° 19'^ — o° 20' wl° 06' — 1° 21 $ — *° 29 j Long. 1800. Lat. o°. Long. i8o°. Lat. io°S. Long. 180°. Lat. 20° S. Long. 1800. Lat. 3o°S. Long. 1800. Lat. 40' S. Long. 1800. Lat. 450 S. Long. 1800. Lat. 50°S. Long. 1800. Lat. 6o° S. Long. 180°. Lat. 70°S. Long. 180°. Lat. 8o° S. Upper Edge. E to W W to E E to W WtoE E to W W to E E to W WtoE E to W W toE E to W WtoE Eto W W to E E to W W to E E to W W toE E to WjW to E Inner Edge. N to S S to N N to S S to N N toS S toN N to S S to N N toS S to N N to S S to N N toS S to N N to S S to N N to S S toN N to S Is to N O i° 30W j 04 W 6° 48 E 3 3*6 E 14 06 E 10 50 E 19 50 eJ 1 7 24 E 21 44 E 20 10 E 21 36 E 20 50 E 20 58 E 20 38 E 17 26 E 17 48 E 0 / 1 1 42 E 12 48 E 0 . L . 5 34 E]6 52 E 30 0 32 4 18 7 38 4 3“ 14 52 1 1 50 20 42 J18 18 22 10 20 40 21 46 21 OO 21 00 20 40 17 26 17 46 11 42 12 48 S 36 |6 5° 60 0 38 E 2 52 8 42 5 20 >5 44 12 42 20 00 *9 34 22 38 21 30 22 10 21 22 21 10 20 52 17 36 18 00 12 00 12 56 S 38 |<> 56 90 2 I4 1 20 9 46 6 18 16 48 13 38 23 00 20 22 22 42 21 40 22 12 21 30 21 00 20 42 17 22 17 48 11 32 12 34 5 08 5 28 120 l6 0 22 IO 48 7 32 18 00 15 00 24 20 21 44 24 02 22 58 23 40 23 OO 22 18 22 02 18 16 18 40 12 08 13 10 5 34 |s 58 150 12 0 26 O 40 7 12 1 1 8 00 15 00 24 10 21 34 | 24 °8 22 50 23 54 23 IO 22 24 22 oS 18 16 18 40 12 04 13 08 5 3° I6 5° i So 12 26 O 46 7 |*7 58 14 58 24 20 21 36 j H 34 1 23 1 6 24 30 23 48 22 50 22 32 ■a 38 1 9 04 12 22 13 20 3 44 |7 <=“ 210 +° 12 11 30 7 58 19 20 *5 54 25 00 22 14 25 24 1 23 56 25 26 24 34 23 4° (23 20 19 12 19 36 12 50 13 $8 6 08 7 20 240 38 10 I 48 8 16 19 22 IS 58 24 50 22 08 j 25 54 J 24 38 25 52 25 10 24 12 23 52 19 46 20 08 13 20 H 22 6 40 |8 00 270 24 12 O 4O 7 °6 17 +8 14 40 23 00 20 28 | 25 08 | 23 38 25 °4 24 20 23 42 |z3 22 19 22 >9 50 13 12 14 l3 6 38 |8 00 300 42 52 9 10 5 4° l6 52 13 z6 1 42 9 34 24 06 j 22 36 24 00 23 18 23 10 I22 48 19 00 19 26 12 50 14 c6 6 30 I7 52 33° 50 w 28 W 7 40 4 14 | 15 18 I I 40 0 22 8 02 22 56 1 21 l8 22 40 21 56 22 00 '21 38 18 18 l8 40 12 28 13 36 6 14 |7 34 Mean Deviations. 45 7 E 58 A W 9 39 r 6 >4t 7 00y 13 48 2 46* 0 >4t 3 47 t j 12 25 * 23 34$ 22 49 i 22 22 L2. ■8 23 $ ■8 47 $ 12 20* ■3 25* S 54} 7 084* Direction of Deviation by rotation. S to W Sto E to W S to E S to W S to E StoW S to E S toW S to E S to W S to E S to W S to E S to E S to W S to E S to W S to E js to W Deviation due to rotation. J 3° 43'$ 3° *4' 1 3° >2'J 2° 3*' h 1° 21' $ °°44't °° »9's — CP 24' — 1°04| ->°>3$ * In adjusting the compass for the observations in long. o°, lat. io°and lat. o°, the north end of the needle pointed 50' W of zero in the box, and consequently 50' should be subtracted from the westerly, and added to the easterly deviations. A similar error of 30' W was made in the adjustment for lat. 8o°, long. i8o°and long. o°, and lat. 900. These will not affect the deviations due to rotation; but the absolute deviations must be increased when. east, and diminished when west. iron arising from its rotation. 379 It appears, from these observations, that, when the plate revolves in the plane of a secondary to the equator and meridian, ist. The deviation due to rotation is a maximum when the centre of the plate is in the equator. 2d. It decreases as the plate approaches the pole, and is o between the latitudes 50° and 6o°, apparently very nearly at 550 ; and from this point it increases till it attains a maximum in a contrary direction at the pole. 3d. At the south pole and on each side down to the lati- tude 550, the deviation of the south end of the needle, due to rotation, is in the direction of the north, or lower edge of the plate : or, from the south pole down to the latitude 550, the south end of the needle moves towards the plate, when the inner edge of the plate moves from the south pole, and from the plate when the inner edge moves towards the south pole. 4th. From the equator towards either pole as far nearly as the latitude 550, the south end of the needle moves in the direction of the south edge of the plate ; that is, it moves towards the plate when the inner edge of the plate moves towards the south pole, and from the plate, when that edge moves from the south pole ; also the north end of the needle moves towards the plate, when the inner edge moves towards the north pole, and from the plate, when that edge moves from the north pole. Consequently towards whichever pole the inner edge moves, the corresponding end of the needle will move towards the plate from the equator to the latitude of 55° nearly, and the contrary will take place from the lati- tude 530 to the pole. The observations which I made with the plate on the north MDCCCXXV. 3 D SSo Mr. Christie on the magnetism of side of the equator, though not so multiplied as those on the south, were sufficient to show, that the deviations due to rotation observed the same laws on that side of the equator as I had noticed on the south side. The deviation due to the rotation of the plate, when its cen- tre is in the secondary to the equator and meridian, having a peculiar character, namely, two greater maxima when the centre is in the equator, two less maxima, in a contrary direction, when the centre is in either pole, and four points where it vanishes, I consider to be particularly well adapted for forming an estimate of the correctness of any theory which may be adopted for the explanation of the phaenomena in general ; since the theory must be perfectly compatible with these peculiarities, before it can be applied to the expla- nation of the less marked phenomena. As it appeared from these observations, that the point where the deviation due to rotation vanishes, is not far from lat. 550, the complement of which, 350, is nearly half the angle of the dip, I wished to ascertain whether the deviation were really o in latitude 540 45', which I considered to be correctly the complement of half the dip 70° 30', although I could not see how the angle which the plane makes with the horizon could have an influence on an angle in the plane itself. The following observations show, that in this instance the devi- ation due to rotation vanishes, or nearly so, when the polar distance of the centre of the plate is equal to half the angle which the dipping needle makes with the horizon. Whether this coincidence is purely accidental, or is a necessary conse- quence of the manner in which the effect is produced, must remain doubtful, until it can be shown how the action takes iron arising from the rotation 381 place ; it, however, led me to ascertain precisely the point at which the deviation due to rotation vanishes VII. Table of the deviations of a magnetic needle caused by the rotation of a circular plate of iron when the centre and plane of the plate were in the secondary to the meridian and equator , and its centre in latitude 54° 45'. Lat. 540 45' S. Lat. 540 45 1 N. Long. 1800. Long. o° Long. 1800. Long. o°. Upper Edge. E to W W to E W to E E to W W to E E to W E to W W to E 0 30 60 90 120 150 l8o 210 24O 27O 3°° 330 0 / 20 42 E 20 30 19 54 19 18 19 50 19 38 20 16 21 30 22 32 22 26 22 02 21 26 0 / 20 42 E 20 32 19 56 19 20 19 52 19 38 20 16 21 26 22 32 22 28 22 04 21 26 » / 20 44 w 19 50 19 30 20 26 20 50 21 42 22 22 22 22 21 34 20 42 20 30 20 36 0 / 20 44W 19 50 19 28 20 24 20 46 21 46 22 24 22 20 21 34 20 42 20 30 ! 20 36 21 36W 21 10 20 50 20 16 20 24 19 52 19 4 6 19 24 19 28 20 28 21 10 21 12 O / 21 40 W 21 10 20 50 20 18 20 22 19 50 19 44 19 20 19 28 20 30 21 10 21 l8 O / 19 56E 20 18 20 44 20 56 20 48 20 34 19 50 19 40 19 09 19 58 19 38 20 00 0 f 19 56E 20 20 20 44 20 58 20 50 20 36 19 50 19 40 19 08 19 00 19 38 20 02 Mean Deviations. 20 50 -f 20 51 20 55 f 20 55 1 20 28 20 28 ^ 20 02 \ 20 03 £ Deviation due to rotation. — o° oof' 4- O0 OO'-y — oc ooy — 0 3 01' General law of the deviation due to rotation deduced from the experiments. Having now ascertained the nature of the effects produced on the horizontal needle by the rotation of the plate in diffe- rent planes, I endeavoured to discover some general law, ac- cording to which the direction of the deviation depended on the direction of the rotation of the plate ; so that the situation of the centre of the plate, the plane in which it revolved, and 382 Mr. Christie on the magnetism of the direction of rotation being given, we might point out immediately the direction in which the deviation would take place. On comparing together all the facts which I have detailed, I found that this might be effected in the following manner. I refer the deviations of the horizontal needle to the devia- tions of magnetic particles in the direction of the dip, or to those of a dipping needle passing through its centre ; so that, in whatever direction this imaginary dipping needle would deviate by the action of the iron, the horizontal needle would deviate in such a manner as to be in the same vertical plane with it : thus, when the north end of the horizontal needle deviates towards the west, and consequently the south end towards the east, I consider that it has obeyed the deviation of the axis of the imaginary dipping needle, whose northern extremity has deviated towards the west and its southern towards the east ; so that the western side of the equator of this dipping needle has deviated towards the south pole of the sphere, and its eastern side towards the north pole. It would follow from this, that if the north and south sides of the equator of the dipping needle (referring to these points in the horizon) deviated towards the poles, no corresponding deviation would be observed in the horizontal needle ; the effect, in this case, taking place in the meridian, would only be observable in the angle which the dipping needle made with the horizon. As it is not my intention at present to advance any hypothesis on the subject, I wish this to be con- sidered only as a method of connecting all the phenomena under one general view. Assuming it then for this purpose, it will be found that the deviations of the horizontal needle due 383 iron arising from its rotation. to rotation are always such as would be produced by the sides of the equator of this imaginary dipping needle deviating in direc- tions contrary to the directions in which the edges of the plate move, that edge of the plate nearest to either edge of the equator producing the greatest effect on it. By referring to the particular laws which I deduced at the time of making the experiments in different planes, it will be seen that they are all comprised under this general law ; but this will be rendered more evident by taking an instance. When the centre of the plate is in the meridian, and its plane a tangent to the sphere, the eastern side of the equator of the imaginary dipping needle, according to the above law, will deviate in a direction contrary to that of the motion of the eastern edge of the plate, and consequently the northern extremity of the axis will deviate in a contrary direction to that of the motion of the plate's northern edge, or it will deviate in the direction in which the southern edge of the plate moves. Hence the horizontal needle obeying the deviations of this dipping needle, the deviations of its north end due to the rotation of the plate will be in the direction in which the south edge of the plate moves, which is the law deduced from the experiments, Table I. . % Experiments with the dipping needle. Having found, in all the experiments which I have de- scribed, that the effects produced on the horizontal needle depended on the situation of the plate with respect to the axis and equator of an imaginary dipping needle passing through the centre of the horizontal needle, my next experi- ments were undertaken with the view of ascertaining whether the effects produced by the rotation of the plate on the dipping 384 Mr. Christie on the magnetism of needle itself corresponded with those which I had observed on the horizontal needle. In making these it was necessary to adjust the dipping needle on a stand detached from the instrument, on the arm of which the iron plate revolved, on account of the diameter of the case of the dipping needle being greater than the distance sn (fig. 1). It was there- fore only in particular positions that I could observe the deviation caused by the rotation of the plate. This however was of the less importance, since, as I expected that the de- viations of the dipping needle would be less than those of the horizontal needle nearly in the ratio of sin. 190 30' to 1, it was only in the cases in which they were the greatest that I was likely to have been able to observe them. As the dipping needle, when in the position of the dip, could only vibrate in the plane of the meridian, no effect corresponding to the deviations of the horizontal needle could be observed, either when the centre of the plate was in the intersection of the meridian and equator, and its plane per- pendicular to the planes of these circles, or when the centre of the plate was in the secondary to the meridian and equator, and its plane in the plane of this secondary. In order there- fore to ascertain the deviations of a needle suspended freely by its centre of gravity, corresponding to those of an hori- zontal needle, when the plate had those positions, and which I considered to be the principal points to be determined, it was necessary to observe the effect produced on the dipping needle when the centre of the plate was in the equator and exactly east or west of the centre of the needle, and its plane parallel to the plane of vibration of the needle; and also when its centre and plane were in the plane of vibration. In making these observations, the instrument was adjusted 38 S iron arising from its rotation. as in fig. 1, the compass being however removed ; the indexes at o, o' were brought to JE, ce, on the moveable limb, and that limb was placed at right angles to the fixed limb, so that the plane of the plate was parallel to the magnetic meridian. The dipping needle was then placed as nearly as possible in the required position, and the levels being carefully adjusted, the needle was made to vibrate freely and left to settle. After the plate had been made to revolve several times in the same direction, the point marked o was brought to coincide with the upper part of a line parallel to the magnetic axis, and passing through the centre of the plate. The needle was then slightly agitated, or made to vibrate through a small arc ; and when it settled, the dip was noted both at the upper and lower extremity, or the south and north end of the needle. This was repeated for the points marked 60, 120, 180, 240, 300. The plate was now made to revolve in the contrary direction, and similar observations made of the dip of the needle when the several points 300, 240, 180, 120, 60, o, coincided with the upper part of the line parallel to the magnetic axis. Continuing the revolution of the plate in this direction, a second set of observations of the dip were made for the several points from 300 to o. After this, the plate was again made to revolve in its first direction, and a second set of observations made of the dip for the points from o to 300. I considered the mean of all the observations in the two sets, when the plate revolved from o to 300, as the mean dip when the plate revolved in this direction ; the mean of all the observations in the two sets, when the plate revolved from 300 to o, as the mean dip when the plate revolved in 386 Mr. Christie on the magnetism of this direction ; and the difference between these mean dips as the deviation due to the rotation of the plate. As I had experienced that the dipping needle, even when of the best construction, was an instrument from which accu- rate results could only be obtained by taking a mean of a great number of observations, I was aware that, by making only two for each point of the plate, I was liable to an error in the observations for each point taken separately, but this I considered would be counteracted in taking the mean for all the points ; so that the mean results could not err far from the truth. The dipping needle which I made use of was a very good instrument, by Jones, of Charing Cross : the needle, made according to Captain Kater's construction, con- sisted of two arcs of a circle ; its length was 7 inches. The plate was the same I had used in the experiments with the horizontal needle. For the better distinguishing of the edges of the plate and the direction of its rotation, I conceive two planes at right angles to each other to pass through its centre ; one, the plane of the equator or a plane parallel to it, which I call the equatorial plane ; the other, the plane of the secondary to the equator and meridian, or a plane parallel to this secondary, which I call the plane of or parallel to the axis. The inter- sections of the first plane with the edges of the plate, I call the equatorial north and south edges ; and the intersections of the second, the polar north and south edges. In the following table, the numbers in the first column in- dicate the point on the plate which was in the polar south ; the inclinations of the needle corresponding to these positions 387 iron arising from its rotation. of the plate are in the following columns, which are in pairs, the one showing the inclination indicated by the southern extremity of the needle, the other, that by the northern. Above the pairs of columns, is indicated the direction in which the upper or polar south edge of the plate revolved, with re- ference to the points in the equator, and also the direction in which the equatorial south edge of the plate revolved with reference to the polar points in the plane of the axis. Under the columns, are the mean inclinations of the needle when the plate revolved in opposite directions, and below these, the mean deviation due to rotation. VIII. Table of the inclinations of the dipping needle when the centre of the plate was in longitude 0°, latitude 0°, and its plane parallel to the meridian ; so that the axis of rotation of the plate was the same as the axis of vibration of the needle : the distance of the centre of the plate from that of the needle being 9.5 inches . Plate No. I. Points on the Plate coincid- ing with the Polar South. Polar South edge of the Plate to Equatorial North, or Equatorial South edge to Polar South. Polar South edge of the Plate to Equatorial South, or Equatorial South edge to Polar North. First Set. Sceond Set. First Set. Second Set. S. end. N. end. S. end. N. end. S. end. N. end. S. end. N. end. O 6o 1 20 180 240 300 0 / 70 30 70 IO 70 45 70 40 7° 55 71 05 0 / 70 45 70 25 71 co- 70 55 71 10 71 20 0 / 70 30 70 3C 70 25 70 25 70 40 70 45 0 , 70 20 70 20 70 15 70 20 70 30 70 35 0 1 7 1 40 7i 45 7 1 25 71 00 7 1 30 71 30 0 / 7 1 35 71 40 71 20 70 55 71 20 72 00 0 / 71 25 71 05 71 05 7 2 00 71 20 71 05 0 / 71 20 71 OO 71 OO 70 55 7 1 15 71 00 Mean dip. 78° 38' 710 1 8' Mean deviation due to rotation. o° 40' From these observations it appears that, in this position of the plate, the deviation of the upper , or south end of the needle, 3 E MDCCCXXV. 388 Mr. Christie on the magnetism of due to rotation , was in the direction in which the north or lozver edge of the plate revolved, and the deviation of the north or lower end of the needle, in the direction of the rotation of the upper or south edge of the plate. It would follow from this, that if a needle could be suspended freely by its centre of gravity, and the centre of the plate were in longitude 90°, latitude o°, and its plane at right angles to the meridian ; then also, the deviation of the south end of the needle due to rotation , would be in the direction of the north or lower edge of the plate, and the deviation of the north end, in the direc- tion in which the south or upper edge revolved ; which are precisely the directions of the deviations of the horizontal needle in this position of the plate. (See Table I.) The law which I have shown to obtain in all the experi- ments on the horizontal needle, viz. that the sides of the equator of the imaginary dipping needle always deviated in directions contrary to those in which the corresponding edges of the plate moved, I had derived previously to having an opportunity of making any experiments with the dipping needle : a comparison of the above results with this law will more fully illustrate its nature, and at the same time show their perfect accordance. In making this comparison, it is necessary to notice that, an increase of the dip of the needle, corresponds to a deviation of the southern edge of its equator towards the south pole, and of the northern edge towards the north pole ; and on the contrary, a diminution of the dip cor- responds to a deviation of the southern edge of the equator towards the north pole, and of the northern edge towards the south pole. Now, when the equatorial south edge of the plate revolved towards the polar south , and consequently the 389 iron arising from its rotation. equatorial north edge towards the polar north, the inclination of the needle was diminished by the rotation ; that is, the south edge of its equator deviated towards the north pole, and the north edge of its equator towards the south pole ; or the edges of the equator , hy the rotation of the plate , deviated in directions contrary to those in which the edges of the plate moved. The same conclusion evidently follows from the observations when the equatorial south edge of the plate revolved towards the polar north, the dip being here increased by the rotation of the plate. The next observations which I made, were of the inclina- tions of the dipping needle, when the plane of the plate was in the plane of the meridian or plane of vibration of the dip- ping needle. IX. Table of the inclinations of the dipping needle , when the centre of the plate was in longitude 90°, latitude 0°, and its plane in the plane of the meridian, or plane of vibration of the dipping needle ; the distance of the centre of the plate from that of the needle being 13.3 inches. Plate No. I. Points on the Plate coincid- ing with the Polar South. Polar South edge of the Plate to Equatorial North, or Equatorial South edge to Polar South. Polar South edge of the Plate to equatorial South, or Equatorial South edge to Polar North. First Set. Second Set. First Set. Second Set. S. end. N. end. S. end. N. end. S. end. N. end. S. end. N. end. O 6o 120 180 240 300 O / 70 25 69 50 69 50 70 45 70 55 70 40 0 / 7° 35 70 05 70 00 70 55 7 1 70 50 O / 7° 45 70 15 69 55 70 35 70 50 70 30 0 / 70 30 70 05 69 50 70 25 70 40 70 15 0 / 69 40 69 20 68 55 69 35 60 30 69 35 0 / 69 35 69 1 5 68 55 69 40 69 35 69 40 £9 35 69 30 69 00 69 35 69 20 69 30 £9 15 69 20 68 45 69 25 69 10 69 20 Mean dip 70° 26' | 690 22'i Mean deviation due to rotation. i° 04' 390 Mr. Christie on the magnetism of From these observations it appears that, the plane of the plate being in the plane of vibration of the needle, and its centre in the equator, the deviation of the upper or south end of the needle, due to rotation, was in the direction of the rota- tion of the upper or south edge of the plate, and of the north end in that of the north edge ; and we may therefore conclude, that if a needle could be freely suspended by its centre of gravity, and the centre of the plate were in the equator, and its plane in that of the secondary to the meridian and equa- tor, the deviation of the south end, due to rotation , would be in the direction in which the south edge of the plate revolved, and of the north end, in that in which the north edge revolved ; w’l ch, again are precisely the directions in which we have seen, that the horizontal needle deviated by the rotation of the plate in this position. X. Table of the inclinations of the dipping needle , when the centre of the plate was in latitude 90° South, and its plane in the plane of the meridian, or plane of vibration of the dipping needle ; the distance of the centre of the plate from that of the needle being 13.3 inches. Plate No. I. Points on the Plate coincid ing with the Polar South. Polar South edge of the Plate to Equatorial North, or Equatorial South edge to Polar South. Polar South edge of the Plate to Equatorial South, or Equatorial South edge to Polar North. First Set. Second Set. First Set. Second Set. S. end. N. end. S. end. N. end. S. end. N. end. S. end. N. end. 0 60 120 1 80 240 300 0 > 71 05 71 00 71 IO 71 40 7 1 40 71 05 0 / 71 03 71 IO 71 15 7l 45 7l 45 71 10 0 i 7i 35 71 10 71 25 7* 35 71 30 71 25 0 / 71 30 71 05 71 25 71 40 7i 35 71 35 O / 71 40 71 35 71 40 72 00 72 05 71 40 0 / 71 40 71 15 71 30 71 50 72 05 71 55 O / 7I 50 71 35 72 15 72 30 72 15 72 00 0 / 71 40 71 25 72 05 72 20 72 05 7* 55 Mean dip. 710 23' \* M lO f* ^ 1 71 52 Mean deviation due to rotation. o° 29' • In these observations the edge of the iron plate was not an inch from the south end of the needle; so that a very small error in the position of the plate’s centre will account for the dip in both directions of rotation being greater than 70° 15', the true dip. 391 iron arising from its rotation. Here, contrary to what took place when the centre of the plate was in the equator, the deviation of the south end of the needle is in the direction in which the lower or north edge of the plate revolved ; and we may therefore infer, that the same would be the case if a needle were suspended freely by its centre of gravity, and the plane of the plate were in the plane of the secondary to the meridian and equator, its centre being in latitude 90° S : which also agrees exactly with the directions of the deviation of the horizontal needle, due to rotation, in this position of the plate. It is evident from these different experiments with the dipping needle, that whatever may be the peculiar effects produced on the iron by its rotation, the deviations of the horizontal needle, due to the rotation , are of the same nature as those that would arise by referring the deviations of the dipping needle to the horizontal plane. Further observations with the horizontal needle. Although, in order to point out the particular laws accord- ing to which the rotation of the iron causes the needle to deviate in particular situations of the plate, and to deduce a general law by which the direction of the deviation might in all cases be determined from the direction of rotation, I have been under the necessity of entering into such a detail of the experiments, as has already extended this paper beyond the limits to which I wished to confine it, I yet think it may not be uninteresting to enquire, how far the adoption of parti- cular hypotheses may enable us to account for the several phaenomena which I have observed. I liave already stated, that I considered that the deviations 39® Mr. Christie on the magnetism of arising from the rotation of the plate, when its centre and plane are in the secondary to the equator and meridian, are those best adapted for forming a comparison with the results obtained from theory. In Table VI. I have given a series of such observed deviations ; but as I was not quite satisfied that in making these observations there had not been some small inaccuracies in the different adjustments, when the centre of the plate was near the equator and when near the pole, I should not on this ground have considered a compa- rison with them as altogether conclusive with respect to the correctness of any theory. In repeating these experiments, I increased the distance of the centre of the plate from that of the needle, as, in order to simplify the calculations, it would be necessary to neglect certain terms, which would be the greater the less was this distance, and consequently if it were increased, the neglecting these terms would the less affect the results of the calculation as compared with the observations. The following Table contains a series of observations similar to those in Table VI, but having the centre of the plate re- moved to the distance 16 inches from the centre of the needle. In making them, the most scrupulous attention was paid to the different adjustments, so that I can place entire confidence in the results. Tv fact lag, 39:, No. 1. Table of the deviations of a magnetic needle, caused by a circular plate of iron, whose centre teas in the secondary to the equator and meridian, and plane in the plane of this secondary, the plate having revolved in opposite directions ; the distance of the centre of the plate from the centre of the needle being 16 inches. Plate No. I. Latitude and Long tude of the plate centre. Lat. o°. Lat. io°S. Lat. 200 S. Lat. 30° S. tat. 40° S. Lat. 50° S. Eat- 54" 45' S- Lat. 6o° S. Lat. 70°S. Lat. 8o°S. Lat. 90° S. Long. o° Long. o°. Long. o°. Long. o°. Long. o°. Long. o°. Long. o°. Long. o°. Long. o°. Long. o°. Direction of rotation of plate’s upper edge Wtol E to Vi W to E Eto W Wtol Eto W W toE Eto W W toE E to W W to E E to W W to E E to W W to E E to W W to E Eto W W to E E to W W to E EtoW Points on the plate coinciding with the line joining the centres of the needle and the plate. o 1 02 Vi 0 32 E 4 50W 3 20W 7 46W 6 30W 9 38 W 8 42 W 10 28 W 9 54 w 0 . 10 38W 6 ✓ 10 28W i°o 08 W 10 08W 8 48 W j9 00 W S ;'2W 7 18W 3 Aw 4 34W 0 40 w °i 24 W 30 1 02 0 36 4 H 2 52 7 10 s 52 9 °4 8 04 10 00 9 22 9 42 9 32 9 18 9 18 7 56 |8 06 6 54 7 20 3 48 4 26 0 24 W 1 08 W 6o 0 58 0 40 4 °4 2 32 6 38 S 22 8 38 7 3S 9 38 9 00 8 56 8 46 8 46 8 46 7 24 1 7 32 6 50 7 >6 3 44 4 '8 0 18 W 0 56 W 9° 0 44 0 54 3 i6 2 04 6 10 4 52 8 12 7 10 9 16 8 36 8 18 8 08 8 20 8 20 6 52 |7 02 6 36 7 02 3 20 4 02 0 08 E 0 36 W 120 0 46 0 52 3 32 2 02 6 12 4 56 8 18 7 '8 9 22 8 42 8 18 8 06 8 26 8 24 6 58 |7 12 6 20 6 48 3 0* 3 48 0 26 E 0 24 w | 150 1 06 0 30 3 5° 2 22 6 34 5 20 8 42 7 44 9 44 9 08 8 36 8 30 8 40 8 42 7 aa |7 36 5 56 6 28 2 40 3 24 0 46 E 0 02 W | l8o t 14 0 26 4 06 2 34 6 58 5 40 9 04 8 02 10 04 9 30 9 02 8 52 9 00 9 02 7 48 |8 00 5 26 5 56 2 18 2 S8 1 08 E 0 22 E 210 . 0 52 0 50 4 04 2 30 7 02 5 44 9 08 8 08 10 12 9 34 9 28 9 18 9 18 9 16 8 10 Is 24 5 00 5 26 2 00 2 38 1 16 E 0 28 E I 240 0 34 1 04 4 02 z 30 7 10 5 52 9 16 8 14 10 16 9 38 9 58 9 52 9 42 9 42 8 36 |8 48 4 48 5 -8 2 02 2 40 1 08 E 0 22 E 1 27O 0 22 1 12 4 10 2 38 7 '8 6 00 9 24 |8 24 10 26 9 So 10 34 10 26 10 14 10 14 9 06 9 18 5 00 5 28 2 20 3 00 0 42 E 0 06 W | 300 0 26 1 06 4 26 2 56 7 34 6 20 9 40 |8 38 10 36 10 00 1 1 04 10 56 10 36 10 40 9 a8 |9 38 5 32 6 02 2 54 3 34 0 06 E 0 38 W 330 0 46 0 42 4 42 3 H 7 48 6 34 9 46 |8 50 10 38 10 06 1 1 04 10 56 10 34 10 36 9 16 [9 3° 6 14 6 42 3 28 4 06 0 24 W 1 04 w Mean deviations. ° 49 * 1° 47 4 08 s 2 37* 7 Olf 5 45 z 9 °4* 8 °4* 10 03 j 9 26* 9 3s* 9 ^9* 9 25 i 9 25 j O 00 nfa 00 0 co 5 57* 6 25* a 57 r 3 37* 0 19 J E 0 >5 J Wj Deviations due to rotation. 1° 31' 1° 164 °°59'* 0° 3<>' y o° 09' — o° 00' 1 — o°u'* — o° 28' — °° 39' * — 0 45 Long. 1800. Long. 1800. Long. 1800. Long. 180°. Long, 180°. Long. 1800. Long. 1800. Long. 1800. Long. 1800. Long. 1800. Lat. 90* N. Direction of rotation of plate's upper edge. Eto WiWtoE Eto W W to E Eto W W to E E to W W to E E to W W to E Eto W W to E Eto W W to E Eto W W to E Eto W W to E E to WjW to E Eto W W to E bo ;s o c a — rt M “■ & s 60 0 .5=3 -a to IS 8-S O 1 20 E 0 14W 4 08 E 2 38 E 7 16 E 5 58 E 9 3° E 8 30 E 10 16 E 9 38 E 10 42 E 10 32 E 0 / 10 06 E • / 10 06 E 9 06 E 9 i*8 E 4 4® E $ 12 E 1 44. E 2 24 E 0 i'6W 0 26 Ej 30 1 10 0 26 52 2 20 7 00 5 42 9 16 8 14 10 10 9 32 10 40 10 30 10 06 10 06 9 >4 9 24 5 »6 5 40 2 08 2 44 0 14 0 30 60 0 58 0 40 38 2 06 6 46 5 26 9 00 8 00 9 54 9 16 10 12 10 02 10 40 9 4° 8 52 9 °4 5 42 6 10 2 28 3 06 0 10 0 34 90 0 28 1 10 16 44 6 22 5 06 8 32 7 36 9 28 8 56 9 32 9 22 9 02 9 02 J 20 8 32 6 08 6 38 2 50 3 24 0 16 0 30 120 0 12 1 22 06 36 10 4 56 8 18 7 20 9 H 8 40 8 8 38 8 20 8 20 7 38 7 50 6 24 6 56 04 3 50 0 06 0 42 *5° 0 08 i 22 >4 44 18 5 00 26 7 26 9 16 8 40 8 24 8 14 8 00 7 58 J4 7 24 6 36 7 06 24 4 06 0 14 0 32 180 0 18 18 28 56 30 S 14 44 7 42 9 32 8 52 8 20 8 08 7 S6 7 54 08 7 16 6 40 7 08 38 4 18 0 32 0 14 210 0 32 06 46 16 56 s 36 00 8 00 9 44 9 04 8 26 8 12 8 02 7 58 10 7 ,8 32 6 58 38 4 16 O 34 0 10 it 2 40 52 46 . 02 30 10 5 52 18 8 18 9 56 9 18 8 42 8 30 8 12 8 12 20 7 28 04 6 31 18 3 58 0 32 0 10 270 00 36 08 |i 38 *4 s 56 22 24 9 56 9 20 | 9 02 8 52 8 28 8 28 32 7 42 26 5 56 46 3 26 0 34 0 12 .S o 300 18 18 18 |z so 24 6 06 32 8 32 IO 08 9 32 | 9 44 8 32 9 04 j 9 04 5 04 8 14 56 24 >4 2 54 0 26 0 18 33o 1S 10 14 |z 48 22 6 06 34 8 36 IO 18 9 40 | 10 24 10 12 9 44 | 9 42 44 8 54 40 08 52 32 0 16 0 28 Mean deviations. 47* 474 45*-|a 1 5i 52* 34* 02 T 8 03 J 9 49* 9 »*i 9 24 i 9 *3 § 8 S3*| 8 52} ot*|8 12 Is 45 i 14 45* 2si O 20f 0 23 * Deviation due to rotation. *° 35* 5 ■°3°'J i° i7' j o- 59' j o°37' o° io'£ + 0“ CO' £ - o" 10' * — o°28'* — o* 40'* — 0 44* To fate page 392, No. II. Considering the centre of the plate to have been in longitude 180°, and consequently the deviations easterly in all the observations, and thus taking a mean of the deviations in the several latitudes, I obtain the following. A. Table of the easterly deviations of the needle, when the centre of the plate was in longitude 180”, or to the west of the needle, the plate having revolved in opposite directions. Latitude of the plate’s centre. O0 IO° 20° 30° 40® 5°° 54° 45' 6o° 70° 8o° 9°° Direction of rotation of plato’s upper edge. EtoW W to E EtoW W to E E to W W to E EtoW W to E EtoW W to E EtoW W to E EtoW W to E EtoW W to E EtoW W to E EtoW W to E EtoW W to E Deviation East. +47 55 -47 55 3 57 20 0 , « z 26 40 6 57 00 0 1 a 5 40 00 9 °3 25 8 03 45 0 / n 9 56 20 9 «9 30 0 / « 9 31 20 0 / n 9 21 25 9 °9 A 9 09 »s 8 05 15 8 16 15 S 5« 35 0 / /, 6 19 40 2 51 25 3 31 30 — 22 25 + 22 25 Deviation due to rotation. i° 35' 5°" 1° 30' 40" • i° 17' 00 o° 59' 4o" o° 36' 50" 0° 09' 55" o° oo' 10" — o° i T 00" — o* 28' 05" — o° 40' 05" — o°44/ 5°" Two sets of observations which I had made more than two years before, had given me the following results ; but as I afterwards suspected that the absolute deviations might have been affected by the proximity of a mass of iron, of which I was not aware at the time of making the observations, I considered it better to repeat them in a situation where no such influence could be exerted, although I did not conceive that this would materially affect the conclusions. B. Table of the mean easterly deviations of the needle, when the centre of the plate ivas in longitude 180°, or to the west of the needle, the plate having revolved in opposite directions ; deduced from two sets of observations made in November 1822 and February 1823. Latitude of the plate’s centre. O0 io° 20° 30° 400 5°* 54° 45' 6o° 70° 8o° 90° Direction of rotation of plate’s upper edge. EtoW W to E EtoW W to E' E to W W to E E to W W to E EtoW ,W toE EtoW W to E EtoW W to E EtoW W to E EtoW W to E EtoW W to E EtoW W to E Deviation j lst 8ct> test- \ ad Set. + 50 25 + 5° 32 -50 25 -50 32 0 1 n 4 35 55 4 25 45 3 00 55 2 48 50 7 39 25 7 36 45 6 19 00 6 11 55 10 07 10 10 08 30 9 04 20 9 02 05 u 11 15 10 53 10 10 33 00 10 14 15 10 48 55 10 40 55 10 36 55 IO 28 I5 No obse 9 53 35 rvation. 9 53 05 9° «3 05 9 11 *5 9 25 30 9 23 50 6 32 15 6 35 30 7 04 55 7 07 45 3 4 s"s 3 °6 45 4 00 35 3 51 25 —25 00 -24 38 + 25 00 + 24 38 Mean deviation East. + 50 28 —50 28 4 3° 5° 2 54 32 7 38 05 6 15 27 10 07 50 9 03 12 11 02 12 10 23 37 io 44 55 10 32 35 9 53 35 9 53 05 9 12 10 9 24 40 6 33 52 7 06 20 3 10 50 3 56 00 —24 49 +24 49 Mean deviation due to rotation. i° 40' 56" 1” 35' 58" 1”2Z' 38" i° 04' 38" 0° 38' 35 o° 12' 20" o°oo' 30' — o° 12' 309 — o° 32' 28" — o° 45' 108 — <=°49' 3 8" iron arising from its rotation . 393 Theoretical Investigations. It has in general been considered that the different devia- tions of the horizontal needle, arising from the action of soft iron on it in different positions, can only be accounted for on the supposition, that the iron is polarised by position, the upper part being a north pole, and the lower a south one, each pole of the iron attracting the pole of the needle of the same name, and repelling that of a contrary name : but if we suppose that each particle of the iron simply attracts in- differently either pole of a magnetic particle, and refer the attraction of the iron to its centre, then if the angular devia- tions of a magnetic particle in the centre of the needle and in the line of the dip, arising from such attraction, be reduced to the horizontal plane, these reduced deviations will agree with the actual deviations of the horizontal needle. In in- vestigating theoretically the effects that are produced by the rotation of a plate of iron, I will first suppose, that, inde- pendently of rotation , the iron acts in this manner, and that by the rotation it becomes polarised in a direction, making a certain angle with the magnetic axis, since from such a polarising of the iron, the law which I have shown to include all the phenomena, would evidently result. On this suppo- sition, each pole of a magnetic particle in the centre of the needle would be urged by an attractive force towards the centre of the iron plate, by an attractive force towards the pole of a contrary name, and by a repulsive force from the pole of the same name in the iron. Suppose now that the centre and plane of the plate are in the secondary to the meridian and equator, that its centre is 394 Mr. Christie on the magnetism of to the west of the needle, or in longitude i8o° ; and in south latitude, as in the observed deviations in Tables A and B, and that its upper edge revolves from east to west. Take the centre of the needle as the origin of the rectangular co- ordinates, the axis x being horizontal, and towards the west, that of % upwards, in the direction of the magnetic axis. We will indicate the north end of the magnetic particle, in the centre of the needle, on which the iron is supposed to act, by N, its south end by S ; the north end of the line joining the poles in the plate by v, its south end by , bv = R sin. x — p cos. \J/ ; S y2 = R2 + r2 — 2 R r sin. x, N 7* == R3 + r* + 2 R r sin. x 5 Si/3 = R2 -f- r2+p9 — 2 Rp sin. (4/ -j- x) — 2r (R sin. x — p cos. -4/); Ni/2 = R2 -f- r2+p2 — 2 Rp sin. (%(/ + x) + 2r(Rsin.x — pcos.\|/); S 3 F m R3 ~Y7 + 3 sin.2 X — 1 (s) MDCCCXXV. 396 Mr. Christie on the magnetism of Also if

p — A) . cos, a — sin, 4 3 sin. (4 + A) . sin. a — cos. 4 3 sin. (4 — a) . sin. a -f cos. <4* whence sin. \j/ . cos. + = o. The value of >(/ which satisfy this equation are o°, 90°, i8oc, 270°; and since o° and 180° would in all cases give 4'=

(«.)• F r 46.0278 = 46 very nearly ; .054571, when x = o, and ==.060986, when x= 90; so that the mean value of is 0.57778 or .058 nearly, the same as before. The equations (5) and (6) in this case become, q-an ft/ l x 3 sin. 2 x + ,o$8 x (3 cos. 2 x+ i) cos. 70° 15' 47 — 3 cos. 2 x + .058 x 3 sin. 2X 'pan ft 1 x 3 sin. 2 x — .058 x ( 3 cos. 2 x + 1 ) / cos. 70° 15' 47 — 3 cos. 2 X — .058 x 3 sin. 2 x We will first compare the situations of the points where the deviation due to rotation vanishes, as deduced from these equations, with the situation as determined by actual obser- vation. When the deviation due to rotation vanishes 0/ = 0 = 0>; we shall therefore have from equations (5J and (6j 3 sin. 2 X 3 cos. 2 x + 1 51 — 3 cos. 2 x 3 sin. 2 x ’ whence cos. 2 x = — .2800000 and x = 530 07' 48". The equations (5^) and (6ft) give 3 sin. 2 x 3 cos. 2x4-1 47 — 3 cos. 2 x 3 sin. 2 x ’ whence cos. 2 x = — .2753623 and x = 52° 59' 30". Now I have uniformly found, in repeated observations which I have made at different distances, that when the centre (SJ- 399 iron arising from its rotation. of the plate was in latitude 540 45', the rotation produced so little effect, that only in one instance did the mean values of 6' and Q, differ by a minute ; and therefore cannot but con- clude that 540 45 is, as nearly as can be ascertained by obser- vation, the true value of x when Q' = and that the value of x as determined by the theory differs from its value derived from observatien by i£° or i^°. Let us now compare the values of 6', and 6' — fy, deduced from the equations (5J, (6j, (5J (6ft), for different values of X, with those actually observed. This comparison is made - in the following tables, where I have computed the values of and to seconds, not that either the observed or computed values can be determined to such a degree of accuracy, but because the omission of the seconds might in some cases affect the value of — d, by more than a minute. Table of the values of 0', 0; and 9' — 07, computed from the equations (5a), (6a) compared with their mean observed values in Table A. X 0' 0, 6' — 0, Observed. Computed. Difference. Observed. Computed. Difference. Observed. Computed. Difference. 0 0 / II O / // / // O 1 // O 1 II / // 0 • II 0 1 11 / // 0 4 47 55 4 49 10 4 1 15 — 47 55 — 49 10 4 1 15 I 35 50 I 38 50 4 2 30 10 3 57 20 + 22 35 4 25 *5 2 26 40 2 49 57 4 23 l7 I 30 40 I 32 28 4 1 58 20 6 57 00 7 *9 21 4 22 21 5 40 00 6 02 21 4 22 21 I 17 00 I 17 00 0 00 3° 9 03 25 9 17 07 4 *3 18 8 °3 45 8 22 06 4 18 2 1 59 40 55 01 — 4 39 40 9 5° 20 10 04 49 4 8 29 9 !9 3° 9 34 13 4 H 3i 36 50 30 48 — 6 02 5° 9 3* 20 9 4* *9 4 9 59 9 21 25 9 34 25 4 J3 00 09 55 06 54 — 3 01 60 8 °5 15 8 13 00 4 7 45 8 16 15 8 26 5° 4 10 35 — n 00 — >3 50 — 2 5° 70 5 5 1 35 5 51 44 4 0 09 6 !9 4° 6 21 41 4 2 01 28 05 — 29 57 — 1 52 80 2 51 25 2 53 40 4 2 *5 3 3 1 3° 3 33 52 4 2 22 — 40 05 — 40 12 — 0 07 90 22 25 2 1 5 1 4 0 34 4 22 x5 4 21 51 0 34 44 50 — 43 42 4 1 08 400 Mr. Christie on the magnetism oj Table of the values of 0', 0, and 0' — 0, computed from the equations (5^), (6^) compared with their mean observed values in Table B. X V e, 6' — 0, Observed. Computed. Difference. Observed. Computed. ^Difference. Observed. Computed. Difference . 0 0 » / n + 50 28 0 1 a + S3 38 0 / // + 3 10 0 in — 50 28 0 1 11 — S3 38 / // — 3 10 0 ! „ 1 40 56 0 / // I 47 16 / // 4 6 20 10 4 3° 5° 4 46 12 + IS 23 2 54 52 3 °S 20 + 10 28 i 35 58 1 4o 53 + 4 55 20 7 38 05 7 59 10 + 21 05 6 15 27 6 35 29 + 20 02 1 22 38 i 23 41 + 1 03 30 10 07 50 10 06 20 1 30 9 03 12 9 °S 40 + 2 28 1 04 38 1 00 40 - 3 58 40 50 60 11 02 12 10 44 55 9 12 10 10 55 28 10 29 02 8 52 55 — 6 44 — IS 53 — 19 15 10 23 37 10 32 35 9 24 40 10 22 47 10 21 56 9 08 05 — 0 50 — 10 39 — 16 35 38 35 12 20 — 12 30 32 41 07 06 — 15 10 — 5 54 — 5 14 — 2 40 70 6 33 52 6 19 59 — 13 53 7 06 20 6 52 26 — 13 54 — 32 28 — 32 27 4 0 01 80 3 10 So 3 07 34 — 3 16 3 56 00 3 Si 32 — 4 28 — 45 10 — 43 58 -4- 1 12 90 — 24 49 — 23 36 -f 1 13 + 24 49 + 23 36 — 1 13 — 49 38 — 47 12 -1- 2 26 The differences here between the observed and computed values of 6' and Q, are not greater than might possibly arise from slight errors in the adjustments of the plate and com- pass in the several positions, and their agreement is I think sufficiently near to prove that the principle which I have assumed, namely, that the attraction of the mass of the iron may be referred to its centre, and on which the most consi- derable of the terms in the formulas depend, will account for the phasnomena independent of the rotation of the iron. Al- though the differences between the observed and computed values of 6' — or of the deviation due to rotation , are abso- lutely less, yet they are relatively greater ; but their general agreement is such, that we can have little doubt of the devi- ations due to the rotation of the iron being, in all cases, nearly the same as would arise from such a polarising of the iron, as we have supposed. We shall however form a better esti- mate of the agreement between the results of the theory and observation, by eliminating from the equations (5) and 401 iron arising from its rotation. F T (6), and deducing the value of — in terms of 6' and and depending principally on 6' — or the deviation due to rota- tion, on the accuracy of the values of which in Table B, I place much greater reliance than on those of the absolute F r values of O' and In this manner we obtain i C 3 cos. 2 h -f- i sin. (0'—^) \ 3 sin. z \ sin. (Q'+ G;) — 2 cos. ^sin. 6' sin. 6, 5 in which the observed values of 6' and corresponding to any value of x, being substituted, ought in all cases to give the same, or very nearly the same numerical value for F r 7T* F v Table of the values of •— computed from the several observed values ofW and 0/J in Tables A and B, corresponding to different latitudes. X Observed values in Table A. Computed value of F r Observed values in Table B. Computed value of F r 0' 6' 0, 2 fp 2fp 0 / « 0 / a 0 / 11 0 / // 0 + 47 55 - 47 55 17.692 -f 50 28 00 N 0 1 18.325 10 3 57 20 2 26 40 1 5.658 4 3° 50 2 54 52 17.144 20 6 57 00 5 40 00 16.320 7 38 05 6 J5 27 16.678 3° 9 °3 25 8 03 45 15.461 10 07 50 9 03 12 15.824 40 9 56 20 9 J9 30 14.088 11 02 12 10 23 37 14.680 50 9 31 20 9 21 25 1 1.886 10 44 55 10 32 35 9*983 60 8 05 15 8 16 15 21 . 214 9 12 10 9 24 40 21 *755 70 5 5i 35 6 19 40 18.328 6 33 52 7 06 20 17.858 80 2 51 25 3 3i 30 17.080 3 10 50 3 56 00 16.907 90 — 22 25 -f 22 25 16.808 - 24 49 + 24 49 l6- 397 Mean value 16.454 Mean value 1 6. 555 F r The values of which differ most from the mean, are, in ZJ e both cases, those corresponding to the values of x, 50° and 6o° ; that is nearest to and on contrary sides of the point where 6' — A/ = o, which again shows clearly, that the theoretical determination of this point does not agree with the observa- 402 Mr. Christie on the magnetism of tions : and although the results of the theory agree in gene- ral very nearly with the observations, and the differences in the other values of are not greater than might possibly be attributed to errors of adjustment or observation, how- ever little I may be disposed to admit the existence of errors to this extent, yet the uniform manner in which these values decrease, indicates that the effects are not produced in pre- cisely the manner we have supposed. In one point our theory is unquestionably at variance with the actual circum- stances of the case ; for we have supposed that no partial magnetism exists in the iron, or that every part of it taken separately would equally affect the needle. It is, I believe, scarcely possible to procure iron that shall possess this uni- formity of action, and it is evident that this was not the case with the plate of iron which I made use of. This species of polarity in iron is of so variable a nature, since by an acci- dental blow it will be transferred from one point to another, that it does not appear possible in any manner to submit its effects to calculation. It was to prevent these effects embar- rassing the results, that I took the mean of twelve observa- tions for each position of the plate; still it is possible that some of the differences between the observations and the results of the theory may have arisen from this cause. As the results of the hypothesis which I have advanced do not precisely agree with the observations, it will be proper to enquire whether we shall obtain a more perfect agreement by means of the hypothesis commonly assumed, in order to account for the effects produced on the needle by a mass of soft iron, viz. that the upper part of every mass of iron acts as a north pole and the lower part as a south pole. Let us 403 iron arising from its rotation. then suppose such poles to exist in the iron plate, in the dia- meter in the direction of the dip, and that the rotation causes the line joining them to describe in the iron an angle $ from this diameter. The whole effect being now produced by the action of these poles, F being equal to o in the equations (2) and (3), we shall, on this supposition, have, 3 sin. (X -f ■4/). cos. X — sin. 4 i an . M R3 —77- 4 3 sin. (X 4 4) • sin. “ cos. 4 2J P 3 sin. (X — 4) • cos. X 4 sin. 4 Tan. (pf m R} 7f7 4 3 sin. (x — 4) • sin. X — cos. 4 (2')> (s'). Tan. <;> = — ? sin- x cos- * —V 4 3 sin.* x— I ZJ P These equations being reduced, give, Tan. 0' = (4')- COS £ 3 sin. 2x4 tan. 4 (3 cos. 2x41) m R3 Tan. 0' = Tan. 0 = „ — (3 cos. 2 X— 1) 4 tan 4 • 3 sin. 2 X J p cos. 4 1 3 sin. 2 x — tan. 4 (3 cos. 2x41) cos. £ m R3 — — (3 cos. 2 x — 1 ) — tan. 4 • 3 sin. 2 x j P cos.4 13 7 J 1 3 sin. 2 x cos. £ m R3 77 — (3 COS. 2 X — I) (5'). («'). (7')- which will be precisely the same as ths equations (5), (6), (7), if tan. \J/ 2 fr F r and / ' p cos. \|/ = ■§■ F r. The numerical values which we should obtain for 0' and from these equations, would, in all cases, be exactly the same as those which we have already obtained from the equations (5) and (6) : so that the agreement between the observations and the results from this theory would not be greater than in the former case. In the explanation of the phaenomena which take place on MDCCCXXV. 3 G 404 Mr. Christie on the magnetism of presenting the different ends of a mass of iron to the poles of a magnetic needle, in addition to the hypothesis, that the upper part becomes a north, and the lower a south pole, by position, it is necessary to suppose also, that in every change of position of the iron there is a corresponding and imme- diate change of its poles ; that is, the upper end becoming the lower, it also immediately becomes a south pole. Now it appears to me, that if we attempt to explain, on this hypo- thesis, the phenomena arising from the rotation of the iron, we shall find that there are circumstances which are wholly incompatible with it. If on turning a mass of iron end for end, the poles are immediately transferred from one end to the other, how can we suppose that the revolution of the iron will cause these poles to move forwards, so that the line joining them shall describe an angle from the line of the dip? or even granting that during the revolution of the iron they may be carried forward, they must, as soon as the iron ceases to revolve, resume their original position in the line of the dip, if they are so immediately transferred from one end of the iron to the other, as it is necessary to suppose in order to account for the phenomena which take place of attraction and repulsion, as they have been called. Imme- diately, then, that the iron becomes stationary in any position, the deviation of the needle ought, on this hypothesis, to be- come the same, whether the iron has been brought into that position by revolving in one direction, or in the contrary. It is hardly necessary for me to say that this would not be the case, since I have stated, that, in all the preceding observa- tions, the iron was stationary previous to the observation being made. 405 iron arising from its rotation . Whatever are the effects produced on the iron by its revo- lution, so far from these effects being of the transient nature which we must suppose them to be on this hypothesis, they appear to have been quite permanent, that is, so long as the iron remained in the same position. The following observation will show the small changes which took place during 12 hours. In order that the needle might be quite free to move, it was suspended in a balance of torsion by a brass wire, of the same diameter as the finest gold wire used for transits, free from torsion, 21.15 inches long. The plane of the plate was in the plane of the secondary to the equator and meri- dian, its centre in latitude o° longitude 180° ; and it was fixed to a wooden axis passing through its centre perpendicular to its plane : the ends of this axis, which revolved with the plate, being made of brass, that I might ascertain whether the effect was independent of friction on the plate itself. The plate was made to revolve in contrary directions, as usual, and the direction of the north end of the needle noted, when the point 180° on the plate coincided with the upper part of a plane parallel to the meridian, and passing through the plate’s centre. After having made the plate revolve so that its upper edge moved from west to east, and noted the direc- tion of the north end of the needle when 180° coincided with the above plane, it was made to revolve from east to west, and 180° being again brought to coincide with this plane, the direction of the north end of the needle was noted at diffe- rent times for more than 12 hours, the plate remaining stationary during that time. 406 Mr. Christie on the magnetism of Direction of ro- tation of plate’s upper edge. u * o w S 0 W to E o 02 E o 02 E o 04W o 06W o 08W E to W Time of observation. 2 50E 2 50 2 46 2 44 2 42 2 46 I 22 2 42 2 42 9 35 10 05 11 10 20 35 21 48 22 OI 22 17 22 28 22 40 24 05 25 35 During this time the plate was kept per- fectly stationary, and care was taken that the apparatus should not be in the least disturbed. f After 2 ih 48“ the plate was made to revolve l slowly once from W to E. J After making the plate revolve several \ times and more rapidly, f Making the plate revolve several times l from E to*W. f Making the plate revolve once so slowly l that the time of rotation was 3™ 26". f The plate kept perfectly stationary since \ 22h 40m. f Making the plate revolve through 30° from W to E, and then bringing it back 30° ( from E to W. C Making the plate revolve through 900 from < W to E, and then bringing it back 90° f from E to W. f Making the plate revolve repeatedly and \ rapidly. From these investigations it appears, that the effect pro- duced on the iron by its rotation is permanent, so long as the plate remains stationary ; that it is independent of friction ; that it is so far independent of velocity, that the iron can scarcely be moved so slowly that the whole effect shall not be produced ; and that the whole effect is produced by mak- ing it perform only one fourth of a revolution. Shortly after I had discovered these pecular effects to be produced by the rotation of iron, I pointed out the general nature of the phenomena and exhibited some of them to Mr. Barlow, and he has since made some experiments on the rotation of spherical shells, in which he has found that iron arising from its rotation. 407 phenomena somewhat analogous take place, but they appear to be dependent on the velocity with which the shell is made to revolve. p ' On computing the several values of from the equation (8), I found that if the term 2 cos. I sin. A' sin. were neglected ; .1 . • -r F r 1 , 3 cos. 2 A + i sin. (0' 4- 0,) • , that is, it — jr- were equal to^ — t — -f— . its numeri- cal values, so determined, would agree very nearly with each other. I was in consequence led to expect that equa- tions from which this value of might arise, would give values of 6' — agreeing more nearly with the observations ; and the result fully answered my expections. 2fp If and Tan. 6' = Tan. = 3 sin. 2 x H — ~~ • (3 cos. 2 X + i) r V 2 m R3 F r 2/p (9). . COS. £ 3 sin. 2X . (3 cos. 2 x + i) Fr 2 m R3 Fr ~ cos. s then we shall have F r 3 cos. 2 X -f i 2fp~ sin. (0' -f- 0 ) sin. (0' — 0 ) (10)> (u). 3 sin. 2 x When the deviation due to rotation vanishes or 0'=:6y the equations (9) and (10) give 3 cos. 2 x + 1 = o and X = 54° 44', which agrees perfectly with the observations. From the observations in Table A, we have in this case, Tan. 9° o9' = ‘°9° z8' ’6" -p7~ • cos. 70 15 F — — 52 very nearly. iTTi . 2 f p i 2 R3 When x = o, f-1 — — • whence = 51-9504 V Fr — --- Fr • COS. S tan. O' = . 061234; and when x = 90, 77 = 7 • .cos. 8 tan. 0'=. 057291 : so that the mean value of is .059262, or nearly .059. 408 * Mr. Christie on the magnetism of The equations (9) and (10 therefore become Ton tJ 3 sin- 2 >■ 4 -Q59 X (3 cos. 2 X + i) / \ . * 52 cos. 70° 15' \9q)i Ton a 3 sin- 2 X - . 059 x- (3 cos, n + i) , \ I an. 52 cos. 70° 15' V iL>a' In the same manner the observations in Table B give, -”?-k = 48.0278 = 48 nearly, and = .059039 = .0 59 nearly. The equations (9) and (10), in this case, become, q^an q# __ 3 sin. 2 X 4 . 059 x (3 cos. 2X41) 48 Tan 6 3 sin. 2 x — . 059 x (3 cos. 2 x + 1) ' 48 (9j)5 (109- Table of the values ofW, 0,, awe/ 6' — 0, computed from the equations (9a), ( I0fl) compared with their observed values in Table A. X 0’ •/ 0 -0, Observed. Computed. Difference. Observed. Computed. Difference. Observed. Computed. Difference. 0 0 / // 0 / // O / II O / /J O 46 // 0 / // / // O / II 0 / r 0 + 47 55 4 46 10 — 1 45 — 47 55 — ID 4 1 45 I 35 5° I 32 20 — 3 30 10 3 57 20 4 °4 26 4 7 06 2 26 40 2 36 3° 4 9 5° I 30 40 I 27 56 — 2 44 20 6 57 00 6 53 20 — 3 4° 5 40 00 5 38 06 1 54 I 17 00 I 15 14 — 1 46 30 9 °3 25 8 52 5° — 10 35 8 03 45 7 56 22 — 7 23 59 4° 56 28 — 3 1 2 40 9 56 20 9 49 43 — 6 37 9 J9 3° 9 J5 34 — 3 56 36 50 34 09 — 2 41 5° 9 31 20 9 38 02 + 6 42 9 21 25 9 27 16 4 5 51 °9 55 10 46 4 0 5 1 60 8 05 *5 8 18 59 + »3 44 8 1 6 1 5 8 30 17 4 14 02 — 1 1 00 — 11 18 — 0 18 70 5 51 35 6 00 57 4 9 22 6 19 40 6 3° 34 4 10 54 28 05 — 29 37 — 1 32 80 2 51 25 2 59 35 4 8 10 3 3i 0 3 41 26 4 9 56 40 05 — 41 51 — 1 46 90 — 22 25 — 23 °5 0 4c 4 22 25 4 23 °5l4 0 40 - ■■ ■ ■ 44 5° 46 10 1 20 .. iron arising from its rotation. 40 9 Table of the values ofW, 0, and 9' — 9, computed from the equations (9^) (10/,) compared with their observed values in Table B. X O' 0 O'— 9, Observed. Computed. Difference. Observed. Computed. Difference. Observed. Computed. Difference. 0 O / // 0 / « O / 0 > n 0 / // 0 / // O r " t 0 / « O / // 0 + 50 28 4 5° 01 — 0 27 — 50 28 — 5° 01 4 0 27 I 40 56 1 40 02 — 0 54 10 4 30 50 4 24 43 — 6 °7 2 54 52 2 49 34 — 5 18 I 35 58 1 35 °9 — 0 49 20 7 38 05 7 27 24 — 10 41 6 1 5 27 6 06 04 — 9 23 I 22 38 1 21 20 — 1 1 8 30 10 °7 5° 9 36 27 3» 23 9 °3 12 8 35 29 — 27 43 I 04 38 1 00 58 — 3 40 40 1 1 02 12 1° 37 47 24 25 10 23 37 IO 00 58 — 22 39 38 35 36 49 — 1 46 50 10 44 55 1025 11 *9 44 10 32 35 IO *3 35 — !9 00 12 20 11 36 — 0 44 60 9 12 IO l 59 55 1 2 *5 9 24 4° 9 12 06 — 1 2 34 — 12 30 — 1 2 1 1 4 0 *9 70 6 33 52 6 30 47 3 °5 7 06 20 7 02 48 — 3 32 — 32 28 — 32 01 4 0 27 80 3 io 50 3 *4 3» + 3 41 3 56 00 3 59 50 + 3 50 — 45 10 — 45 J9 — 0 09 90 1 24 49 — 25 01 r 0 12 4 24 49 4 25 01 4 0 1 2 49 38 — 50 02 0 24 The agreement between the computed and observed values of 6' — 6/ also of A' and in the first table is such, that had I been assured of the correctness of the formulas, I should cer- tainly not have expected it to be more perfect. In the second table, the agreement between the computed and observed values of b' — is equally close, but there is a greater differ- ence between those values of the angles O', 07 themselves. In determining the value of from the observation when A = 54° 45', and I had in the first instance in conse- quence of an error in computation, found it 47 instead of 48, and having computed the several values of O' and 0; from this value of 2 !! R , I found that the difference between these F r 7 and the observed values was less than 8', except in two in- stances, in one of which it amounted to n' and in the other to 19'. Now the observations when a = 50° and a = 6o° would give the value of R even less than 470, as will be 410 Mr. Christie on the magnetism of seen when we compute it for these values of x, which would still further diminish these differences. I have therefore no doubt that the differences between the computed and ob- served values of 6' and 6, in this table are to be attributed to an error of about 1 5' in the observed value of 0' when A = 54° 45'. The best criterion, however, of the correctness of the formulas is in the agreement of the values of the con- stants derived from them by means of the observations. If we eliminate ~ from the equations (9) and (10), we shall obtain 2 twR* F r 6 sin. 2 X cos. 0' . cos. 0, cos. S ' sin. (0' + 0,) (12) Substituting in the equations (11) and (12) the several ob- served values of 0' and 0, in tables A and B, we obtain the values of and contained in the following table. ft Fr Table of the values of the constants 2 m R3 Fr and 2 F r -j— computed from the several observed values of 6' and 9, in tables A and B, by means of the equations (12) and (11). X Observed values in Table A. Computed values. Observed values in Table B. Computed values. 0' 0 / 2 m R3 2 F r 0' 0' 2 R3 2 F r Fr /P F r fp 0 O IO 20 30 40 50 60 70 80 9° 0 /11 + 47 55 3 57 20 6 57 00 9 °3 25 9 56 20 Q 31 20 8 05 15 5 5i 35 2 51 25 — 22 25 O / P — 47 55 2 26 40 5 40 00 8 03 45 9 19 30 9 21 25 8 1 6 15 6 19 40 3 31 30 + 22 25 co. 103 54.301 51.615 51.077 51.516 52.587 53-492 53- 452 54- 463 53-551 16.331 1 5 - 733 16.681 16.321 15.852 18.188 16- 939 1 7 • 397 16.902 1 7 • 45 5 0 1 a + 50 28 4 3° 5° 7 38 05 10 07 50 11 02 12 10 44 55 9 12 10 6 33 52 3 10 50 — 24 49 0 1 a — 50 28 2 54 52 6 15 27 9 03 1 2 10 23 37 10 32 35 9 24 4° 7 06 20 3 c6 00 |+ 24 49 47-57* 46.767 46.834 45.492 46.203 46.512 46.915 47.609 48.846 48.372 16.798 17.240 17.085 16.819 16.759 16.412 16.894 16.849 16.712 17.081 Mean values 52.616 16.780 Mean values 47.112 16.865 iron arising from its rotation . 411 On comparing together the several values of 2 and also of ~j~~> conta”lec^ m this table, there can, I think, be no doubt that if the formulas (9) and (10), on which these values depend, be not absolutely correct, they will, at least, give in all cases, as close approximations to the values of and 6, that would be obtained by actual observation, as the nature of the case appears to admit of. It is very possible that some modification in the theory which I have examined might lead to the omission of the terms 2 cos. x — 1 + . 3 sin. 2 x in the formulae (5) and (6) ; and should this be the case, that the formulae (9) and (10) were to be derived from the theory so modified, it would, I think, be a very strong presumption in favour of the truth of such a theory. Since it appears from all the observations which I have detailed, that the direction of the magnetic polarity, which iron acquires by rotation about an axis , whether it be at right angles to the line of the dip, as would follow from the theory which I have investigated, or not, has always reference to the direction of the terrestrial magnetic forces, we must infer that this magnetism is communicated to it from the earth. It does not therefore appear from this, that a body can become polarised by rotation alone, independently of the action of another body : so that if from these experiments we might be led to attribute the magnetic polarity of the earth to its rotation, we must at the same time suppose a source from which magnetic influence is derived. Is it not then possible that the sun may be the centre of such influence, as well as the source of light and heat, and that by their rotation, the MDCCCXXV. 3 H 41S Mr. Christie on the magnetism of earth and other planets may receive polarity from it ? If so, further experiments and observations on the magnetic effects produced by the rotation of bodies may indicate the cause of the situations of the earth's magnetic poles, and of their progressive movements or oscillations. Comparison of the magnetic al effects produced by slow and by rapid rotation. With the view of ascertaining how far the effects pro- duced on a magnetic needle by a plate of iron during its rapid rotation, corresponded with those that I have described as nearly independent of the velocity of rotation, and as con- tinuing after the rotation had ceased, I placed the same plate of iron, which I had used in my former experiments, in the plane of the magnetic meridian, on an axis perpendicular to its plane, and about which it could be made to revolve with any velocity, not exceeding 10 revolutions in a second. I then placed a small compass, with a light needle delicately suspended, on a platform wholly detached from the iron plate, in certain positions opposite to the edge of the plate, both to the east and to the west of it, as near to the surface as the compass box would admit. The compass being adjusted, the plate was made to revolve once, slowly, so that its upper edge moved from north to south, and the point o coinciding with the plane perpendicular to the plane of the plate, and passing through its centre and that of the needle, the direc- tion of the north end of the needle was observed ; and also when 180 coincided with the plane, the same observation was made. The plate was now made to revolve rapidly in the same direction, about 8 times in a second ; and when the 413 iron arising from its rotation. needle became stationary during the rotation, the direction of its north end was observed. The point o on the plate was again made to coincide as quickly after the rapid rotation as possible, and the direction of the needle observed, in order to see if that rotation had produced any permanent change in the iron ; the same was done when the point 180 again coin- cided. Observations precisely similar to these were made when the upper edge of the plate revolved from south to north. Although the centre of the plate was stationary, and the needle was placed in certain positions with respect to it, I consider, as before, the situation of the centre of the plate with reference to the plane passing through the centre of the needle perpendicular to the dip ; and its angular distance from this plane, the equator, was measured on a circle of 9 inches radius parallel to the meridian, passing through the centre of the needle, and at the distance 1.45 inches from it, so that the centre of the needle was always at this distance from the edge of the plate, east or west. As the needle was only two inches in length, and the rim of the compass divided into degrees, the direction of the needle could not be observed nearer than to 5', and indeed scarcely to that de- gree of accuracy. The mode which 1 was under the neces- sity of adopting in adjusting the compass to the several posi- tions did not admit of extreme accuracy, so that these positions may be considered as liable to errors amounting to i°, or perhaps rather more, in angular distance from the equator ; but as my principal object was the comparison of the deviation due to the slow and rapid rotation of the plate, when its centre was in precisely the same position with re- spect to that of the needle, this was not very material : it 414 Mr. Christie on the magnetism of will however account for any disagreements that may be noticed in the absolute deviations in corresponding positions, as the greatest accuracy of adjustment would be requisite for their perfect agreement, when the plate is so near to the poles of the needle. Having ascertained, by the observations when the plate was to the west of the needle, that the rapid rotation pro- duced no permanent change in the iron beyond that arising from the slow rotation, the deviations when any particular points of the plate were opposite to the needle being, as near as could be expected, the same after the rapid rotation as they were after the slow rotation in the first instance, the errors being sometimes in excess, sometimes in defect, as will appear by inspection of the first table, I did not repeat the observations on the effects of the slow rotation after the rapid, when the plate was to the east of the needle. The following tables contain the observations. The first four columns of deviations, are those which were observed when the plate was stationary, after having very slowly revolved, and also those when the needle pointed steadily during the rapid rotations. The deviations in the 5th and 6th columns are obtained by taking half the difference be- tween those in the 1st and 2nd, and between those in the 3rd and 4th columns, as the deviation due to the rotation when the plate's upper edge revolved from north to south. iron arising from its rotation. 415 Tables of the deviations of a magnetic needle , caused by the rapid rotation of a plate of iron , observed during rotation , compared ivith the deviations due to the slow rotation of the plate , and permanent after the rotation had ceased. 1st. The iron plate , 18 inches in diameter , to the west of the compass. Direction of the N. end of the needle when plate sta- tionary after slow rotation, and also while the plate was rapidly revolving. Angular velocity ! Angular dis- of the plate, and Deviation due to the rota- . tance of the points opposite Piate’s centre in N. lat. Plate's centre in S. lat. tion of the plate’s upper { plate’s centre to the needle edge from N to S, when from the when plate sta- ulate’s centre was equator. tionary. Upper edge of the plate revolving : n tos S to N N to S S to N in N. lat. in S. lat. [slow [.80 0 , 2 45W 4 55 E 0 / 0 / 0 / 0 / f 14 25 E 23 40 E 6 40 E H 15 8 10W 2 05 E ! 8 59W 6 54 E o< 8 rev. per sec. 3 55 w 19 25 E H 3o 4 40 w 11 40W 9 35 E rH jG 4-» Lslow { .80 2 55W 6 30 E 13 55 E 24 40 E 6 40 H 5o 7 50 w 2 05 E | 8 45W 6 49 E 1 3 O f Slow \ o° 32 50W 27 30W 40 55 33 20 ( 2 2C 1 3 ir r* 1 l 180 27 40 23 00 42 25 37 °° • H 20< 8 rev. per sec. 3° 55 24 35 41 25 32 40 3 *0 4 22 * Lsiow {.so 32 50 28 00 27 35 22 40 40 40 42 25 33 35 36 45 | 2 34 3 22 jC G o s!ow { . so 43 5° 40 30 41 25 38 00 54 00 53 05 5 1 00 5° 4o J 1 H 1 2 1 $o< 8 rev. per sec. 42 25 39 lS 53 30 49 00 1 1 35 j 2 15 s o vfc; L 1 180 43 45 40 15 41 25 38 00 54 10 53 5 1 20 51 00 | 1 09 1 r5 T3 C rt "slow {.so 52 3° 49 10 51 00 47 00 59 25 59 °° 57 20 56 40 ] 0 55 1 06 7°-< 8 rev. per sec. 5 1 05 48 20 57 4° 54 4o x 1 23 1 30 Slow ^ 0 52 30 50 50 59 4° 57 25 f 0 55 1 04 xs ( 1 80 48 55 46 55 S8 4° 56 40 o fQ1 ( 0 62 00 60 20 68 30 66 40 1 c c slow \ 180 57 4° 56 00 67 45 66 io / 0 5° ! 0 51 9°^ 8 rev. per sec. 60 35 57 25 66 53 64 20 1 35 1 17 | Ut 4-* G i5l0W l 180 54 °o 73 45 78 15 84 25 8 rev. per sec. 57 55 78 20 69 40 80 30 10 12 E 5 25 Slow •! 0 76 10 83 40 76 05 82 00 \ * 51°w ) 180 _ v 53 20 72 5° 78 10 84 20 J 6 45 3 01 416 Mr. Christie on the effects of temperature on 2nd . The same iron plate to the east of the compass. Angular distance of the plate’s centre fTom the equator. Angular velocity of the plate, and points opposite to the needle when plate sta- tionary. -c c n -M Ui C G CD ti u. 4-< f_"‘‘ S u 3 co O * -d Cue J 180 per sec S 0 l 180 Direction of the N. end of the needle when plate sta- tionary after slow rotation, and also while the plate was rapidly revolving. \ 8 rev. per S Slow { l 1 o 180 8 rev. Plate’s centre in N. lat. Plate’s centre in S. lat. Upper edge of the plate revolving. N to S S to N N to S S to N 0 / O / 0 / O / 9 55 E i 25W 8 50W 5 20 E 5 00 E 7 25W 16 30 4 45W 11 05 4 25W *6 35 1 35 E 35 15 29 25 E 39 4o 33 3oW 3i 55 26 25 42 20 37 30 34 5° 27 25 42 25 34 55 42 30 40 05 53 45 50 50 39 5° 37 30 54 25 52 15 42 10 38 5o 53 20 49 10 48 55 47 5o 59 *5 56 20 45 3° 43 55 59 30 57 15 • 48 35 45 45 58 50 55 4o 59 45 57 55 66 35 64 40 56 00 54 3o 66 50 65 00 58 25 55 4o 66 25 63 35 71 00 69 30 75 10 73 4° 67 10 65 5o 75 10 73 55 . 70 40 68 30 74 20 7 2 10 83 25 83 3o 81 10 80 45 80 20 80 15 83 00 83 00 82 20 81 45 81 15 80 15 86 35 87 3o 81 30 82 20 83 00 84 25 84 50 85 20 . 85 5° 86 40 82 20 82 40 77 00 85 20 68 00 77 20 47 3° 73 J5 72 35 81 15 . 51 40 81 40 67 10 79 4° Deviation due to the rota- tion of the plate’s upper edge from N to S, when plate’s centre was in N. lat. in S. lat. -> ° ' 0 , } 5 56 E 6 29W 7 45 E J 0 05W j 2 50 2 45 3 43 3 45 j 1 °9 1 16 I 4O 2 05 040 1 18 1 25 *\ 1 35 j 0 50 0 57 1 23 1 25 [ 0 43 0 41 1 05 1 05 I 0 00 0 06 0 18 0 30 | 0 35W 0 20 E J 0 25W 0 10 E | 8 31W 4 3° 15 00 6 15 From the inspection of these tables, it appears that the forces which are exerted on the needle during the rapid rota- tion of the plate, are always in the same direction as the forces which are derived from the slowest rotation, and which .continue to act after the rotation has ceased ; but that the 417 iron arising from its rotation. former forces are greater than the latter, there being only one instance of the contrary, and that in a position where the effects are so small, that a trifling error of observation would account for the difference. Taking a mean of all the obser- vations, these forces appear to be in the ratio of 19 to 13, or very nearly 3 to 2. It is evident then that the polarising of the iron in the same direction will account for the pheno- mena in both cases, but that the intensity of the polarity during the rapid rotation is greater than of that which appears to be permanent after the rotation, whether slow or rapid, has ceased ; and that the phenomena observed during rapid rotation are such as we should expect from those which I have so fully described as arising from rotation, without regard to its velocity. [ 418 ] XVII. Some account of the transit instrument made by Mr. Dollond, and lately put up at the Cambridge Observatory . Communicated April 13, 1825. By Robert Wood house, A. M. F. R. S. Read May 19, 1825. As I am inclined to hope that the observations to be made at the Observatory lately established at Cambridge may, at some future period, be useful to astronomical science, I beg leave to send a brief description of our transit telescope, the only large instrument which we are at present possessed of. The annexed drawings, which I have caused to be made of the instrument, will explain its construction. Its dimensions are nearly the same as those of the Green- wich transit made by Mr. Troughton. Ft. In. Its focal length is - - 9 10 Its aperture - - -05 The length of the axis between the piers 3 6 The weight of the instrument is eoolbs. The instrument is counterpoised ; and the whole lengths ( 2 inches) of the pivots rest on the Y .9. Seven fixed wires are placed in the focus of the object glass, and two other wires moveable by a micrometer screw ; the interval of which wires is equal to the interval between any two of the fixed wires, and, equatorially , is 17*. 88. The two small graduated circles (see the figure) with their spirit levels, fixed near to the eye- piece, are for the Mr. Woodhouse's account , &c. 4i 9 purpose of finding a star's place in the meridian. Each circle is furnished with two verniers; one for polar, the other for zenith distances. I wish to add a few words respecting the determining the place of the transit room, and the adjusting the instrument to the plane of the meridian ; which, as we had in the begin- ning no astronomical point to stand on, was a matter of some trouble. Our first object was, if possible, so to fix the site of the transit room, that its meridian mark might be placed on the steeple of Granchester church, distant to the south about 21- miles from the field on which the observatory was to be built. The first approximations to such site were made by ad- justing the middle wire of a small transit telescope ( 18 inches long) to the spire, or iron rod of the steeple, and by com- paring the sun's transit with the time brought up by chrono- meters from Mr. Catton's observatory at St. John's College. Our second approximations were made by observations of high and low stars with the small transit instrument above mentioned. According to the results thus obtained the piers of the transit were placed; and when, in June 1824, the instrument was put upon them, were found to be placed with consider- able exactness. From the above time observations have been constantly made with the instruments described in this paper, and with a clock made by Molyneux and Cope. The first operation was to determine the clock's rate , which was done by observations of the same stars on succes- sive days : the next, to determine the clock's error, which was found in the usual way, by deducting the observed mdcccxxv. 3 I 420 Mr. Woodhouse’s account of the passages of stars from their tabulated, or computed right ascensions. The clock’s error, as it was to he expected, was found, after allowing for its rate, different with different stars ; which is a sign of the instrument being out of adjustment in some of its parts. The error might be in the line of colli- mation ; in the axis not being horizontal ; or, which was pro- bably the chief cause of error, in the transit deviating from the plane of the meridian. Any one, or two, or all of these circumstances might occasion the noted difference in the clock’s errors. For instance, the clock being before sidereal time, its error from a Cygni was found to be less than from a. Aquilae: This might arise from the western end of the axis being too high, or from the line of collimation deviating to the east, or from the transit deviating to the west. A single observation such as this, or any number of the same stars, would leave us in doubt respecting the causes of the want of adjustment ; but a third star would lessen this doubt. Thus, if, the clock’s error after allowing for its rate being from a. Cygni 48.72i, and from a Aquilae 4s. 8 54, we attributed the difference of errors to a defect of horizontally in the axis, the quantity of such defect would become known. Let it be expressed by H, the clock’s error by e ; then for the latitude of Cambridge we should have two simple equations between H and e, from which both may be found — 4.721 + s = 1.39 H, x Cygni — 4.854 + s = .75 H, a Aquilae ; and, accordingly, H = os.2, nearly. With this value of H, the error of time for a Urs. maj. transit instrument at the Cambridge Observatory. 421 would be o*.4288 (= o\2 x 2144) ; which not being found to agree with the observed error (or rather the difference of its observed passage and its computed right ascension), showed that the difference of the errors of the clock had been wrongly, or partially, assigned. If we suppose the difference of the errors of the clock to arise from two causes — the want of horizontally and the de- viation of the transit from the plane of the meridian, then, calling the latter deviation H, we have, instead of the former, these equations : — 4.721 + 6 = !-S9 H + .185 Z — 4.854 + e == .73 H + .7 Z to which a third similar equation must be added for a. Urs. maj. If from such three equations we determined H and Z, we might proceed as before, and examine, by means of a fourth star, whether it were necessary to suppose the existence of a third cause (an error in the line of oollimation for instance) to account for the differences in the clock's error. If C should denote the error of collimation, dt the error of time, c the colatitude of the place of observation, $ the star's north polar distance, the general form of the equations for determining H, Z, &c. is 1 1 1 ri cos. (c — o) | r-r sin. (c — I C — d t + s = H + Z . 7— 4- sin. s 1 sin. S 1 sin. s In this way we might consider the subject in all its gene- rality (as foreign writers express themselves) ; and from observations alone, arrive at a knowledge of the defects of the instrument. And this mode of considering the subject is ’ not without its use, since it may be applied to recorded and ancient observations ; as Bessel has done in the case of 4 22 Mr. Woodhouse's account of the Bradley's Observations. But no practical astronomer, I apprehend, can be so fond of encountering difficulties,* as to adopt this mode of adjusting his instrument; for, if from one set of equations he deduced the values of H, Z and C, he could not, by reason of his imperfect knowledge and manage- ment of the screws of his instrument, at once adjust it ; but would be again and again obliged to repeat his observations, and the solutions of the resulting equations. But this is not all. The differences of the clock's errors are the differences of the differences of the observed culmi- nations of stars, and their tabulated or computed right ascen- sions, and therefore must partake of the uncertainties to which the latter quantities are subject. The point to be aimed at in adjusting an instrument is, to adjust it by means that do not rest on the results of astronomical science. * As a kind of proof of the great uncertainty of determining the deviations of the instrument by the method of equations, I subjoin the following instance : October 13, 1824. Time by Clock. M Errors, h. m. s. s. s. a Aquarii 21 56 52,86 48.72 4*x4 a. Pegasi 22 56 8.74 4 -4 4-34 a Andromedse 23 59 27 .7 23.25 445 whence, the axis being horizontal, and the clock going sidereal time, we have these equations : — q3. 14. -J- * — .8028 Z -j- C — 4.34 + £ = .6347Z + 1.032 C — 4.45 + s zz .4627 Z -f 1. 1 14 C from which, Z = 1*48, C =: 1 ".52 ; but if an error of o’.i had occurred in the ob- servations, or if we suppose the tables to be erroneous to that degree, and the second equation had been — 4S.44 -f- £•= .6347Z + 1.032 C, then, instead of the preceding values of Z and C, we should have had these : Z = 28.935 C = 6. 033 transit instrument at the Cambridge Observatory. 425 The old methods of adjusting a transit instrument do not rest on such results ; and the old method of proceeding seems to me the most sensible one, that of separately and succes- sively correcting each cause of defective adjustment. The axis can be made horizontal, or its defect of horizon- tality known, by the level, the plumb line, or by reflection. The line of collimation can be adjusted by means of a small object in, or near to, the horizon. In this operation a small defect in the horizontally of the axis will have scarcely any effect on the accuracy of the operation. If the mark should, for instance, be 20 above the horizon, and one end of the axis 5" higher than the other, the error in collimating from that cause would, in the latitude of Cambridge, be only o".io75. The error in the same operation with the pole star, supposing it be fixed, would be i' 11". 5. The third adjustment, which is the most troublesome, is to place the transit instrument in the plane of the meridian ; and there are two methods of effecting this : one, by high and low stars ; the other, by circumpolar stars, or, as it almost always happens in practice, by the pole star. The essential difference in these two methods is, that the former rests on the results of astronomical science, whilst the latter does not so rest ; and this circumstance gives the latter a decided advantage over the former, when it is necessary to make a nice adjustment. Yet there is not wanting consider- able astronomical authority for placing the two methods on a level, the one with the other. Baron de Zach, for instance, views each as an equally good method ; and in his Tabulae speciales Aberr*. et Nut5, gives instances of the adjustment of a transit instrument (a 5-feet one by Dollond) ; the first, by the comparison of the passages over the meridian of 424 Mr. Woodhouse's account of the Capella and Rigel ; the second, by the passages of Capella above and below the pole : and the result, equal to a deviation of 12".685 to the east, is in each case the same ; a coincidence of marvellous accuracy ; and which, if the observations were exactly noted, we must suppose to have arisen from a fortui- tous balancing of the errors of the observations with those of the tables. In the method of high and low stars I suppose, which is almost always the case, that the clock's error is found by subtracting from the observed passage of the star its com- puted right ascension. The error may indeed be found by equal altitudes , should the observer possess an altitude and azimuth instrument of sufficient accuracy for that purpose. But should he not, the adjustment of the transit instrument by high and low stars must partake of that uncertainty to which we are subject in computing tlie true apparent right ascensions of stars. We have only to look at the catalogues of stars by different astronomers to be convinced of the existence of such uncer- tainty. If, indeed, the tabulated right ascensions differed only by a constant quantity, the difference of the errors of the clock, on which the method of high and low stars depends, would be the same, whether we employed Bessel's or the Greenwich catalogue. But it is otherwise : to instance this, on the 8th October, 1824, the clock going very nearly side- real time, the passages of Arcturus and §> Urs. min*, were as follow : Time by Clock. At by N.A. Error. At by Schumacher. Error. Arcturus 0 Urs. min. - h. m. s. 14 7 44.56 14 51 20.43 s. 40.18 14.67 4-38 5.76 s. 39-98 I4-95 00 00 l-r\ transit instrument at the Cambridge Observatory. 425 Hence for determining the deviations of the transit instru- ment we have, respectively, the following equations : By Nautical Almanack. — 4.38 -f- e = .5657 Z „ ry 5 L 1 1 52 5.77 — £ = I.48 Z By Schumacher’s Tables. — 4.58 e = .5657 Z , z = o'. 98. 5.48 6 = I.48 Z The value of the deviation (Z) is uncertain then to the amount, and more, of half a second of time. From such kind of uncertainty, the method of circumpolar stars is entirely free; its characteristic excellence, as it has been already said, consists in its being independent of the results of astronomical science. In what I have said, I must be supposed to speak of the exact adjustment of large instruments. The method of high and low stars is very convenient, and easily practised ; it in- forms us, in the space of a few hours, of the nature and degree of the deviation of the instrument ; and in some cases, when the transit instrument is prevented by its situation from being directed to stars beneath the pole, it is almost an indis- pensable method. I wish to add a few words respecting the adjustment of the line of collimation by means of the reversion of the transit instrument during the passage of the pole star. This method has indeed the air of being philosophical ; but, according to my opinion, is neither so easily practised, nor so certain as the old method. It is liable to the uncertainty of the times of the pole star's passages over the wires ; and always re- quires, before and after the observation, the examination of 426 Mr. Woodhouse's account of the the horizontality of the axis. Without attention to this latter circumstance the method is worth nothing ; for, if H should be the error in horizontality, the corresponding error in time would, in the latitude of Cambridge, be equal to about 28.6 H. When we adjust according to the old plan, the colli- mation by means of an object near the horizon, the opera- tion of levelling is not required ; which in large instruments is rather a troublesome one ; and certainly is not, what M. Delambre states it to be, “ the affair of an instant/'* The level indicating the degree of the defect of horizon- tality, enables us to correct the time and this correction is made on the supposition that the instrument is in the same state when the star is observed, as it was during its examin- ation by the level. It is therefore, other things being equal, expedient to examine by the level, as nearly as it is possible, at the time of observation. But this I am unable to do ; as I will show, by stating a circumstance rather deserving of attention. The tube of the telescope is braced to the axis (see the figure) by four tubes. The stations of the two * II ne faut pas commencer d’observations sans avoir rectify l’horizontalite de l’axe, ce qui est l’affaire d’un instant. Astron. tom. i, p. 431. Mr. Dot.t.ovti rnnciHers the value of 1 division of the scale of the level to be equal to 1". I have determined its value astronomically. Previously to a star's culmination, I lowered the eastern end of the axis 10 or 12 divisions, and observed the star’s passages across the four first wires. I then caused the western end to be lowered, and observed the star’s' passages across the three remaining wires, and then examined the level. The following are the results : # // £Cephei - - 1.014 a. Cygni - - 0.9 ^Draconis - - 1.005 a Cephei - - .855 Polaris - - 0.9516 Meano".945i. transit instrument at the Cambridge Observatory. 427 persons who level are opposite, and contiguous to the south- west and north-east braces. Being in the constant habit of examining the meridian mark, in order to know what degree of stability the instrument possesses, I found, after levelling, that the south meridian mark was to the east of the middle wire. In about 10 minutes the middle wire returned to the meridian mark, and bisected it. I noted this circumstance a second, third, and fourth time, and then began to inquire whether I had conjectured rightly in attributing it to the expansion of the tubes or braces. For this end, I placed a heated blanket across the south-west and north-east braces, and found the meridian mark deviating to the east of the middle wire : a contrary effect was produced by placing the blanket across the south-east and north-west braces. In these trials the object glass was towards the south : contrary effects took place when it was turned to the north.* As yet I am unable to say whether or not the sun’s rays falling on the braces, during an observation of his transit, affect the accuracy of the observation. I am enquiring into that point, and have ordered a screen to be made to protect the braces from the rays of the sun. After repeated trials, I have been obliged to abandon the counterpoises instead of relieving the instrument, they render it unsteady. It has happened with them (as it has happened in cases of a different nature), they have overpow- ered what they were meant only to assist. * The effect I have noted is somewhat of the same kind as that which was com- plained of in Halley’s transit. See Bradley’s Observations, vol. i. p. 2. + They are now with Mr. Dollond, who is endeavouring to remedy their defects. SK MDCCCXXV. 428 Mr. Woodhouse's account of, &c. My chief study, since the fixing up of the instrument, has been to obtain a thorough knowledge of it : to find out its defects, should it have any, their nature and degree. The observations of stars have been chiefly made for, and have served that end ; but they are not, I think, otherwise useful, nor worth registering. TML. Trans. MXK X :CXXV Tl&tzWSS. H ■ ' - Basire sculp!. rivnx MDCICXW l%a. WVill^ Elevation of one ha//' o/' f/jr opposite Y Elevntirn e/' cue ha/e' with the p/ate / ii/deil of Y o o o\ o o\ > O |>o oij o o r - £ \ H — — : Section of the 2n ft? ■/ uncut, to cal Ictu/th .9. 10. \ I1 1 ■tn : fit/.*/ re . .iralp* C 429 3 XVIII. On the fossil Elk of Ireland. By Thomas Weaver, Esq. Member of the Royal Irish Academy, of the Royal Dublin Society, and of the Wernerian and Geological Societies . Read May 19, 1825. JNJ* otwithstanding the frequent occurrence of the remains of the gigantic elk in Ireland, it is remarkable that precise accounts should not have been kept of all the peculiar cir- cumstances under which they occur entombed in its super- ficial strata. To obtain an opportunity of examining these relations had long been my desire ; and as fortunately, dur- ing my avocations last autumn in the north of Ireland, a discovery came to my knowledge that seemed likely to throw light on the subject, I proceeded to its investigation, intending, should the results be found deserving of attention, to place them on record. These results have proved the more interesting, as they apparently lead to the conclusion, that this magnificent animal lived in the countries in which its remains are now found, at a period of time which, in the history of the earth, can be considered only as modern. I had advanced thus far when I became apprized of an analogous discovery made last year in the west of Ireland by the Rev. W. Wray Maunsell, Archdeacon of Limerick ; which is not only confirmative of my own experience, but has the additional value of embracing particulars not hitherto noticed by any other observer. Mr. Maunsell’s researches, 430 Mr. Weaver on the elucidated by the able assistance of Mr. John Hart, Member of the Royal College of Surgeons, have been communicated from time to time to the Royal Dublin Society in the form of letters, and have been entered upon their minutes ; and, it is to be hoped, that a distinct publication on the subject may hereafter appear, illustrated by a description of the splendid specimen of the skeleton of the animal now deposited by the liberality of the Reverend Archdeacon in the museum of that Society. In the mean time I propose, after giving a concise account of my own inquiries, to refer briefly to the more prominent points in Mr. Maunsell's discoveries, in as far as they bear immediately on the question of the ancient or modern origin of those remains. The spot which I examined is situated in the county of Down, about lj mile to the west of the village of Dundrum. That part of the country consists of an alternating series of beds of clay slate and fine grained grey wacke, with occasional subordinate rocks, which it is needless at present to mention ; the whole distinguished by numerous small contemporaneous veins of calcareous spar and quartz, and traversed in some places by true rake veins that are metalliferous. Hills of mo- derate elevation, from 150 to 300 feet high, are thus com- posed. In a concavity between two of these hills is placed the bog of Kilmegan, forming a narrow slip, which extends about one mile in a nearly N. and S. direction. The natural hollow which it occupies appears formerly to have been a lake, which in process of time became nearly filled by the continued growth and decay of marshy plants, and the con- sequent formation of peat. The latter, however, from the flooded state of its surface, afforded little advantage as fuel, 431 fossil elk of Ireland. until the present Marquis of Downshire caused a level to be brought up from the eastward (part of it being a tunnel), and thus laid the bog dry. This measure was attended with a two-fold benefit to the tenantry, the provision of a valuable combustible, and the discovery of an excellent manure in the form of white marl beneath the peat. The latter extends from a few feet to twenty feet in depth ; and the subjacent marl from one to three, four, and five feet in thickness. The marl when fresh dug has partly a grayish tinge, but on losing its moisture it becomes white. In cutting down the peat to the bed of marl, the remains of the gigantic elk have frequently been met with ; and invariably, as I am assured by the concurrent testimony of the tenantry, placed between the peat and the marl, or merely impressed in the latter. It is stated that at least a dozen heads with the branches, accompanied by other remains, have thus been found from time to time : but being unfor- tunately deemed of no value by the country people, they have for the most part been scattered and destroyed. It is to be hoped, however, that a sufficient inducement will lead them to bestow greater care on the preservation of whatever remains may be hereafter discovered. The marl, upon examination, appears in a great measure composed of an earthy calcareous base, containing commi- nuted portions of shells ; and that these are all derived from fresh water species, is proved by the myriads of these shells that remain in the marl, still preserving their perfect forms. They are however bleached, very brittle, and retain little of their animal matter ; but in all other respects they have the characters of recent shells. After examining several 432 Mr. Weaver on the masses of the marl, I found the whole of the shells referable to three species, two univalves, and one bivalve : namely, 1. The helix putris of Linnaeus. See Donovan's British Shells, Pl. 168, fig. 1, and Lister, Conch. Tab. 123, ffg. 23. N. B. Of the two, Lister's figure is the more exact representation of the shell. 2. The turbo fontinalis. Donovan, PI. 102. 3. The tellina cornea. Donovan, PL 96. Of these shells some prevail more in one spot than in ano- ther ; but generally speaking they appear distributed through the upper portion of the marl in nearly equal quantities ; in • the lower portion they are less frequent, if not altogether absent. The circumstances which I have related seem to remove all idea of these remains of the Irish elk being of any other than comparatively recent origin. In seeking a cause for the nearly constant distribution of these remains in Ireland in swampy spots, may we not conjecture that this animal often sought the waters and the marshy land as a place of refuge from its enemies, and thus not unfrequently found a grave where it had looked for protection ? The foregoing conjecture appears supported by the follow- ing details of circumstances, observed by the Rev. Mr. Maunsell in the peat bog of Rathcannon, situated about four miles to the west of the town of BrufF, in the county of Limerick. This bog covers a space of about twenty planta- tion acres, occupying a small valley, surrounded on every side by a ridge of the carboniferous or mountain limestone, except on the S. W., where it opens into an extensive flat. 433 fossil elk of Ireland. The peat is from one to two feet thick ; and beneath this is a bed of white shell marl, varying from l-j- to 2j feet in thick- ness, succeeded below by bluish clay marl, of an unascer- tained depth, but in one place it was found to exceed 12 feet. This bluish clay marl becomes white, and falls to powder on being dried. Coarse gravel is said to occur, partially at least, below the marl. In this small valley portions of the skeletons of eight indi- viduals were found, seven of adult, and one of a young ani- mal, all belonging to the gigantic elk. With these also occurred the pelvis of an adult animal, probably referable to the red deer ; and the skull of a dog, of the size of that of % an ordinary water spaniel. The bones that were first discovered were found at the depth of two or three feet below the surface; and Mr. Maunsell had the advantage of seeing them before they were displaced. Most of the above mentioned remains were lodged in the shell marl ; many of them, however, appeared to rest on the clay marl, and to be merely covered by the shell marl. But parts of some of the bones were immersed in the peat also : these were tinged of a blackish colour, and were so extremely soft in consequence of the moisture they had imbibed, that it was with difficulty the horns found in this situation could be preserved entire ; yet, when carefully handled and allowed to dry, they became as firm and hard as the rest. Some of the bones of the elk showed marks of having been diseased ; and one rib had evidently been broken, and afterwards reunited. Another rib exhibited a remarkable perforation of an oval form, about half an inch long, and 434 Mr. Weaver on the one-eighth of an inch broad, the longer axis being parallel to the side of the rib ; the margin of this opening was depressed on the outer, and raised on the inner surface ; while a bony point projected from the upper edge of the rib, which devi- ated from its natural line of direction to an extent equal to the length of the aperture. The only cause that could have produced this perforation is a wound by a sharp instrument, which did not penetrate deep enough to prove fatal, and be- tween which event and the death of the animal a year at least must have elapsed, as the edges of the opening are quite smooth. The bones are so well preserved, that in the cavity of one shank bone which was broken, marrow was found, having all the appearance of fresh rendered suet, and which blazed on the application of a lighted taper. They appear to con- tain all the principles to be found in fresh bones, with per- haps the addition of some carbonate of lime, imbibed with the moisture of the soft marl in which they had lain. The remains of the eight individuals were disposed in such a manner as to prevent the possibility of referring the component parts exactly to each skeleton ; but all the heads with their branches were found ; and one specimen is parti- cularly fine, displaying the broad expanded palms, with almost every antler and projecting point in a perfect state. By joining this head to a selection from the other remains, a nearly perfect skeleton of the largest size has been formed by Mr. Hart ; one rib, a few of the carpal and tarsal bones, and the bones of the tail being only wanting. Of the shells found in the white marl many are preserved entire ; but the greater part are broken into small fragments. 435 fossil elk of Ireland. They are all univalves, and belong to fresh water species, which exist at the present day. It is added, that so frequently have the remains of the fossil elk been discovered in the county of Limerick, that one gentleman enumerated thirty heads which had been dug up at different times within the space of the last twenty years. From Professor Henslow's account of the curraghs, or peat bogs of the Isle of Man, it would appear that the remains of the gigantic elk are there also distributed in a manner analogous to that in which they are found in Ireland. That gentleman supposes a herd of elks to have perished there ; and his description of the white, or grayish marl, in which their remains are found, answers in most respects to that of the white marl which so frequently forms the sub-stratum of the peat bogs in Ireland. Upon the whole, the preceding details appear to justify the conclusion, that the extinction of the gigantic species of elk is attributable rather to the continued persecution it endured from its enemies, accelerated perhaps by incidental natural local causes, than to a general catastrophe which overwhelmed the surface of the globe. In a word, it may be inferred that these remains are not of diluvian, but of post diluvian origin. T. WEAVER. Kenmare , April 12, 1825. 3 L MDCCCXXV. C 436 3 XIX. Microscopical observations on the Materials of the Brain , and of the Ova of Animals , to show the analogy that exists between them. By Sir Everard Home, Bart. V . P. R. S. Read at the Society for promoting Animal Chemistry , April 12, 1825'. • Read at the Royal Society June 3, 1825. Half a century ago, when I began my professional educa- cation under Mr. Hunter, he was deeply engaged in investi- gating the properties of the blood, and ascertaining the changes it underwent in different circumstances. His ob- ject in this inquiry was to prove that the blood possessed within itself a principle of life, by which all these changes were regulated. By his direction I made the following experiment, which proved that when frozen and thawed it had undergone no change. Two inches in length of the jugular vein distended with blood and secured at each end by a ligature, when immersed in a cooling mixture and frozen, was found after it was thawed to remain fluid, and to coagulate on exposure like recently drawn blood. From this fact, which is published in his work on the blood, corroborated by many others, he concluded that as the principle of life resided in the blood, and no change was produced in that fluid by the act of freezing, none were to be expected to arise from its action I 4S7 Sir E. Home's microscopical observations , &c. on the other parts of the body ; and had we been able to produce the necessary degree of cold, he certainly would have tried the experiment. From the time of Mr. Hunter's death to that of the ex- pedition to the polar circle being fitted out, the subject had never recurred to my mind ; it was then revived ; and I had no doubt of being fully informed upon its return, whether animals after being frozen could be revived ; but in this I was disappointed. In the winter before last an experiment was made in the presence of several Members of this Society, of freezing a frog, inclosed in tin foil, in a mixture cooled to zero. The frog recovered ; but there was reason to doubt of the brain having been frozen ; and this experiment was repeated by Mr. Faraday, in the laboratory of the Royal Institution, in the presence of Sir H. Davy, Professor Brande, and myself, in the following manner. Two healthy frogs, nearly of the same size, were sepa- rately wrapped up in tin foil, and immersed in a cooling mixture at zero. At the end of four hours one of them was examined ; the brain and heart were found completely frozen ; the other was allowed to thaw gradually, but had no remains of life. Upon opening the skull the brain was dissolved, and the cavity contained nothing but a watery fluid, with some gelatinous matter. By this experiment it is decided that an animal whose brain has been frozen can never be restored to life. Having, in the Croonian Lecture for 1823, illustrated the more minute structure of the human brain by three drawings, magnified in different degrees by Mr. Bauer, made from a 438 >SzrE. Home’s microscopical observations on the healthy brain very recently after death, I became desirous of decomposing a similar portion of brain by the act of freezing, and then having drawings similar to the others made, to show the contrast between the two. For this purpose I got Mr. Faraday to inclose in tin foil a thin slice of human brain soon after death, then weigh the tin foil in which it was enveloped in the balance belonging to the Royal Institution. After being thus accurately weighed, it was immersed in a cooling mixture as low as zero. When it had remained there for four hours it was taken out, and the tin foil unfolded that it might thaw gradually ; a quantity of watery fluid had separated in the act of thawing from the por- tion of brain : this was allowed to drain off, and the tin foil with its contents was re-weighed, and had lost 20 per cent from its decomposition. Mr. Bauer’s drawings of it in this state, magnified in three different degrees, to correspond with the others, are annexed. These two sets of drawings establish the real appearance of the more minute structure of the brain, and the changes that structure undergoes when exposed to the effects of having been frozen, and led me on to ascertain the effects of freezing upon the molecule of the pullet’s egg after it has been impregnated, that I might ascertain whether the opinion I had formed, of its more minute parts corresponding with those of the brain, was correct ; and as I have given draw- ings of the molecules highly magnified, similar drawings made after it had been frozen, would enable me to preserve the difference in appearance between the two. To freeze the egg without disturbing the molecule, I en- closed it in a leaden case, with a cover exactly fitted to it ; 439 materials of the brain and ova of animals. then exposed the molecule, put on the cover, and immersed the whole into a cold mixture, and carried it to Kew, that Mr. Bauer might represent the appearance. EXPLANATION OF PLATE XXVII. Fig. 1. A small portion of the cortical and medullary sub- stance of the human brain that had been frozen and thawed, magnified 5 times. Fig. 2. A part of the above, magnified 25 times. Fig. 3. A still smaller part of the above, magnified 200 times. These three drawings correspond with three that have a a place in the Philosophical Transactions : taken from the human brain recently after death, in a natural state. Fig. 4. The molecule of the pullet’s egg after impregna- tion, that had been frozen and thawed, magnified 10 times, to correspond with a similar drawing of the molecule in a natural state. C 440 ] XX. On new compounds of carbon and hydrogen , and on certain other products obtained during the decomposition of oil by heat. Ey M. Faraday, F. R. S. Cor. Mem. Royal Academy of Sciences of Paris , &c. Read June 16, 1825. The object of the paper which I have the honour of sub- mitting at this time to the attention of the Royal Society, is to describe particularly two new compounds of carbon and hydrogen, and generally, other products obtained during the decomposition of oil by heat. My attention was first called to the substances formed in oil at moderate and at high tem- peratures, in the year 1820 ; and since then I have endea- voured to lay hold of every opportunity for obtaining infor- mation on the subject. A particularly favourable one has been afforded me lately through the kindness of Mr. Gordon* who has furnished me with considerable quantities of a fluid obtained during the compression of oil gas, of which I had some years since possessed small portions, sufficient to excite great interest, but not to satisfy it. It is now generally known, that in the operations of the Portable Gas Company, when the oil gas used is compressed in the vessels, a fluid is deposited, which may be drawn off' and preserved in the liquid state. The pressure applied amounts to 30 atmospheres ; and in the operation, the gas previously contained in a gasometer over water, first passes into a large strong receiver, and from it, by pipes, into the of carbon and hydrogen , &c. 44 1 portable vessels. It is in the receiver that the condensation principally takes place ; and it is from that vessel that the liquid I have worked with has been taken. The fluid is drawn off at the bottom by opening a conical valve : at first a portion of water generally comes out, and then the liquid. It effervesces as it issues forth ; and by the difference of re- fractive power it may be seen, that a dense transparent vapour is descending through the air from the aperture. The effervescence immediately ceases ; and the liquid may be readily retained in ordinary stoppered, or even corked bottles ; a thin phial being sufficiently strong to confine it. I understand that 1000 cubical feet of good gas yield nearly one gallon of the fluid. The substance appears as a thin light fluid ; sometimes transparent and colourless, at others opalescent, being yellow or brown by transmitted, and green by reflected light. It has the odour of oil gas. When the bottle containing it is opened, evaporation takes place from the surface of the liquid ; and it may be seen by the stride in the air that vapour is passing off' from it. Sometimes in such circum- stances it will boil, if the bottle and its contents have had their temperature raised a few degrees. After a short time this abundant evolution of vapour ceases, and the remaining portion is comparatively fixed. The specific gravity of this substance is 0.821. It does not solidify at a temperature of o° F. It is insoluble, or nearly so, in water ; very soluble in alcohol, ether, and vola- tile and fixed oils. It is neutral to test colours It is not more soluble in alkaline solutions than in water ; and only a small portion is acted upon by them. Muriatic acid has no 442 Mr. Faraday on new compounds action upon it. Nitric acid gradually acts upon it, producing nitrous acid, nitric oxide gas, carbonic, and sometimes hydro- cyanic acid, &c. but the action is not violent. Sulphuric acid acts upon it in a very remarkable and peculiar manner, which I shall have occasion to refer to more particularly presently. This fluid is a mixture of various bodies ; which, though they resemble each other in being highly combustible, and throwing off much smoke when burnt in large flame, may yet by their difference of volatility be separated in part from each other. Some of it drawn from the condenser, after the pres- sure had been repeatedly raised to 30 atmospheres, and at a time when it was at 28 atmospheres, then introduced rapidly into a stoppered bottle and closed up, was, when brought home, put into a flask and distilled, its temperature being raised by the hand. The vapour which came off, and which caused the appearance of boiling, was passed through a glass tube at o°, and then conducted to the mercurial trough ; but little uncondensed vapour came over, not more than thrice the bulk of the liquid ; a portion of fluid collected in the cold tube, which boiled and evaporated when the temperature was allowed to rise ; and the great bulk of the liquid which remained, might now be raised to a comparatively high point, before it entered into ebullition. A thermometer being introduced into another portion of the fluid, heat was applied, so as to keep the temperature just at the boiling point. When the vessel containing it was opened, it began to boil at 6 o° F. As the more volatile por- tions were dissipated, the temperature rose : before a tenth part had been thrown off, the temperature was above ioo°. 443 of carbon and hydrogen , &c. The heat continued gradually to rise, and before the substance was all volatized, it had attained 250°. With the hope of separating some distinct substances from this evident mixture, a quantity of it was distilled, and the vapours condensed at a temperature of o° into separate por- tions, the receiver being changed with each rise of 10" in the retort, and the liquid retained in a state of incipient ebullition. In this way a succession of products were obtained ; but they were by no means constant ; for the portions, for instance, which came over when the fluid was boiling from 160° to 170°, when redistilled, began to boil at 130°, and a part re- mained which did not rise under 200°. By repeatedly recti- fying all these portions, and adding similar products toge- ther, I was able to diminish these differences of temperature, and at last bring them more nearly to resemble a series of substances of different volatility. During these operations I had occasion to remark, that the boiling point was more constant at, or between 176° and 190°, than at any other temperature ; large quantity of fluid distilling over without any change in the degree ; whilst in other parts of the series it was constantly rising. This induced me to search in the products obtained between these points for some definite substance, and I ultimately succeeded in separating a new compound of carbon and hydrogen, which I may by anticipa- tion distinguish as bi-carburet of hydrogen. Bi-carburet of hydrogen. This substance was obtained in the first instance in the following manner : tubes containing portions of the above rectified products were introduced into a freezing mixture at mdcccxxv. 3 M 444 Mr. Faraday on new compounds o°; many of them became turbid, probably from the pre- sence of water ; one, received at 17 6°, (by which is meant that that was the boiling point of the contents of the retort when it came over) became partly solid, crystals forming round the side, and a fluid remaining in the centre ; whilst two other portions, one received at 18 6°, and the other at 190°, became quite hard. A cold glass rod being introduced into one of these tubes, the mass within was found to resist considerable pressure ; but by breaking it down, a solid part was thrust to the bottom of the tube, whilst a fluid remained above : the fluid was poured off', and in this way the solid portion partly purified. The contents of the tube were then allowed to fuse, were introduced into a larger and stronger tube, furnished with another which entered loosely within it, both being closed of course at the lower end ; then again lowering the temperature of the whole to o°, bibulous paper was introduced, and pressed on to the surface of the solid substance in the large tube by the end of the smaller one. In this way much fluid was removed by successive portions of paper, and a solid substance remained, which did not become fluid until raised to 28° or 290. To complete the separation of the permanently fluid part, the substance was allowed to melt, then cast into a cake in a tin foil mould, and pressed between many folds of bibulous paper in a Bramah's press, care having been taken to cool the paper, tin foil, flannel, boards, and other things used, as near to o° as possible, to prevent solution of the solid substance in the fluid part to be removed. It was ultimately distilled from off caustic lime, to separate any water it might contain. The general process, which appears to me to be the best 445 of carbon and hydrogen , &c. for the preparation of this substance only, is to distil a por- tion of the fluid deposited during the condensation of oil gas, to set aside the product obtained before the temperature rises to 170°, to collect that which comes over by 180°, again separately that which comes over by 190°, and also the por- tion up to 200° or 2100. That before 170° will upon re- distillation yield portions to be added to those of 180° and 190°; and the part obtained from 190° upwards will also, when redistilled, yield quantities boiling over at 180°, 190°, &c. Having then these three portions obtained at 180°, 190°, and 200°, let them be rectified one after the other, and the products between 1750 and 1950 received in three or four parts at successive temperatures. Then proceed with these as before described. It will sometimes happen, when the proportion of bi-car- % buret of hydrogen is small in the liquid, that the rectifications must be many times repeated before the fluids at 185° and 190° will deposit crystals on cooling; that is to say, before sufficient of the permanently fluid part at low temperatures has been removed, to leave a solution so saturated as to crystallize at o°. Bi-carburet of hydrogen appears in common circumstances as a colourless transparent liquid, having an odour resem- bling that of oil gas, and partaking also of that of al- monds. Its specific gravity is nearly 0.85 at 6o°. When cooled to about 32° it crystallizes, becoming solid ; and the portions which are on the sides of the glass exhibit dendritical forms. By having tubes containing thin solid films of it in ice-cold water, and allowing the temperature to rise slowly, its fusing point was found to be very nearly 42° F. ; but when 446 Mr. Faraday on new compounds liquid it may, like water and some saline solutions, be cooled much below that point before any part becomes solid. It contracts very much on congealing, 9 parts in bulk be- coming 8 very nearly ; hence its specific gravity in that state is about 0.956. At o° it appears as a white or transparent substance, brittle, pulverulent, and of the hardness nearly of loaf sugar. It evaporates entirely when exposed to the air. Its boiling point in contact with glass is 1860. The specific gravity of its vapour, corrected to a temperature of 6o°, is nearly 40 Hydrogen being 1; for 2.3 grains became 3.52 cubic inches of vapour at 21 20. Barometer 29.98. Other experiments gave a mean approaching very closely to this result. It does not conduct electricity. This substance is very slightly soluble in water ; very soluble in fixed and volatile oils, in ether, alcohol, &c. ; the alcoholic solution being precipitated by water. It burns with a bright flame and much smoke. When admitted to oxygen gas, so much vapour rises as to make a powerfully detona- ting mixture. When passed through a red hot tube it gra- dually deposits carbon, yielding carburetted hydrogen gas. Chlorine introduced to the substance in a retort exerted but little action until placed in sun-light, when dense fumes were formed, without the evolution of much heat ; and ulti- mately much muriatic acid was produced, and two other substances, one a solid crystalline body, the other a dense thick fluid. It was found by further examination, that neither of these were soluble in water ; that both were soluble in alcohol — the liquid readily, the solid with more difficulty. Both of them appeared to be triple compounds of chlorine, 447 oj carbon and hydrogen , &c. carbon, and hydrogen ; but I reserve the consideration of these, and of other similar compounds, to another oppor- tunity. Iodine appears to exert no action upon the substance in several days in sun-light ; it dissolves in the liquid in small quantity, forming a crimson solution. Potassium heated in the liquid did not lose its brilliancy, or exert any action upon it, at a temperature of 1860. Solution of alkalis, or their carbonates, had no action upon it. Nitric acid acted slowly upon the substance and became red, the fluid remaining colourless. When cooled to 3 2°, the substance became solid and of a fine red colour, which dis- appeared upon fusion. The odour of the substance with the acid was exceedingly like that of almonds, and it is probable that hydrocyanic acid was formed. When washed with water, it appeared to have undergone little or no change. Sulphuric acid added to it over mercury exerted a moderate action upon it, little or no heat was evolved, no blackening took place, no sulphurous acid was formed ; but the acid became of a light yellow colour, and a portion of a clear colourless fluid floated, which appeared to be a product of the action. When separated, it was found to be bright and clear, not affected by water or more sulphuric acid, solidifying at about 34°, and being then white, crystalline, and dendritical. The substance was lighter than water, soluble in alcohol, the solution being precipitated by a small quantity of water, but becoming clear by great excess.* • The action of sulphuric acid on this and the other compounds to be described, is very remakable. It is frequently accompanied with heat ; and large quantities of 448 Mr. Faraday on new compounds With regard to the composition of this substance, my ex- periments tend to prove it a binary compound of carbon and hydrogen, two proportionals of the former element being united to one of the latter. The absence of oxygen is proved by the inaction of potassium, and the results obtained when passed through a red hot tube. The following is a result obtained when it was passed in vapour over heated oxide of copper. 0.776 grains of the substance produced 5.6 cubic inches of carbonic acid gas, at a temperature of 6o°, and pressure 29.98 inches ; and 0.58 grains of water were collected. The 5.6 cubic inches of gas are equivalent to 0.711704 grains of carbon by calculation, and the 0.58 grains of water to 0.064444 of hydrogen. Carbon . . 0.711704 or 11.44 Hydrogen . 0.064444 or 1. These quantities nearly equal in weight the weight of the substance used; and making the hydrogen 1, the carbon is not far removed from 12, or two proportionals. those bodies which have elasticity enough to exist as vapours when alone at common pressures, are absorbed. No sulphurous acid is produced; nor when the acid is diluted, does any separation of the gas, vapour or substance take place, except of a small portion of a peculiar product resulting from the action of the acid on the substances, and dissolved by it. The acid combines directly with carbon and hydrogen ; and I find when united with bases forms a peculiar class of salts, some- what resembling the sulphovinates, but still different from them. I find also that sulphuric acid will condense and combine with olefiant gas, no carbon being sepa- rated, or sulphurous or carbonic acid being formed ; and this absorption has in the course of 18 days amounted to 84.7 volumes of olefiant gas to 1 volume of sul- phuric acid. The acid produced combines with bases, &c. forming peculiar salts, which I have not yet had time, but which it is my intention, to examine, as well as the products formed by the action of sulphuric acid on naphtha, essential oils. See. and even upon starch and lignine, in the production of sugar, gum, & c. where no carbonization takes place, but where similar results seem to occur. 449 of carbon and hydrogen , &c. Four other experiments gave results all approximating to the above. The mean result was 1 hydrogen, 11.5 76 carbon. Now considering that the substance must, according to the manner in which it was prepared, still retain a portion of the body boiling at 1860, but remaining fluid at o , and which substance I find, as will be seen hereafter, to contain less carbon than the crystalline compound, (only about 8.25 to 1 of hydrogen,) it may be admitted, I think, that the con- stant though small deficit of carbon found in the experiments is due to the portion so retained ; and that the crystalline compound would, if pure, yield 12 of carbon for each 1 of hydrogen ; or two proportionals of the former element and one of the latter. 2 Proportionals carbon . ia ) bi.carburet 0f hydrogen. 1 hydrogen 1 ) This result is confirmed by such data as I have been able to obtain by detonating the vapour of the substance with oxygen. Thus in one experiment 1092 mercury grain mea- sures of oxygen at 620 had such quantity of the substance introduced into it as would entirely rise in vapour ; the volume increased to 8505, hence the vapour amounted to 413 parts, or of the mixture nearly. Seven volumes of this mixture were detonated in an eudiometer tube by an electric spark, and diminished in consequence nearly to 6.1 : these acted upon by potash were further diminished to 4, which were pure oxygen. Hence 3 volumes of mixture had been detonated, of which nearly 0.34 was vapour of the sub- stance, and 2 .65 oxygen. The carbonic acid amounted to 2.1 volumes, and must have consumed an equal bulk of oxygen gas ; so that 0.55 remain as the quantity of oxygen which 450 Mr. Faraday on new compounds has combined with the hydrogen to form water, and which with the 0.34 of vapour nearly make the diminution of 0.9. It will be seen at once that the oxygen required for the carbon is four times that for the hydrogen; and that the whole statement is but little different from the following theoretical one, deduced partly from the former experiments. 1 volume of vapour requires 7.5 volumes of oxygen for its combustion ; 6 of the latter combine with carbon to form 6 of carbonic acid, and the 1.5 remaining combine with hydrogen to form water. The hydrogen present therefore in this compound is equivalent to 3 volumes, though con- densed into one volume in union with the carbon ; and of the latter elements there are present six proportionals, or 36 by weight. A volume therefore of the substance in vapour contains Carbon - 6 x 6 = 36 Hydrogen - 1x3=3 39 and its weight or specific gravity will be 39, hydrogen being 1 . Other experiments of oqi same kind gave results according with these. Among the liquid products obtained from the original fluid was one which, procured as before mentioned, by sub- mitting to o° the portion distilling over at 180° or 190°, corresponded with the substance already described, as to boiling points, but differed from it in remaining fluid at low temperatures ; and I was desirous of comparing the two together. I had no means of separating this body from the of carbon and hydrogen , &c. 451 bi-carburet of hydrogen, of which it would of course be a saturated solution at o°. Its boiling point was very constantly 1860. In its general characters of solubility, combustibility, action of potassium, &c. it agreed with the substance already described. Its specific gravity was 0.86 at 6o°. When raised in vapour 1.11 grain of it gavei.573 cubic inches of vapour at 2120, equal to 1.212 cubic inches at 6o°. Hence 100 cubic inches would weigh about 91.6 grains, and its specific gravity would be 43.25 nearly. In another experi- ment, 1.72 grains gave 2.4 cubic inches at 2120, equal to 1.849 cubic inches at 6o° ; from which the weight of 100 cubic inches would be deduced as 93 grains ; and its specific gravity to hydrogen as 44 to 1. Hence probably the reason why, experimentally, the specific gravity of bi-carburet of hydrogen in vapour was found higher, than by theory it would appear to be when pure. Sulphuric acid acted much more powerfully upon this sub- stance than upon the bi-carburet : great heat was evolved, much discolouration occasioned, and a separation took place into a thick black acid, and a yellow lighter liquid, resisting any further action at common temperatures. 0.64 grains of this substance were passed over heated oxide of copper ; 4.51 cubic inches of carbonic acid gas were obtained, and 0.6 grains of water. The carbonic acid and water are equivalent to Carbon - 0.573176, or 8.764 Hydrogen - 0.066666 1. but as the substance must have contained much bi-carburet of hydrogen, it is evident that, if in a pure state, the carbon would fall far short of the above quantity, and the compound MDCCCXXV. 3 N 452 Mr. Faraday on new compounds would approximate of course to a simple carburet of hydrogen containing single proportionals. New carburet of hydrogen. Of the various other products from the condensed liquor, the next most definite to the bi-carburet of hydrogen appears to be that which is most volatile. If a portion of the original liquid be warmed by the hand, or otherwise, and the vapour which passes off be passed through a tube at o°, very little uncondensed vapour will go on to the mercurial trough ; but there will be found after a time a portion of fluid in the tube, distinguished by the following properties. Though a liquid at o°, it upon slight elevation of temperature begins to boil, and before it has attained 32°, is all resolved into vapour or gas, which may be received and preserved over mercury. This gas is very combustible, and burns with a brilliant flame. The specific gravity of the portion I obtained was between 27 and 28, hydrogen being 1 : for 39 cubic inches introduced into an exhausted glass globe were found to in- crease its weight 22.4 grains at 6o° F. bar. 29.94. Hence 100 cubic inches weigh nearly 57.44 grains. When cooled to o° it condensed again, and inclosed in this state in a tube of known capacity, and hermetically sealed up, the bulk of a given weight of the substance at common temperatures was ascertained. This compared with water gave the specific gravity of the liquid as 0.627 at 54°. It is therefore among solids or liquids the lightest body known. This gas or vapour when agitated with water is absorbed in small quantities. Alcohol dissolves it in large quantity ; and a solution is obtained, which, upon the addition of water, 453 of carbon and hydrogen , &c . effervesces, and a considerable quantity of the gas is liberated. The alcoholic solution has a peculiar taste, and is neutral to test papers. Olive oil dissolves about six volumes of the gas. Solution of alkali does not affect it ; nor does muriatic acid. Sulphuric acid condenses the gas in very large quantity ; 1 volume of the acid condensing above 100 volumes of the vapour. Sometimes the condensation is perfect, at other times a small quantity of residual gas is left, which burns with a pale blue flame, and seems to be a product of too rapid action. Great heat is produced during the action ; no sulphurous acid is formed ; the acid is much blackened, has a peculiar odour, and upon dilution generally becomes turbid, but no gas is evolved. A permanent compound of the acid with carbon and hydrogen is produced, and enters as before mentioned into combination with bases. A mixture of 2 volumes of this vapour with 14 volumes of pure oxygen was made, and a portion detonated in an eudio- meter tube. 8.8 volumes of the mixture diminished by the spark to 5.7 volumes, and these by solution of potash to 1.4 volumes, which were oxygen. Hence 7.4 volumes had been consumed, consisting of Vapour of substance - - 1.1 Oxygen - - 6.3 Carbonic acid formed - - 4 .3 Oxygen in carbonic acid - 4.3 Oxygen combining with hydrogen 2.0 Diminution by spark - - 3.1 This is nearly as if 1 volume of the vapour or gas had required 6 volumes of oxygen, had consumed 4 of them in 454 Mr. Faraday on new compounds producing 4 of carbonic acid gas, and had occupied the other 2 by 4 of hydrogen to form water. Upon which view, 4 volumes or proportionals of hydrogen = 4, are combined with 4 proportionals of carbon = 24, to form one volume of the vapour, the specific gravity of which would therefore be 28. Now this is but little removed from the actual specific gravity obtained by the preceding experiments ; and know- ing that this vapour must contain small portions of other substances in solution, there appears no reason to doubt that, if obtained pure, it would be found thus constituted. As the proportions of the elements in this vapour appear to be the same as in olefiant gas, it became interesting to ascertain whether chlorine had the same action upon it as on the latter body. Chlorine and the vapour were therefore mixed in an exhausted retort : rapid combination took place, much heat was evolved, and a liquor produced resembling hydro-chloride of carbon, or the substance obtained by the same process from olefiant gas. It was transparent, colour- less, and heavier than water. It had the same sweet taste, but accompanied by an after aromatic bitterness, very per- sistent. Further, it was composed of nearly equal volumes of the vapour and chlorine : it could not therefore be the same as the hydro-chloride of carbon from olefiant gas, since it contained twice as much carbon and hydrogen. It was therefore treated with excess of chlorine in sun-light : action slowly took place, more chlorine combined with the substance, muriatic acid was formed, and ultimately a fluid tenacious triple compound of chlorine, carbon, and hydrogen was obtained ; but no chloride of carbon. This is a remark- able circumstance, and assists in showing, that though the 455 \ of carbon and hydrogen , &c. elements are the same, and in the same proportions as in olefiant gas, they are in a very different state of combination. The tension of the most volatile part of the condensed oil gas liquid, and indeed of the substance next beneath olefiant gas in elasticity existing in the mixture constituting oil gas, appears to be equal to about 4 atmospheres at the tempera- ture of 6o.° To ascertain this a tube was prepared, like the one delineated in the sketch, Fig. 1, containing a mercurial gauge at a. c. and the extremities being open. It was then cooled to o° from a to b , and in that state made the receiver into which the first product from a portion of the original fluid was distilled. The part at b was then closed by a spirit lamp ; and having raised enough vapour to make it issue at Note. The particular inclination of the parts of the tube one to another was given, that the fluid when required might be returned from a to d without passing on to b. 4 456 Mr. Faraday on new compounds cy that was also closed. The instrument now placed as at Fig. 2, had a and d cooled to o°, whilst the fluid collected in 6 was warmed by the hand or the air ; and when a portion had collected in d sufficient for the purpose, the whole instru- ment was immersed in water at 6o° ; and before the vapour had returned and been all dissolved by the liquid at 6, the pressure upon the gauge within was noted. Sometimes the fluid at d was rectified by warming that part of the tube, and cooling a only, the reabsorption at b being prevented or rather retarded, in consequence of the superior levity of the fluid at d, so that the first portions which returned to b lay upon it in a stratum, and prevented sudden solution in the mass below. This difference in specific gravity was easily seen upon agitation, in consequence of the striag produced during the mixture. Proceeding in this way it was found, as before stated, that the highest elastic power that could be obtained from the substances in the tube, was about 4 atmospheres at 6 o° ; and as there seems no reason to doubt, but that portions of the most volatile substances in oil gas beneath olefiant gas were contained in the fluid, inasmuch as even olefiant gas itself is dissolved by it in small proportions, it may be presumed that there is no substance in oil gas much more volatile than the one requiring a pressure of 4 atmospheres at 6o°, except the well known compounds ; or, in other words, that there is not a series of substances passing upwards from this body to olefiant gas, and possessing every intermediate degree of elasticity, as there seems to be from this body downwards, to compounds requiring 250° or 300° for their ebullition. In reference to these more volatile products, I may state 457 of carbon and hydrogen , &c. that I have frequently observed a substance come over in small quantity, rising with the vapour which boils off' at 50° or 6o°, and crystallizing in spiculae in the receiver at o°. A temperature of 8° or io° causes its fusion and disappearance. It is doubtless a peculiar and definite body, but the quantity is extremely small, or else it is very soluble in the accompa- nying fluids. I have not yet been able to separate it, or examine it minutely. I ventured some time since upon the condensation of vari- ous gases,* to suggest the possibility of forming a vapour lamp, which containing a brilliantly combustible substance, liquid at a pressure of two, three, or four atmospheres at common temperatures, but a vapour at less pressure, should furnish a constant light for a length of time, without requiring high, or involving inconstant, pressure. Such a lamp I have now formed, feeding it with the substance just described ; and though at present it is only a matter of curiosity, and perhaps may continue so, yet there is a possibility that pro- cesses may be devised, by which the substance may be formed in larger quantity, and render an application of this kind practically useful. On the remaining portions of the condensed oil gas liquor. It has been before mentioned, that by repeated distillations various products were obtained, boiling within limits of tem- perature which did not vary much ; and which when distilled were not resolved into other portions, differing far from each other in volatility, as always happened in the earlier distilla- tions. Though conscious that there were mixtures, perhaps * Quarterly Journal of Science, XVI. 240. 458 Mr. Faraday on new compounds of unknown bodies, and certainly in unknown proportions ; yet experiments were made on their composition by passing them over oxide of copper, in hopes of results which might assist in suggesting correct views of their nature. They all appeared to be binary compounds of carbon and hydrogen, and the following table exhibits the proportions obtained : the first column expressing the boiling temperature at which the products were distilled, as before mentioned ; the second the hydrogen, made a constant quantity ; and the third the carbon. 140° - 1 - 7.58 150° - 1 - 8.38 160° - 1 - 7.90 176° - 1 - 8.25 190° - 1 - 8.7 6 200° - 1 - 9.17 210° - 1 - 8.91 220° — 1 — 8.46 These substances generally possess the properties before described, as belonging to the bi-carburet of hydrogen. They all resist the action of alkali, even that which requires a temperature above 250° for its ebullition ; and in that point are strongly distinguished from the oils from which they are produced. Sulphuric acid acts upon them instantly with phenomena already briefly referred to. Dr. Henry, whilst detailing the results of his numerous and exact experiments in papers laid before the Royal Society, mentions in that read February 22, 1821,* the discovery * Philosophical Transactions. 459 of carbon and hydrogen , &c. made by Mr. Dalton, of a vapour in oil gas of greater spe- cific gravity than olefiant gas, requiring much more oxygen for its combustion, but yet condensible by chlorine. Mr. Dalton appears to consider all that was condensible by chlorine as a new and constant compound of carbon and hydrogen ; but Dr. Henry, who had observed that the pro- portion of oxygen required for its combustion varied from 4,5 to 5 volumes, and the quantity of carbonic acid produced, from 2,5 to 3 volumes, was inclined to consider it as a mix- ture of the vapour of a highly volatile oil with the olefiant and other combustible gases ; and he further mentions, that naphtha in contact with hydrogen gas will send up such a vapour ; and that he has been informed, that when oil gas was condensed in Gordon's lamp, it deposited a portion of highly volatile oil. A writer in the Annals of Philosophy, N. S. III. 37, has deduced from Dr. Henry's experiments, that the substance, the existence of which was pointed out by Mr. Dalton, was not a new gas sui generis, “ but a modification of olefiant gas, constituted of the same elements as that fluid, and in the same proportions, with this only difference, that the compound atoms are triple instead of double:" and Dr. Thomson has adopted this opinion in his Principles of Che- mistry. This, I believe, is the first time that two gaseous compounds have been supposed to exist, differing from each each other in nothing but density ; and though the propor- tion of 3 to 2 is not confirmed, yet the more important part of the statement is, by the existence of the compound de- scribed at page 452, which though composed of carbon and mdcccxxv. 3 O 460 Mr. Faraday on new compounds hydrogen in the same proportion as in olefiant gas, is of double the density.* It is evident, that the vapour observed by Mr. Dalton and Dr. Henry must have contained not only this compound, and a portion of the bi-carburet of hydrogen, but also por- tions of the other, as yet apparently indefinite substances ; and there can be no doubt that the quantity of these vapours will vary from the point of full saturation of the gas, when * In reference to the existence of bodies composed of the same elements and in the same proportions, but differing in their qualities, it may be observed, that now we are taught to look for them, they will probably multiply upon us. I had occasion formerly to describe a compound of olefiant gas and iodine (Phil. Trans. CXI. 72), which upon analysis yielded one proportional of iodine, two proportionals of carbon, and two of hydrogen, (Quarterly Journal, XIII. 429). M. Serrulas, by the action of potassium upon an alcoholic solution of iodine, obtained a compound decidedly different from the preceding in its properties ; yet when analysed, it yielded the ^ame elements in the same proportions, (Ann. de Chimie, XX. 245, XXII. 172). Again. MM. Liebig and Gay Lussac, after an elaborate and beautiful investi- gation of the nature of fulminating compounds of silver, mercury, &c. were led to the conclusion that they were salts, containing a new acid, and owed their explo- sive powers to the facility with which the elements of this acid separated from each other. (Annales de Chimie, XXIV. 294, XXV. 285). The acid itself being com- posed of one proportional of oxygen, one of nitrogen, and two of carbon, is equiva- lent to a proportional of oxygen + a proportional of cyanogen, and is therefore considered as a true cyanic acid. But M. Wohler, by deflagrating together a mixture of ferro-prussilate of potash and nitre, has formed a salt, which, ac- cording to his analysis, is a true cyanate of potash. The acid consists of one pro- portion of oxygen, one of nitrogen, and two of carbon. It may be transferred to various other bases, as the earths, the oxides of lead, silver, &c. ; but the salts formed have nothing in common with the similar salts of MM. Liebig and Gay Lussac, except their composition, (Gilbert’s Annalen, LXXI1I. 157. Ann. de Chimie, XXVII. 190]. M. Gay Lussac observes, that if the analysis be cor- rect, the difference can only be accounted for by admitting a different mode of combination. 4*61 of carbon and hydrogen, &c. standing over water and oil, to unknown, but much smaller proportions. It is therefore an object in the analysis of oil and coal gas, to possess means by which their presence and quantity may be ascertained ; and this I find may be done with considerable exactness by the use of sulphuric acid, oil, &c. in consequence of their solvent power over them. Sulphuric acid is in this respect a very excellent agent. It acts upon all these substances instantly, evolving no sul- phurous acid ; and though, when the quantity of substance is considerable as compared with the acid, a body is left unde- composed by, or uncombined with the acid, and volatile, so as constantly to afford a certain portion of vapour ; yet when the original substance is in small quantity, as where it exists in vapour in a given volume of gas, this does not interfere, in consequence of the solubility of the vapour of the new com- pound produced by the action of the acid in the acid itself in small quantities: and I found that when 1 volume of the vapour of any of the products of the oil gas liquor was acted upon, either alone, or mixed with 1, 2, 3, 4, up to 12 volumes of air, oxygen or hydrogen, by from half a volume to a volume of sulphuric acid, it was entirely absorbed and removed. When olefiant gas is present, additional care is required in analytical experiments, in consequence of the gradual combination of the olefiant gas with the sulphuric acid. I found that 1 volume of sulphuric acid in abundance of ole- fiant gas, absorbed about 7 volumes in 24 hours in the dull light of a room ; sun-shine seemed to increase the action a little. When the olefiant gas was diluted with air or hydro- gen, the quantity absorbed in a given time was much dimi- nished ; and in those cases it was hardly appreciable in 462 Mr. Faraday on new compounds two hours : a length of time which appears to be quite suffi- cient for the removal of any of the peculiar vapours from oil or coal gas. My mode of operating was generally in glass tubes over clean mercury,* introducing the gas, vapour or mixture, and then throwing up the sulphuric acid by means of a bent tube with a bulb blown in it, passing the acid through the mer- cury by the force of the mouth. The following results are given as illustrations of the process : Oil gas from a gasometer. in 8' in . 1 hour. 2 hours. diminution. 188 vol. + 9.5 vol. sulphuric acid diminished to 155 H8-5 146.4 22.12 per cent. 107 + 13- 88.5 84.5 82.0 23-33 138 + 5.2 - 113.7 108.0 106.5 22.82 Oil gas from Gordon’s lamp. ls' 3°' 3 hours. 214 + 6.8 - 183.3 180.8 176. 1 7-75 159 + 5.9 - *37*5 136.0 13°-4 17.98 113 + 12.2 1 1 I 1 VO 00 o 96.0 92.0 18.58 Coal gas of poor quality. 548.6 + 27.6 533-3 529.2 529 3-57 273.6 + N 00 1 1 - - - - 267.9 266 266 2.78 190.6 + 13.1 - 186. OO 4- b 184.1 3-41 Oil may also be used in a similar manner for the separa- tion of these vapours. It condenses about 6 volumes of the most elastic vapour at common temperatures, and it dissolves with greater facility the vapour of those liquids requiring higher temperatures for their ebullition. I found that in • If the mercury contain oxidizable metals, the sulphuric acid acts upon it, and evolves sulphurous acid gas. It may be cleaned sufficiently by being left in contact with sulphuric acid for 24 hours, agitating it frequently at intervals. 46 3 of carbon and hydrogen , &c. mixtures made with air or oxygen for detonation, I could readily separate the vapour by means of olive oil ; and when olefiant and other gases were present, its solvent power over them was prevented, by first agitating the oil with olefiant gas or with a portion of the gas to saturate it, and then using it for the removal of the vapours. In the same way some of the more fixed essential oils may be used, as dry oil of turpentine ; and even a portion of the condensed liquor itself, as that part which requires a tempe- rature of 220° or 230° for its ebullition : care being taken to estimate the expansion of the gas by the vapour of the liquid, which may readily be done by a known portion of common air preserved over the liquid as a standard. With reference to the proportions of the different sub- stances in the liquid as obtained by condensation of oil gas, it is extremely difficult to obtain any thing like precise results, in consequence of the immense number of rectifications re- quired to separate the more volatile from the less volatile portions ; but the following table will furnish an approxima- tion. It contains the loss of 100 parts by weight of the original fluid by evaporation in a flask for every io° in ele- vation of temperature, the substance being retained irf a state of ebullition. 100 parts at 580 had lost at 70° parts. 1.1 . differences. 1.9 0 0 00 - 3.0 - 2.2 90° - 52 - - 2-5 ioo° - 7-7 - - 2.4 1 1 o° - - 10.1 - 3.1 Mr. Faraday 120° on new compounds 13.2 2.9 130° - - 16.1 - - 3-2 140° - - 19.3 - - 3.1 150° - - 22.4 - - 3.2 160° - - 25.6 - - 3-4 170° - - 29.0 - - 15.7 l8o° - - 44-7 - - 23.4 1900 - - 68.1 - - 23.4 200° - - 84.2 - - 16.1 210° - - 91-6 - - 7.4 220° - - 95-3 - - 3.7 230° - - 96.6 - - 1-3 The residue 3.4 parts was dissipated before 250° with slight decomposition. The third column expresses the quantity volatilized between each io°, and indicates the existence of what has been described as bi-carburet of hydrogen in con- siderable quantity. - — - t The importance of these vapours in oil gas, as contributing to its very high illuminating powers, will be appreciated, when it is considered that with many of them, and those of the denser kind, it is quite saturated. On distilling a portion of liquid, which had condensed in the pipes leading to an oil gas gas- ometer, and given to me by Mr. Hennel, of the Apothecaries’ Hall, I found it to contain portions of the bi-carburet of hydrogen. It was detected by submitting the small quantity of liquid which distilled over before 190° to a cold of o°, when the substance crystallized from the solution. It is evident therefore, that the gas from which it was deposited must have been saturated with it. On distilling a portion of recent 4 6$ of carbon and hydrogen , coal gas tar, as was expected, none could be detected in it, but the action of sulphuric acid is sufficient to show the ex- istence of some of these bodies in the coal gas itself. With respect to the probable uses of the fluid from com- pressed oil gas, it is evident in the first place, that being thus volatile, it will if introduced into gas which burns with a pale flame, give such quantity of vapour as to make it brightly illuminating ; and even the vapour of those portions which require temperatures of 170° 180° or higher for their ebulli- tion, is so dense as to be fully sufficient for this purpose in small quantities. A taper was burnt out in a jar of common air over water ; a portion of fluid boiling at 190° was thrown up into it, and agitated ; the mixture then burnt from a large aperture with the bright flame and appearance of oil gas, though of course many times the quantity that would have been required of oil gas for the same light was consumed : at the same time there was no mixture of blueness with the flame, whether it were large or small. Mr. Gordon has I understand proposed using it in this manner. The fluid is also an excellent solvent of caoutchouc, sur- passing every other substance in this quality. It has already been applied to this purpose. It will answer all the purposes to which the essential oils are applied as solvents, as in varnishes, &c. and in some cases where volatility is required, when rectified it will far surpass them. It is possible that, at some future time, when we better understand the minute changes which take place during the decomposition of oil, fat, and other substances by heat, and have more command of the process, that this substance, 466 Mr. Faraday on new compounds , &c. among others, may furnish the fuel for a lamp, which re- maining a fluid at the pressure of two or three atmospheres, but becoming a vapour at less pressure, shall possess all the advantages of a gas lamp, without involving the necessity of high pressure. Royal Institution , June 7, 1825, 1 467 n XXL Account of the repetition of M. Arago's experiments on the magnetism manifested by various substances during the act of rotation. By C. Babbage, Esq. F. R. S. and J. F. W. Herschel, Esq. Sec. R . S. Read June 16, 1825. 1. JLhe curious experiments of M. Arago described by M. Gay Lussac during his visit to London in the spring of the present year, in which plates of copper and other sub- stances set in rapid rotation beneath a magnetized needle, caused it to deviate from its direction, and finally dragged it round with them, naturally excited much attention, and the investigation of their various circumstances, and of their con- nexion with the effects observed by Mr. Barlow in Decem- ber, to be produced by the rotation of masses of iron, and described by him in a paper read to the Society,* became an object of considerable interest. Accordingly, having erected at Mr. Babbage’s house, in Devonshire-street, an apparatus for setting a copper plate in rotation about a vertical axis by the aid of a turning lathe, we proceeded to try its effect on a magnetized needle suspended over it. The first attempt failed from the use of too small a needle ; but this being re- placed by a magnetic bar of considerable weight delicately suspended by a silk thread, we had the satisfaction of seeing it deviate several degrees from its point of rest in a direction * See N°. XIV. of the present volume, MDCCCXXV, 3 P 468 Mr. Babbage and Mr. Herschel's account of the corresponding with that of the rotation of the copper plate ; and on employing instead of this bar, a very delicate azimuth compass, belonging to and the invention of Captain Kater, the influence of zinc, brass, and lead was similarly rendered sensible, 2. In this first trial, having neither the command of a very rapid rotation, nor of massive metallic discs, the deviation of the compass observed did not exceed 10 or 11 degrees. In order therefore to enlarge the visible effect, and at the same time disencumber ourselves of the limit set to it by the polarity of the needle, it occurred to us to reverse the expe- riment, and ascertain whether discs of copper or other non- magnetic substances (in the usual acceptation of the word) might not be set in rotation if freely suspended over a re- volving magnet. In order to make this experiment, we mounted a powerful compound horse-shoe magnet, capable of lifting 20 pounds, in such a manner as to receive a rapid rotation about its axis of symmetry placed vertically, the line joining the poles being horizontal and the poles upwards. A circular disc of copper, 6 inches in diameter and 0.05 inch thick, was suspended centrally over it by a silk thread with- out torsion, just capable of supporting it. A sheet of paper properly stretched was interposed, and no sooner was the magnet set in rotation than the copper commenced revolving in the same direction, at first slowly, but with a velocity gra- dually and steadily accelerating. The motion of the magnet being reversed, the velocity of the copper was gradually destroyed ; it rested for an instant, and then immediately commenced revolving in the opposite direction, and so on alternately, as often as we pleased. repetition of Mr. Arago’s experiments on magnetism , &c. 4 69 , 3. The rotation of the copper being performed with great regularity, it was evident that by noting the times of suc- cessive revolutions, we should acquire a precise and delicate measure of the intensity of the force urging it, provided we took care to neutralize the torsion of the suspending thread. To make the experiment strictly comparable proved however a matter of much delicacy, as the slightest change in the distance of the plate from the magnet was found to produce a material alteration in the time of its gyration. 4. Our first enquiry was directed to ascertain the effect of the interposition of different bodies as screens in cutting off or modifying the peculiar rotatory effect. The substances tried were, paper, glass, wood, copper, tin, zinc, lead, bis- muth, antimony, and tinned iron plate. The comparative effects of these may be seen by the following tabulated ob- servations, in making which we had the advantage of Mr. Barlow’s and Mr. Christie’s presence and assistance. TABLE I. No. of revolut. performed. Times of their performance. Nothing Paper Wood Antimony Antimony int. Antimony int. interposed. interposed. interposed. interposed, l. 2d trial. 3d trial. 0 0.0 0.0 0.0 0.0 0.0 0.0 I 34 36.2 37-2 37-o 36.0 35-° 2 48 51.O 52.2 51.0 50.5 50.0 3 59 62.0 63-5 62.0 61.5 61.5 4 68 7 1-5 73-° 72.5 71.O 71.0 5 76.5 80.0 81.5 80.5 79.2 79-7 6 83-5 87.5 89.0 88.0 86.5 87.2 7 90 0 95.0 96.2 95-3 93-7 94.0 8 97.0 10 1. 0 103.0 — 100 0 101.0 9 103-5 107.5 109.8 108.0 106.5 107. s 10 109.0 U3-5 115.5 1 14.0 1 1 2.5 1 *3-7 I T-V. — 470 Mr. Babbage and Mr. Herschei/s account of the TABLE II. No. of rev. performed. Times of their performance. Zinc interposed. Bismuth interposed. Copper interposed. Lead interposed. Tin interposed. 0 0.0 0.0 0.0 0.0 0.0 I 32.O 31.5 32.2 32.0 32.O 2 44-5 44-7 46.0 46.0 45-5 3 64.0 54-3 56.0 56.0 55 2 4 63.0 64.7 64.7 64.0 5 72.0 70.7 72.7 72.6 7^-5 6 79.0 77-5 79 5 80.0 79.0 7 86.0 84.0 86.0 86.0 85.0 8 92.0 89.8 92.0 92.0 91.2 9 97-5 95-5 97-5 98.0 96.5 10 ' 101.6 103.0 103.5 102.2 5. The metallic plates here interposed, as also the wooden ones, were circular discs of 10 inches in diameter and half an inch in thickness, the metals being all cast for the pur- pose, the wooden disc serving for a pattern. Such only are arranged together as were made under such circum- stances as to be strictly comparable. It will be seen by these results that the various substances examined exert no sensible interceptive power, the slight excess of velocity in table 1. col. 1. when nothing was interposed, being evi- dently referable to the eddy caused in the air by the revolv- ing magnet. Glass in like manner had no effect ; but when the substance interposed was iron, the case was widely dif- ferent, the magnetic influence being greatly diminished by one, and almost annihilated by two thicknesses of common tinned iron plate, as the following table will shew. TABLE TIL Revolutions performed. Time occupied. Paper One sheet of tinned Two sheets of tinned interposed. iron interposed. iron interposed. O 0.0 3 0.0 s 0.0 3 X 2 - 89.7 164.7 I 22.5 128.2 — - 1 59-5 — 2 3*-5 1 86.7 — - 2} - 21 1.5 — 3 38.5 234-7 — repetition of M Arago's experiments on magnetism, 47* When the poles of the revolving magnet were connected by a piece of soft iron, the rotation of the copper disc was in like manner almost entirely annihilated. 6. Resuming now the original form of the experiment, the copper disc of 10 inches diameter and ■§• inch thick, was placed on the vertical axis, and made to revolve with a velo- city of 7 turns in a second, a velocity which it was found convenient to give, and easy to maintain, corresponding as it did with one stroke per second of the treadle of the lathe ; and this velocity, unless the contrary is mentioned, is to be understood of all the rotations so communicated, spoken of in the remainder of this account. 7. The copper plate thus revolving, the disc of copper mentioned in Art. 2 was suspended over it ; but though at first it seemed to be very slightly affected, yet on frequent and most careful repetition of the experiment, with every precaution to guard against currents of air, not the most trifling effect could be perceived. This remarkable result, while it stands opposed to any theory of magnetic vortices generated by the rotation of one body, and transferring a part of its motion to others, is, on the other hand, perfectly consonant with, and indeed a necessary consequence of the view which will be taken of the subject in the sequel. 8. In like manner a bar of hardened, but not magnetised steel, was very slightly, if at all, set in rotation by the re- volving copper, not more than probably would correspond to the small degree of magnetism unavoidably developed in it in the act of hardening ; but when magnetised to saturation, it was made to revolve rapidly. This experiment appears decisive as to the origin of the magnetic virtue exhibited by 472 Mr. Babbage and Mr. Herschei/s account of the the copper and other bodies in these experiments. It is ob- viously induced by the action of the magnetic bar, compass needle, &c. on their molecules. 9. Our next enquiry was directed to the degree in which this developement of magnetic virtue takes place in different metals and other bodies. For this purpose two different processes were adopted. The first consisted in securing each of the 10-inch discs already spoken of successively on the vertical axis of our machine (which was now fitted up more firmly). Giving them thus a rotation in their own planes, the azimuth compass above mentioned was placed on a convenient stand centrally over each at the same distance, The deviations observed, and the ratios of their sines to that of the deviation produced by one of them ( copper ) chosen as a standard, were as follows, TABLE IV. Name of the revolving hody. (Motion of the disc direct, or screwing.) (Motion retrograde, or unscrewing.) Mean. Ratio of the force to that of copper. Copper o / II 30 0 / II 17 O t II 24 1 .00 Zinc 10 7 IO IC 10 II 0.90 Tin . - 5 3° 5 12 5 2* 0.47 Lead 2 50 2 55 2 53 0.25 Antimony * 1 12 1 1 7 1 1 6 0. 1 1 Bismuth 0 6 0 6 0 6 0,01 Wood 0 0 0 0 0 0 0.00 The experiment was repeated (some weeks afterwards), placing the compass (by a more advantageous adjustment of the apparatus) much nearer the revolving disc. The results were as follows. repetition of M. Arago's experiments on magnetism , &c. 473 TABLE V. Name of the revolving substanee. Mean of deviations screwing and un- screwing. Ratio of force to that of copper. Copper O / 28 54 I .OO Zinc 26 42 o-93 Tin 12 54 0.46 Lead 7 0 0.25 Antimony - 2 27 0.09 Bismuth - O 32 0.02 Agreeing as nearly as could possibly have been expected with the foregoing. 10. The extension of the same mode of examination to other simple and compound bodies, differing widely in their relations to heat, electricity, gravity, and other chemical and mechanical agents, presents an extensive and most interest- ing field of enquiry, and one which promises a nearer insight into the nature of magnetism, both permanent and transient, than we have yet attained. Our examination has necessarily been limited, partly from the imperfection of our apparatus, but chiefly from want of time ; indeed on reperusing the present notice, it is impossible not to regard it as in many respects imperfect and hasty ; and nothing certainly but the strong interest of the subject, and the uncertainty whether we shall have it in our power to prosecute it with greater assiduity in future, could induce us to present our results in their pre- sent state. Such as they are, however, we shall give them. 11. Of the other metals, silver appears to hold a high rank, and gold a very low one in the scale of magnetic energy. Indeed the latter metal rendered standard by copper was 474 Mr . Babbage and Mr. Herschel's account of the scarcely more powerfully set in rotation than seemed fairly attributable to the quantity of its alloy. 12. The examination of mercury presented peculiar in- terest from its fluidity, and the facility with which iron might be excluded from the experiment ; to make which, a flat ring of box- wood was cemented with wax between two cir- cular glass discs, so as to form a hollow cylinder, 2 inches in internal diameter, and 0.10 in its interior height. This being suspended, empty, by a long delicate silk thread over the horse-shoe magnet, was not in the slightest visible degree affected by its rotation, however long continued. It was then detached and filled with mercury, which, from having been thrice distilled, and afterwards having stood upwards of a twelvemonth in a bottle in contact with a solution of the nitrate of that metal, might assuredly be regarded as abso- lutely free from iron. Being again suspended as before, it now readily, though feebly, obeyed the rotation of the mag- net in either direction, being fully commanded by it, and set in motion, stopped, or reversed in its gyrations at pleasure by merely continuing or changing properly the motion of the magnet. This experiment was witnessed, among others, by our illustrious President, The place which mercury ap- pears to hold in the scale of magnetic energy was judged to be between antimony and bismuth, certainly superior to the latter, and certainly inferior to lead. 13. In wood, glass, wax, rosin, sulphur, sulphuric acid, water, & c. we have not hitherto succeeded in obtaining un- equivocal traces of magnetism. The experiment with unan- nealed glass succeeded no better than with annealed. In the case only of one non-metallic body ( unless a minute portion repetition of M. Arago's experiments on magnetism , &c. 475 of iron present may have deceived us) a decisive result has been obtained ; and, what is very singular, this body is carbon, in that peculiar state in which its density, lustre, degree of hardness, and high conducting quality, both as regards heat and electricity, seem to give it some title to a place among the metals. This is the state in which it is precipitated by a red heat from coal-gas. It is found in thick masses encrust- ing the interior of the retorts, gradually blocking them up, and in time rendering them useless. It is composed of coats frequently curved round a centre, and exhibiting a radiated structure, but oftener in laminae of a fine close grain, a beautiful gray colour, and in some varieties of a shining me- tallic brilliancy, between that of plumbago and hardened steel ; some portions yield readily to the knife, but others of a darker hue and dull earthy fracture, resist obstinately, and give copious sparks with steel. The two sorts are found alternating or intermixed in the same specimen. The mag- netism developed in this singular substance is, however, too feeble to admit of precise measurement, and is only rendered barely sensible by delicate management. 14. The second process alluded to as employed by us to compare the relative magnetic forces of the different bodies examined, consists in suspending magnetised bars over re- volving discs of them, and observing, not the point of equili- brium but the velocity generated, or the time required for the description of certain spaces ; in other words, by measur- ing not the statical, but the dynamical effect. These me- thods, for distinction's sake, may be called he statical and dynamical methods of observation. In the original experiment of M. Arago, a magnetic mdcccxxv. 3 Q 476 Mr. Babbage and Mr. Herschel’s account of the needle was made to deviate or revolve by the rotation of a plate beneath it. The motion of the needle must of course be rendered irregular by the effects of its polarity, and sub- ject to periodical accelerations or retardations ; and it is ob- vious, that in the case of a very weak magnetic force in the plate it can never execute an entire revolution, but must oscillate backwards and forwards till reduced to rest by the friction and resistance of the air. It occurred to us, how- ever, that much more regular and uniform results might be obtained by this means, could the polarity of the needle be destroyed without at the same time destroying its magnetism ; in other words, could the earth's action on it be so precisely neutralised as to allow of its resting indifferently in all direc- tions. The obvious mode of doing this, by the approach of a powerful magnet acting in opposition to the earth, proved much too coarse for our purpose, which however, after a few trials, we found might be accomplished to any required degree of precision by the following simple contrivance. If two exactly equal and similar magnets of equal strength be placed parallel to each other, but in a reverse position, and at such a distance as not mutually to affect each others' mag- netism, and if in this situation they be firmly attached to a piece of wood, glass, &c. the system so formed will have no polarity, i. e. no tendency to rest in one rather than another situation, however suspended. This is clear ; because what- ever be the inclination (£) of one of the magnets to the line of dip, that of the other will necessarily be (180 + Q), and the directive forces being represented by the sines of these two angles will always be equal and opposite, so that each magnet urges the system with equal force, but in opposite repetition oj M. Arago's experiments on magnetism , &c. 477 directions. The truth of this proposition, it is no less evi- dent, is independent of the axis of suspension, which may pass through a part of the system any how situated with re- spect to the magnets, in virtue of the property of a magnet whose force to turn a system of which it makes a part, round a fixed centre, is the same wherever in the system it is placed, and the same as if it were in the centre. Hence it follows, that if two equal and similar magnets be laid parallel to each other, but in a reversed position on a horizontal glass plate freely suspended by a thread, the sys- tem will be devoid of any polar tendency, ( which we shall express by calling such a system neutral ). It is difficult however to procure two magnets exactly equal, and of equal force. But fortunately this is of no consequence, as a slight deviation from perfect neutrality may be corrected by inclin- ing the stronger needle a little more or less to the plane of the plate. In fact the proposition is general ; and by a proper adjustment of the positions of two magnets however unequal, with respect to the axis and to each other, they may be made to neutralize each other. 15. As this adjustment however is nice, and as magnets influence each other, and our object moreover called for the utmost delicacy, we adopted a more refined application of the principle just detailed. A circular glass disc was prepared, 8 inches in diameter, and suspended by three silk threads from a filament of silk, descending along the axis of a copper tube about 5 feet long, passing with stiff friction through collars in the deling of the apartment, and serving nicely by means of an index to regulate the height of the glass disc. 478 Mr. Babbage and Mr. Herschel's account of the At the opposite extremities of two diameters at right angles to each other, four equal small bar magnets were fixed in a vertical position, having alternately their north and south poles downwards. This position promised to present two material advantages ; first, that in neutralizing the system we have not the whole polarity of the magnets to contend with, but only the small remains of directive tendency which arises from the magnetic axis in each not being precisely coincident with its axis of figure, since it is evident that an infinitely thin magnetic cylinder placed perpendicularly to the horizon, would from that cause alone be indifferent as to situation ; sdly, That in this situation their poles interfere with each other's action on the plate revolving below them, less than in any other. Instead of four we might (and as will be seen ) occasionally did place a greater number of magnets round the circle, or within its area, but for the experiments now in view four were enough. 1 6. The system so constructed was found to require no after adjustment, being to all appearance perfectly neutral, so that this part of our purpose was completely accomplished, and the earth's action eliminated from the enquiry. The irregular torsion of the silk thread however still embarrassed us a good deal. But though this undoubtedly caused indi- vidual results to differ more from the mean than we had expected, it is not sufficient to account for a singular ano- maly observed not only in the mean results of a great number of trials, but in all individual cases ; viz. that by this mode of observation, zinc was invariably found to stand above copper in the scale of magnetic action, whereas in the determination by the statical method, where the deviation of repetition of M, Arago's experiments on magnetism , &c. 479 the compass was observed, the former metal was as invaria- bly found to be placed below the latter, the other metals retaining their order. A possible explanation of this anomaly (should future experiments show that the fact depends on no fallacy) may be found in the principles hereafter to be explained, but we wish to be understood as speaking with reserve on this point. 17. The following table is constructed in the same way as Tables I. II. III. with the addition only of the accelerating forces deduced on the supposition of uniform acceleration from the expression TABLE VI. N° of revo- lutions or parts, s — Tj Copper mes of thf Zinc fir perforn Tin nance. F Lead or Antimo. t — Forces Copper f- deduce Zinc / = d from 10000c Tin the exp s >0 — t* Lead / = ression Antim. / = 0.25 0.50 0. 75 1 . 0 38.3 54.2 68.5 79.8 36.1 51.7 63*9 74.o 5«'7 74.8 92.8 107.8 70.9 102.5 128.0 151 .2 109.6 1 57*9 x97*4 232.4 170 1 70 160 *57 192 187 184 x83 93 89 87 86 42 48 46 44 21 20 '9 l9 2. 0 3. 0. 4. 0 5* 0 1 10.6 136.9 1 60.0 180.4 106.2 i3I*4 152.8 172.8 156.8 1 95 * 5 229.5 260.3 221.8 281.3 335-° 385.6 3 5 1 • 7 460.7 164 160 156 *53 l77 *74 1 7 1 167 81 78 76 74 41 38 36 34 16 H Mean of all - - Mean of first six - - 161 179 83 41 — 163 18 The effect of torsion, resistance and friction, is very evident in the apparent diminution of the accelerating force in each revolution, so that only the numbers in the same horizontal lines can be regarded as comparable. Comparing accordingly the means of all for copper, zinc, tin, lead, and of the six first 48 o Mr. Babbage and Mr. Herschei/s account of the for copper and antimony, the proportional intensity of mag netic action for each respectively will be Zinc 1.11 Copper 1.00 Tin 0.51 Lead - 0.25 Antimony - 0.01 The smallness of the number for antimony is here also very remarkable. That for bismuth deduced by this means would be still more minute, so small indeed that the torsion of the thread would not allow of its magnitude being fairly determined, the suspended system merely performing exten- sive oscillations in very long times. 18. This method however requires us to operate on very considerable quantities of the substances under examination? a great disadvantage, as it cannot be applied to the scarcer metals, and does not admit of the use of the common ones in a state of rigorous purity. A method at once more simple and expeditious, and allowing of our acting on small quan- tities of matter, is to suspend portions of the different bodies we would try, similar in form and exactly equal in size, over the revolving magnet, and noting either, dynamically the times of successive revolutions, or, statically the point of equili- brium between the rotatory force and the torsion of the string. This method we pursued in a very interesting part of the enquiry, viz. in investigating (after M. Arago) the effect of a solution of continuity, partial or total in the mass acted on. 19. A disc of lead of 2 inches in diameter and ~ thick, was suspended in a small thin wooden tray at a given distance from the horse-shoe magnet, revolving with the usual velo- repetition of M. Aragos's experiments on magnetism , &c. 481 city, at first entire, and then successively cut with a chisel in radii nearly up to the centre, as here represented. Fig- i. Fig- 2. Fig. 3. Fig. 4. Fig. 5. The times observed and forces deduced in the several cases were as follows : Rev. Disc uncut. Disc cut as in Fig- 1- Disc cut as in Fig. 2. Disc cut as in Fig. 3. Disc cut as in Fig. 4. Disc cut as in Fig. 5. t — /= t zn. /= t zz. / = t — / = t ' /= t zz / = I 28 .2 1258 30.9 1047 33-i 9*3 42.I 564 48.1 432 55.6 324 2 41 .2 1178 44-5 47*4 59.8 69.0 81.4 302 3 50.6 1 172 55.0 59.0 74.7 86.6 io3 °3 281 4 58.7 1 1 6 1 63-9 68.3 88.0 102. 1 124.5 258 5 66.4 1 1 34 72.0 77.2 100.0 1 15.8 145.9 235 Similar effects were observed in other metals, but in dif- ferent degrees. For instance, in the case of soft tinned iron, the same number of cuts, made in the same manner, pro- duced a very slight diminution of force, while in copper the effect of the same operation was to reduce the force in the ratio of 1 to 0.20. 20. A thin disc of copper suspended at a given distance over the revolving magnet, performed 6 revolutions from rest in 54®. 8. It was then cut in 8 places in the direction of radii nearly up to the centre and 45° asunder, by which ope- ration its magnetic virtue was so weakened, that it now required 121s. 3 to execute the same number of revolutions. The cuts were now soldered up with tin , and the magnetic action was now found to be so far restored as to enable it to 48s Mr. Babbage and Mr. Herschei/s account of the perform its six revolutions in 57**3, that is to say, very nearly in the same time as when entire. This is the more remark- able, since tin, as we have seen, is not above half so ener- getic as copper when acting directly. This indirect mode of action therefore affords us a means of magnifying small magnetic susceptibilities which may hereafter prove very valuable. 21. To illustrate this more strongly, we suspended a brass disc of 2in.25 in diameter, and oin.i5 in thickness, as in the last case, and noted the time of its performing successive revolutions, as follows : l rev; 2 rev. 3 rev. 4 rev. 5 rev. 20*. 2 29.1 35.2 40.8 45*7 It was now cut, as in the last case but it being necessary for this purpose to use a saw, the abraded portions, which were pretty copious, were strewed over it with the intervention of a piece of thin paper, to obviate the effect of loss of weight, as nearly as might be. The times were now found increased as follows : 1 rev. 2 rev. 3 rev. 4 rev. 5 rev. 41.1 57*9 7i-o 83.0 93.7 being almost exactly doubled, and of course the force was reduced in the ratio of about 4 to 1 . The cuts were now cleanly soldered with bismuth ; and though, as we have seen, the direct force of bismuth is so small as to be scarce perceptible, yet its indirect effect in restoring the magnetism of the brass was such as to cause the same arcs to be described in the following numbers of seconds, repetition of M. Arago's experiments on magnetism , &c. 483 1 rev. 2 rev. 3 rev. 4 rev. 5 rev. 28.2 39.7 48.4 56.3 63.0 which require the exertion of an accelerating force more than double of that developed in the last trial. The bismuth was now melted out, and the cuts being carefully washed with melted tin, were filled with fresh tin, which was allowed to fix, and the disc being trimmed, and replaced, the times were now found to be 21.7 30.8 38.0 43-5 48.7 The restoration of energy, as in the case of the copper disc is here very manifest, the times of rotation being nearly reduced to their original magnitude. The comparison of these, reduced by the formula/ = 1000000 ~ , and the means of the five results taken in each case, gives for the accele- rating forces Brass, uncut - 1.00 cut - 0.24 soldered with bismuth 0.53 soldered with tin - 0.88 The effects of soldering with lead and with fusible metal were also tried, and found to be both represented on the same scale by the same fraction, viz. 0.85, being but very little inferior to tin. 22. When the soldering is imperfect, the effect in restoring the magnetic action is proportionally weaker, but the influence of ever so small a free metallic communication is sensible. 23. A disc of lead cut in 8 radii as above was found to make one revolution in 58 *.3. It was then wetted so as to fill the cuts with sulphuric acid, and the time of revolution was found to be 57.3 ; so that the influence of sulphuric acid, 3 R Copper uncut - 1.00 cut - - 0.20 soldered with tin 0.91 MDCCCXXV. 484 Mr. Babbage and Mr. Herschei/s account of the even when thus magnified, is still equivocal ; and its mag- netism, if it exist, can hardly be estimated at a thousandth part of that of copper, and is probably still lower. 24. The reduction of the metals to filings or to powder, was found to produce a still more striking diminution of their magnetic energy ; and a class of experiments of great in- terest, as to the effect of the agglutination of these powders by metallic and non-metallic cements and liquids, immediately presents itself, into which want of leisure only has hitherto prevented our entering, as well as on the important subject of the magnetism of metallic alloys and atomic combinations, with which this branch of the enquiry is essentially connected. 25. When we come to reason on the above facts, much caution is doubtless necessary to avoid over-hasty generali- zation. Whoever has considered the progress of our know- ledge respecting the magnetic virtue, which, first supposed to belong only to iron and its compounds, was at length reluc- tantly conceded to nickel and cobalt, though in a much weaker degree — then suspected to belong to titanium, and now extended, apparently with an extraordinary range of degrees of intensity to all the metals — will hardly be inclined to stop short here, but will readily admit, at least the proba- bility, of all bodies in nature participating in it more or less. Yet if the electro-dynamical theory of magnetism be well founded, it is difficult to conceive how that internal circula- tion of electricity, which has been regarded as necessary for the production of magnetism, can be excited or maintained in non-conducting bodies. Without pretending to draw a line however, in what is perhaps at last only a question of degree, one thing is certain, that all the unequivocal cases of mag- repetition of M. Arago’s experiments on magnetism , &c. 485 netic action observed by us, lie among the best conductors of electricity.* Another feature, no less striking, is the extreme feebleness of this species of action compared with that which takes place in cases of sensible attraction and polarity. This will appear more evidently, if we consider the mode of action which probably obtains in these experiments, and the me- chanism, if we may so express it, by which the effects of such almost infinitesimal forces are rendered perceptible in them. 26. The rationale of these phenomena, as well as of those observed by Mr. Barlow in the rotation of iron, which form only a particular case (though certainly the most prominent of any) of the class in question, seems to depend on a principle which, whether it has or has not been before entertained or distinctly stated in words, it may be as well, once for all, to assume here as a postulatum, viz. that in the induction of mag- netism, time enters as an essential element , and that no f?iite degree of magnetic polarity can be coinmunicated to , or taken from any body whatever susceptible of magnetism , in an instant, f * The meagre statements and imperfect reports which have hitherto reached us of M. Arago’s researches, had prepared us to expect a much more appreciable amount of magnetic force in non-metallic bodies than we have observed. Glass, wood, water, ice, and indeed every description of substance, have been included in the list of bodies capable of producing a notable deviation from the magnetic meri • dian in a suspended bar, by their rotation. This naturally renders us desirous of seeing that eminent philosopher’s own account of the means employed by him to render sensible such very minute forces, which must have been unusually delicate. This may perhaps be the proper place to mention, that the numerical estimates in this paper are merely intended to be received as gross approximations, valuable only in the absence of all other information of the kind. The metals used were those of commerce, no pains having been taken to free them from iron. Much refinement would have been thrown away on such materials. f It is now some years since one of the authors of this account (Mr. Babbage) 486 Mr. Babbage and Mr. Herschel's account of the 27. This principle will, if we mistake not, be found to afford at least a plausible explanation of most, if not all the phenomena above described, without the necessity of calling in any additional hypothesis, or new doctrine in magnetism. For the other principle we shall have occasion to employ, that magnetic bodies differ exceedingly, both in susceptibility of this quality and in the degree of the pertinacity with which they retain it (which may be called their retentive power), is not an hypothesis, but an acknowledged fact. It is only in the mode of its extension to new cases of magnetics that we can be led into any fallacies. Whether these two qualities (susceptibility and retentive power) be, or be not mutually dependent, this is not the place to enquire. Probably they are not so, at least directly : and the new facts almost con- vert this probability into certainty ; at all events, at present we shall for greater generality suppose them independent. observed the following facts, which set the principle stated in the text in a very clear light. A natural magnet, armed with soft iron, terminating in a cylindrical surface, was made to support a load hooked on to another piece of soft iron, termi- nating also in a cylindrical surface, so that its contact with the former was limited to a physical line. The weight it would usually support varied from 27 to 33 lbs., according to the caution used in increasing the load. On loading it with 30 lbs. it became necessary to add the remaining weight by degrees, a quarter of a pound at a time, and to wait a short time after each addition. At about 32^ lbs. the weights usually fell from the magnet, and it was observed on replacing them, that it would no longer support more than 30, and that some minutes must be suffered to elapse before it could be brought to its former load. It was thus evident that the magnet required time for the developement of its full virtue. Again, having loaded the magnet by degrees up to 32 lbs., if the contact was broken for an instant by seuing the iron to which the load was suspended with both hands, detaching it suddenly and instantly restoring it, the magnet now continued to suspend 32 lbs., though, had the separation been of longer duration, 30 only would have been suspended. Time therefore is required to lose, as well as to gain magnetism. repetition of M. Arago's experiments on magnetism , &c. 487 28. Conceive now a plate of any thickness, and of indefinite superficial extent, of a metal or other magnetic, whose retentive power is very small. If either pole (suppose the north) of a magnet be brought vertically over a point in its surface, it will there produce a pole of the contrary name in the plate, the maximum of polarity being immediately under the magnet. Now let the magnet be moved horizontally along the surface, preserving the same distance from it. The points over which in succession it becomes vertical, not instantly receiving all the magnetism of which they are susceptible, will not have reached their maximum of polarity at the pre- cise moment of nearest appulse, but will continue to receive fresh accessions during the whole of that certain small por- tion of time when the distance (being at or near its minimum) undergoes no change, or only a certain very minute one. In like manner, the points which have attained their maximum of polarity, being left behind by the magnet, will by degrees lose their magnetism ; but the loss not being sudden, they will continue near their maximum for a certain finite time, during the whole of which the magnet continues receding from them, and leaving them farther and farther behind. Thus from both causes, there will be always in arrear of the magnet a space both more extensive and more strongly impregnated with the opposite polarity, than in advance of it ; and as the magnet moves forward, the point of actual maximum (or the pole ) of the plate, instead of keeping pace with it and being always precisely under it, will lag behind. There will thus arise an oblique action between the pole of the magnet and the opposite pole of the plate so lagging behind it ; and were the plate free to move in its own plane, the resolved portion 488 Mr. Babbage and Mr. Herschel's account of the of this action parallel to its surface, would continually urge it in the direction of the magnet's motion. 29. But besides the attracting pole of the opposite name (south) produced by the (north) pole of the magnet at the spot immediately under it, there will also be developed a corresponding repulsion or north polarity in the plate. This however will not, like the attractive, be concentrated nearly in one spot immediately below the magnet, but must of necessity be diffused round it in a much less intense and more uniform state throughout the more distant parts of the mass, and may be conceived as arranged in spherical or other concave strata about the point vertically under the magnet as a centre. Now when the magnet by its motion is carried out of the axis of these strata, it is obvious that the resultant force of each of them will be less and less oblique to the surface as its radius is greater. The general resultant therefore of all the repulsive forces exerted throughout the whole extent of the plate is necessarily less oblique to the surface than that of the attractive ones, whose influence, from this cause alone, must therefore preponderate, and must necessarily produce a dragging or oblique action, such as above described. This force, however minute, acting con- stantly, must at length produce a finite and sensible velocity, provided the whole mass of the plate to be set in motion be finite, and the force of the magnet sufficient to overcome friction, resistance, &c. go. Vice versa, if the plate be drawn along in its own plane, and the magnet be free to move in a horizontal direc- tion, the former ought to drag the latter along in the same repetition of M. Arago's experiments on magnetism , &c. 489 direction with a velocity continually accelerating, till they move on together with equal velocities. 31. It is manifest that, casteris paribus, the greater the relative velocity, the more will the pole developed in the plate lag behind the magnet, or the magnet (in the reverse case) behind the pole. The more oblique therefore will be the action, and the greater the resolved part of the force, and the velocity produced by it dato tempore. The same effect must also be produced by an increase in the absolute force, or lifting power of the magnet ; so that in such expe- riments there is an advantage in using large magnets which have great lifting powers, over small ones with intense directive forces, and this is perfectly consonant to experience* 3 2. Hitherto we have only considered the case of rectili- near motion. If we regard the magnetism of the plate as very transient, and the velocity moderate, the whole space occupied by the magnetised portion of the plate will still be small, and confined to the immediate neighbourhood of the point vertically under the magnet. If the motion of the latter change its direction, the momentary pull communi- cated to the plate will always be in the direction of a tangent to the curve described. If therefore it describe a circle, it will tend at every instant to impress a gyratory motion on the plate about a centre vertically under the centre of its own motion, and vice versa, if the plate be made to revolve about a centre, it will tend to drag the magnet round with a conti- nually accelerated motion, provided its rectilinear recess from the centre of motion (or its centrifugal force) be prevented by a proper mechanism. The former is the case of a disc of copper suspended by its centre, and set in rotation by a 490 Mr. Babbage and Mr. Herschel's account of the magnet revolving beneath it. The latter is that of a com- pass needle, or of our neutralised system of vertical magnets suspended over a revolving disc of copper. A very pretty illustration of the direction of these forces is obtained by suspending a circular disc of zinc or copper from the end of a counterbalanced arm, which is itself suspended by its middle, thus constituting a kind of double balance of torsion. If the length of the arm be so adjusted, that the circumfer- ence of the disc shall be an exterior tangent to the circle de- scribed by the poles of a revolving magnet, the whole disc will be swept round in an orbit concentric with the motion of the magnet, while it at the same time acquires a rotatory motion on its own centre in the contrary sense. The centri- fugal force is here overcome by the arm and the weight of the disc, and the velocity goes on accelerating till the increase of resistance puts a stop to further accessions. 33. In Mr. Barlow's experiments, the earth is our induc- ing magnet ; its two poles both act on every particle of the revolving shell employed in that gentleman's experiments, and their action when complete produces two poles, a north and a south, at opposite extremities of the diameter parallel to the dip. This is the case when the shell is at rest. Let it now be set in motion about any axis, anyhow inclined to the dip. If the communication and loss of magnetism were instantaneous, the places of the poles (i. e. the points of maximum polarity ) would be unaffected by the rotation ; but as that is not the case, these points, in virtue of the principles already stated, will shift their places, and decline from the direction of the dip in the same direction as the shell's mo- tion, that is to say, in the direction of a tangent to a small repetition of M. Arago's experiments on magnetism , &c. 491 circle, whose axis is the axis of rotation, and whose circum- ference passes through the extremities of the diameter parallel to the dip. The extent of this declination will depend on the velocity of rotation and the diameter of this small circle, and will be proportional to both, that is, to the velocity of rotation multiplied into the sine of the angle made by the axis of rota- tion with the direction of the dip. It will therefore be a maxi- mum when the axis of rotation is perpendicular to the magnetic meridian, and vanish when the shell is made to revolve on an axis parallel to the line of dip. These consequences are perfectly consonant to the results obtained by Mr. Barlow in his paper ; and in fact, the general result announced by him in (page 326 of this volume) comes to the very same thing as above stated ; for it is obvious, that the new axis of polar- ization there spoken of, acting in combination with the origi- nal, or, as we may call it, the primary axis developed in the quiescent state of the shell, will exert a compound force on the needle, such as would be exerted by a single equivalent axis situated intermediately between them, but much nearer to the more intense than to the more feeble one. The position of this equivalent axis will necessarily be in the great circle passing through the two component ones. Now the small circle described by the point which was first the pole of the stronger or primary axis about the axis of rotation is a tan- gent to this great circle, and the equivalent axis (being but little removed from the primary one, by reason of the small intensity of the other), will therefore have its pole situate indifferently in either circle. Or conversely, the single axis produced in our view of the subject being resolved into two ; one of which is that corresponding to the quiescent state of mdcccxxv. 3 S 492 Mr. Babbage and Mr. Herschel's account of the the shell, and the other 90° removed from it in the same place, this latter will be identical with Mr. Barlow's secon- dary axis. 34. In what has been said, the velocity of rotation has been supposed commensurate to the velocity with which magnetism is propagated through the iron of the shell. But if we conceive in this, or in the general case, either the re- tentive power of the shell, disc, or lamina great, or the velo- city of motion excessive, it may be instructive to consider the modifications thus introduced into the effect. It is evident that the induced pole will lag farther and farther behind the magnet in proportion as either of these conditions obtains. In the case of rectilinear motion, this will, up to a certain point, increase the oblique action, and the dragging effect will be strengthened ; but if the velocity be excessive, or the reten- tive force considerable, as in steel, the pole may lag so far behind as to carry it altogether out of the sphere of the mag- net's attraction; and the magnetised portion, remaining Within its limits, may have not had time enough to acquire a high degree of polarity. From both causes the drag (the expression, though uncouth, is convenient) should be weak- ened. In the case of circular motion this effect may go so far, that a complete circumference shall have been described before the polarity of any one point shall have been either completely induced, or completely destroyed. I11 this case the effect observed will be a general weakening of the total polarity of the disc or sphere ; and (supposing the latter of iron, or soft steel) a directive virtue on a small compass needle placed near it, not probably towards any particular place, but to a resultant imaginary point depending on the repetitim of M. Arago's experiments on magnetism , &c. 493 situation of the compass, the dip, and the axis of rotation, by laws not very easy to assign. This will explain some ex- pressions quoted by Mr. Barlow from his correspondence with one of the authors of this paper, which may appear otherwise to militate against the general view here taken. 35. This diminution of the total effect by a more general distribution of the magnetism, was imitated by sticking a great number of needles vertically through a light cork circle, all being strongly magnetised, and having their north poles downwards, so as to form a circle, or, as it were, a coronet of magnets. This apparatus suspended centrally over a re- volving copper disc, was not sensibly set in rotation. In this case, when at rest, the south polarity induced in the plate would be disposed in spots accumulated under each needle ; but these spots, elongated and blended by the effect of rota- tion, must produce a nearly uniform circle of south polarity, whose equal and contrary actions on all the needles would keep up the equilibrium, and prevent the coronet from ac- quiring a tendency either way. 36. One consequence of this reasoning, which deserves trial, is this — that if the axis of rotation of an iron shell be situated in the direction of the dip, the spots occupied by its poles will not change their places by rotation, and conse- quently no deviation of the compass ought to take place from that cause. The experiment however is very delicate ; and care must be taken to remove any magnetised bodies whose influence might induce subordinate poles in the shell, whose places would shift by rotation. The compass therefore in this case cannot be neutralized by a magnet ;* but we must * In Mr. Barlow’s experiments, the large and powerful bar magnets used to 494 Mr. Babbage and Mr. Herschei/s account of the have recourse to some neutral system, such as that described in the foregoing pages, in its place, or it may be left unneu- tralized. It ought too to be so small, or so remote, as not to produce induced polarity in the shell, which would react on itself when the sphere is set in motion, and destroy the suc- cess of the experiment. 37. The effect of a solution of continuity in the revolving bodies comes next to be considered. It is difficult ; but the difficulty is not a consequence of our principles of explana- tion, but of our ignorance of the very complicated laws which regulate the distribution and communication of mag- netism in bodies of irregular figure. So far however as the operation of the general principle can be traced, its results are consonant to observation. 38. In the first place, it is obvious that where one or more slits are cut in a metallic plate, over which the pole of a magnet is revolving, that immediate and free communication between particle and particle, on which probably the rapid, and certainly the intense developement of magnetism depends, is destroyed. The induced pole (by which we mean now the whole of that space in which sensible magnetism is deve- loped, and which is, of course, a spot of sensible, and proba- bly considerable magnitude — of a figure more or less elon- gated according to the velocity of the motion) — instead of travelling regularly round, retaining a constant magnetism and force, will now be in a perpetual state of change. Instead of being carried uniformly across the slit, it will die away in intensity, and shrink into a point in dimension on the hinder neutralize the earth’s action on the compass needle, cannot be without some dis- turbing influence of this kind. repetition of M. Arago's experiments on magnetism , &c\ 4 95 side, and be again renewed on the side in advance, but at first not in its full intensity ; so that it is not merely the diminution of surface arising from the abstraction of a part of the metal, but a much more considerable defalcation of mag- netic force which takes place on either side of the slit, that operates. Now this operation is always to weaken the drag between the magnet and the disc, and no reason, a priori, can be assigned why this effect should not take place to any extent. 39 The validity of this reasoning is shown by taking the extreme case in which the substance acted on is in the state of powder. Each particle of this becomes necessarily a feeble magnet, and its north and south poles, being at the same distance (almost precisely) from the pole of the magnet, counteract each other’s action. The extreme feebleness of their magnetism prevents the particles from affecting each other by induction across the intervals which separate them ; so that each acts as an individual, and destroys in great measure its own effect. The moment however a metallic , i. e. a magnetic contact is established between them, their mutual induction acts, and the result is a general develope- ment of one polarity in the region adjacent to the magnet ; and of the other, feebler and more diffused, in the parts of the mass remote from it. This is probably the rationale of the restoration of virtue which takes place when a cut disc is soldered up. And it is not difficult to conceive that a weak magnetism may be thus very faithfully transmitted through substances, such as bismuth and lead, whose direct action is very small, because, as we have seen, the intensity of their direct action depends, for one of its causes, on the retentive 49 6 Mr. Babbage a nd Mr. Herschei/s account , &c, power of the substance, which is out of question in the indi- rect mode of action here considered. In fact, if the retentive power of the solder were reduced to nothing, i. e. if it gained and lost magnetism instantaneously, it would still act as a conductor, and probably the better for this quality ; so that the communication between opposite sides of a slit, or conti- guous portions of two adjacent particles of a powder, would still be kept up by it, provided it were susceptible of mag- netism at alb The observed and very striking fact then of the powerful action of bismuth as a conductor, while its ac- tion as a magnet is so extremely feeble, is in itself a strong argument for the independence of these two qualities, which we have designated by the expressions— susceptibility, and retentive power , and may possibly be made the foundation of a mode of distinguishing and measuring their degrees in different substances, C, B? J, F. W, H, C 497 3 XXII. On the magnetism developed in copper and other substances during rotation. In a Letter from Samuel Hunter Christie, Esq. M. A. &c. to J, F. W. Herschel, Esq. Sec. R. S. Com • municated by J. F. W. Herschel, Esq. Read June 1 6, 1825. Dear Sir, A s you inform me that you are drawing up an account of your magnetical experiments, I send you a brief account of those which I have made : they may possibly bear upon some of the points which you have had under consideration ; and in this case you will not be displeased at being able to compare independent results. After having made experiments with a thin copper disk suspended over a horse-shoe magnet, similar to those which I witnessed at Mr. Babbage’s, I made the following. A disk of drawing paper was suspended by the finest brass wire (No. 37) over the horse-shoe magnet, with a paper screen between. A rapid rotation of the magnet (20 to 30 times per second) caused no rotation in the paper, but it occasion- ally dipped on the sides, as if attracted by the screen, which might be the effect of electricity excited in the screen by the friction of the air beneath it. A disk of glass was similarly suspended over the magnet : no effect produced by the rotation. A disk of mica was similarly suspended : no effect. The horse-shoe magnet was replaced by two bar magnets, each 7.5 inches long, and weighing 3 oz. 16 dwt. each, placed 49$ Mr. Christie on the magnetism developed in horizontally parallel to each other, and having their poles of the same name contiguous. These produced quick rotation in a heavy disk of copper 6 inches in diameter, and suspended by a wire, No. 20. A bar magnet 4 inches long, and having both its ends south poles, was made to revolve rapidly under a copper disk. The disk revolved in the same direction as the magnets. The two bar magnets before mentioned were adjusted to the axis of rotation, so that their upper ends were at the distance of 5 inches from each other, and their lower ends 1.8 inch apart. They were first made to revolve rapidly under the copper disk with poles of the same name nearest to the disk, and then with poles of a contrary name : the times in which the several rotations of the disk took place were as nearly as possible the same in the two cases. No. of Revolutions. Poles of the same name nearest to the disk. Poles of a contrary name nearest to the disk. Screw.* Unscrew.* Screw. Unscrew. Time. Time. Time. Time. I 15 sec. 15 sec. i 5 sec. 15.4 2 21 21 21 21.5 3 26 26 26 26.3 4 3° 30 3° 3°.° In the first three, I could only remark the time to the nearest second, having no assistance. Should the times agree precisely, which I have very little doubt they would be found to do, the result would, I think, be singular. It would * These expressions refer to the direction with respect to the spectator in which the rotation was performed. 499 copper and other substances during rotation , show that the magnetism in the disk is instantaneously deve- loped by one pole of the magnet, and as instantaneously de- stroyed, and a contrary magnetism developed by the contrary pole ; or rather it would indicate, that the time during which the disk retained the induced magnetism was less than the time of half a revolution of the magnet. The same two bar magnets were laid horizontally by the side of each other, ^ inch a part. They were first made to revolve rapidly under the disk with their poles of the same name adjacent, and then with those of a contrary name adjacent. No. of revolutions. Poles of the same name adjacent. Poles of a contrary name adjacent. Screw. Unscrew. Screw. Unscrew. Time. Time. Time. Time. m. s. m. s. m. s. m. s. I 2 9 28 31 32 2 40 57 42 46 3 48 46 52 58 4 56 53 1 01 I 07 5 1 03 1 00 1 1 1 1 15 6 1 10 1 06 1 18 I 23 7 1 16 1 12 1 25 1 30 8 1 21 1 17 1 31 I 36 9 1 26 1 22 1 37 1 43 IO 1 3i 1 27 1 43 1 49 From these it appears that the effect was but little dimi- nished by placing poles of a contrary name so close to each other. The adjacent poles being of the same name, they were connected by a piece of soft iron ± inch thick, and ~ inch wide. After revolutions of the disk (screw), the torsion of the wire was equal to the force of the magnets, and the mdcccxxv. 3 T 500 Mr. Christie on the magnetism developed in same was the case at 4^ revolutions (unscrew). So that although the effects- were greatly diminished by connecting the poles, they were by no means destroyed. The magnets were now placed over each other, first with poles of a contrary name, and then with those of the same name contiguous. No. of revolutions. Poles of a contrary name contiguous. No. of revolutions. Poles of the same name contiguous. Screw. Unscrew. Serew. Unscrew. Time. Time. Time. Time. 1 2 2A At 2-j^- (sc torsion of the of the magnet m. s. I 48 3 20 3 5° rew) and 2^ wire was eq s. m. s. 1 32 2 40 /Rev. \ ( +5 (unscrew) the ual to the force 1 2 3 4 5 6 s. 21 3° 36 42 47 5* s. 21 29 34 39 44 48 So that although the upper magnet was nearer to the disk, by its own thickness, than in the 4th experiment, the effect when poles of contrary name contiguous was not half what it was when they were connected by the iron. A thick copper plate 8 inches in diameter and 1 inch thick, was placed on the axis of rapid rotation, its plane horizontal. A thin copper disk 4 inches diameter, and weighing 23.5 dwts. was very delicately suspended over it by a fine brass wire (No. 37), with a paper screen between the plate and the disk. The distance between the surfaces of the plate and disk -/q inch. The plate being put in rapid rotation, no sen- sible effect was produced on the disk. A bar magnet was placed on the screen under the disk : still no effect produced by the rotation. 501 copper and other substances during rotation. A light needle, weight 42.5 grains, 6 inches long, on a pivot in a compass box, being placed over the plate, the rota- tion caused a deviation of 20° ; but when a heavy needle, weighing 197 grains, and of the same length, was similarly placed over the plate, it immediately revolved rapidly with the plate. A bar magnet, weighing 3 oz. 15 dwts. 19 grs. suspended by a wire, No. 20, revolved rapidly with the plate. A horse-shoe magnet, weighing nearly a pound, and sus- pended by the same wire, revolved with the disk. The following experiments were made with the view of ascertaining whether the effects increased nearly according to any power of the decrease of the distance. A strong needle, 6 inches in length, weighing 197 grains, and vibrating 22 times in a minute, delicately suspended on an agate within a rim accurately graduated, was placed with its centre exactly over that of the copper plate, and being ac- curately adjusted, so that the distance between the centre of the copper and that of the needle was such as I required for the observation, the copper was made to revolve rapidly (always as nearly as possible 12 times per second), and when the needle became stationary, the direction of its south end (being that most convenient for observation) was noted. This was done with the copper revolving in both directions, “ screw” and “ unscrew.” The direction of the south end of the needle was also observed before the rotation. 502 Mr. Christie on the magnetism developed in Distance. 4.0 in. 3.5 in. 3.0 in. 2.5 in. 2.0 in. Screw - - 0 , 1 46W 0 / 3 20W 6 20 W 0 / 14 30W 0 / 29 40W 7 Directionofsouth Unscrew - 1 32 E 3 °8 E 6 00 E 1 3 5° E 29 00 Ej end of the needle. Mean - - 1 39 3 M 6 10 14 10 29 20 On diminishing the distance to 1.5 inch, the needle re- volved with the plate, and very shortly so rapidly, that it had the appearance of an entire circle. After this I replaced the needle by others which were lighter, letting every thing else remain the same, that is, the distance still 1.5 inch. Needle weighing 42.5 grs. Needle weighing 25.5 grs. Screw - - Unscrew - 0 / 24 40W 25 20 E 0 / IO 30W 10 40 E (I should mention that the needles were not at all neutralized). From the latter observations, it is evident that the effect produced depends upon the intensity of the magnetism in the needle employed ; and this I think proves clearly that the effect arises from the magnetism induced in the copper from the needle itself. If we suppose the tang, of the deviation to vary as then 0 and being two deviations at the distances d and d' , we shall have n = tan. S' -log. log. a — log. a. Computing n from this, by a comparison of every two observations we have the following values of n ; copper and other substances during rotation . 50S 5 *°4' 4.60 4.62 4.29 4.20 4*45 4. 10 4.65 4 -°7 3-59 Mean 4.361 X » 3 o Xi £ QJ O , 03 u co B o If we suppose that the poles of the needle are urged by forces in the direction of the motion of the copper, which being constant in the copper, would affect the needle recipro- cally as the square of the distance ; then these forces in the copper being derived from the needle itself, we must suppose that their intensity will vary also reciprocally as the square of the distance : so that the force on the needle arising from this mutual action, would vary reciprocally as the fourth power of the distance. Taking the mean between the mean values of 11 above, when the distance is measured from the centre of the copper and from its surface, would give the value of n for an intermediate point 3.983, which is as near to 4, supposing that such ought to be the value, as we could expect the observations to give. The next experiments which I made were with the view of determining the law of force as regards the distance, when magnets act upon a copper disk. For this purpose I made use of the suspending wire as a balance of torsion. The re- sults which I have obtained in this manner give a much less rapid diminution of the force, as the distance increases, than appears to take place when a thick copper plate acts upon a small magnet, as in the former experiments, which agrees with what you have mentioned as following from your Mr, Christie on the magnetism developed in results. The results obtained in the former case appear to indicate, that every particle in the copper urges the needle from the magnetic meridian with a force varying as ^dfstance)^’ which law would arise from the magnetism in the needle developing the magnetism in the particles of copper, so that its intensity would vary as and this magnetism again acting on the poles of the needle with a force varying as . Supposing this to be the case, if z is the distance of a lamina of copper from the plane of the needle, s the arc of a circle in this lamina at the distance r from the axis of rotation, R the radius of the copper cylinder, t its thickness, c the distance of its upper surface from the needle, and a the distance of the pole of the needle from its centre : then the whole force with which the cylinder urges the needle will be proportional to Although this may be integrable, the integral would be in so complicated a form, that it would be very ill suited for comparison with the results obtained from observation ; but if we consider only the annulus of the copper immediately under the pole of the needle, which will be the most efficient part, we may readily make this comparison. For calling Q the deviation, we should have sin. G = /— x const, or sin. G = (£• — jrhf) * const S and consequently T C7 = const. (c + 0» 605 copper and other substances during rotation. From my experiments t being 1, I should obtain the fol T • "I n sin. G lowing values of — c * (c + 03 C G O / 3-5 1 39 3-o 3 *4 2.5 6 10 2.0 14 10 1.5 29 20 Although there is a considerable difference in the num- bers, especially the last, yet as the parts whose action is not considered have here the greatest effect, and all the observa- tions are liable to errors arising from the difficulty of making the copper revolve with the same velocity in all cases, I think the agreement is sufficiently near to indicate that the copper acts as I have supposed. A thick copper ring would be best adapted for obtaining results for comparison ; and when I have leisure I propose making use of one. For the purpose of determining the law according to which magnets act upon a copper disk at different distances, I sus- pended, successively, two copper disks over the bar magnets placed horizontally by the side of each other, with their poles of the same name adjacent. The magnets were made to re- volve until the torsion of the wire caused the disk to return in the contrary direction, when I considered that the force of torsion would be double the force with which the magnets urged the disk. The time in which this took place was noted, and also the degree of torsion. After this the magnets were made to revolve again with the same velocity, and the sin. G (c + ty 2.3316' 2.6341 2.6409 V-Mean 2.505 2.8144 J 2 . 1 040 J 506 Mr. Christie on the magnetism developed in torsion noted where the disk remained stationary by the action of the opposite forces of torsion and of the magnets. This was done at several distances ; and those distances, be- tween the magnets and the disk ascertained very accurately. In the observations with the disk which I have named A, the magnets were made to revolve with two different velocities ; one of nearly 12 revolutions per second, the other of nearly 24 revolutions per second ; but with the disk C the magnets always revolved with the velocity 24 revolutions per second, as I found that I could keep more steadily to this velocity than to the other. The length of the suspending wire (No. 22) was the same in both cases 34.25 inches. The thickness of the magnets is * inch, so that I have added -j— to the mea- sured distances between the upper surface of the magnets and the copper, to reduce them to the distances between the plane of the copper and a horizontal plane passing through the axes of the magnets. The following tables contain the results. Disk A, weight =3 1305 grains. Screw. Unscrew. Distance. Unscrews. Arc of torsion = force. Screws. Arc of torsion = force. Arc. Time, Vel. 12. Vel. 24. Arc. Time. Vel. 12. Vel. 24. 0.6 I . I i .6 2.1 2.6 0 i33° 480 275 *35 80 Not obs, ImIO’ I IO I IO I 06 0 760 270 1 1 8 60 44 0 1870 656 270 142 72 6 1 160 455 260 1 10 78 m. s. 1 09 1 12 1 09 1 07 1 12 6 700 25O 95 48 36 0 1710 604 236 120 56 copper and other substances during rotation . Disk C, weight = 2724 grains . 507 Screw. Unscrew. Distance. Unserews. Arc of torsion = force. Screws. Arc of torsion = force. Arc. Time. Vel. 12. Vel. 24. Arc. Time. Vel. 12. Vel. 24. 0. 6 1 . I i .6 2.1 2.6 O 7270 346s 1670 700 308 m. s. 1 44 1 42 x 40 1 39 1 38 0 3642 I77° 834 347 184 775° 3380 H56 680 320 m. s. I 43 1 40 1 40 1 39 * 39 3874 1680 726 354 180 It is evident from these results, that the force with which the magnets urge the disk, as the distance increases, de- creases much less rapidly than in the case of the copper plate revolving. If we suppose it to vary as ^ B, then calling c and c' two distances and T and T' the correspond- ing torsions, which are equal to the forces of the magnets, n — log. T— log. T' log. c' — log. c ‘ Comparing the preceding results, the several values of n will be. Values of n Disk A. Disk C. -1.723 1 .285 1 *995 1.556 2.087 1 . 864 2.271 2.065 2.436 2.118 2.429 2.406 2.658 2.614 2.420 2.803 • 2.831 2.998 1.3*354 3.246 These differ too widely from each other for us to suppose that the force varies as any exact power of the distance ; mdcccxxv. 3 U 508 Mr, Christie on the magnetism developed in but the approximation is evidently towards the inverse square. With regard to the forces with which different disks are urged at the same distance, they appear to be very accu- rately proportional to the weights of the disks when their distances from the magnets are small ; but as the distances are increased, the forces appear to increase in a greater ratio than that of the weights of the disks. Distance .6 I . I i .6 2.1 2.6 Torsion Weight = 1.372 .483 .194 . 100 .049 Disk A. Torsion Weight H • UA 00 0 •633 .286 •134 .067 Disk B. As it was only by a rough estimate, that I considered the velocity with which the magnets revolved under the disk A, was double in one case of what it was in the other, I would not, from these observations, pretend to determine the ratio of the forces as depending upon the velocities, but I should have little doubt that they are proportional. From these experiments it appears, that the time in which the disk begins to return, by the torsion of the wire, is the same at all distances ; and from another experiment it ap- peared to be independent of the velocity of rotation. This ought to be the case, the force accelerating the disk being constant ; and the retarding force, the torsion, varying as the distance from a fixed point. I fear that I have trespassed too long on your time by this account of the experiments which I have made, but had no idea of rendering it so long when I began. I shall be happy if any of these experiments throw any light upon the copper and other substances during rotation. 509 subject ; and I beg you will make whatever use you think proper of them, and likewise of the account I before sent you.* I am, dear Sir, very truly your's, S. H. CHRISTIE. * In a former letter, dated May i i : the experiments related in which are embo- died in this communication. (H.) Royal Military Academy, 1 zth June, 1825. C 510 3 XXIII. On the annual variations of some of the principal fixed Stars . By J. Pond, F.R. S. Astron. Royal. Read June 1 6, 1825. W henever any difference of opinion exists on philosophical subjects depending on experiment or observation, it is much more useful simply to state facts, than to reason on them prematurely. Plaving this principle in view, I am induced to transmit to the Society the annexed small Table, which con- tains the annual variations of some of the fixed stars, as deduced both from Dr. Brinkley's observations and my own, and by which each may be compared with the annual variations determined by very distant observations, according to the more usual method. Of sixteen stars south of the zenith, observed at Dublin, it will be seen, by the table, that thirteen of them either indicate, or at least are not incon- sistent with that irregularity which I have noticed under the name of southern deviation ; of these thirteen, about half indicate rather a greater deviation than I have assigned to them, the other half deviate less. The three remaining stars, Castor, a Aquilse, a Cygni, deviate in a contrary direction. The difference in cc Cygni is considerable, and not easily to be accounted for, as this star is one of those most frequently observed at each observatory, and is so near the zenith as not to be easily affected by the uncertainty of astronomical refraction. I fear the examination of these tables will rather increase than diminish that tendency to scepticism which does and Mr. Pond on the annual variation, &c. 511 indeed ought to exist, relative to the determination of such very small quantities by astronomical observation ; but I deem it peculiarly incumbent on any one, placed in the situa- tion which I hold, not to be influenced by these considera- tions : on the contrary, the difficulty and perplexity of the subject should only act as an incentive to contrive more powerful methods of investigation. Nothing has ever been farther from my intention, than to place this subject in a controversial point of view. It would be worse than useless so to do, since the difficulty will in the space of a very few years in all probability be satisfactorily explained. 512 Mr. Pond on the annual variation , &c.- Dr. Brinkley, 1813. Dr. Brinkley, 1819. Annual Variation from Dublin Obs. of 1813 and 1319. Annual Variation from Greenwich Obs. of 1813 and 1823. Annual Variation from Greenwich Obs. of 1758 and 1813. 1 2 a Cassiopeiae. Polaris. 34.29.22.59 34.27.23.47 — 19.85 19.70 19.85 3 4 5 a Arietis. a Ceti. a Persei. 67.25.36.76 67.23.53.25 — 17.25 17.22 I7.40 6 7 8 Aldebaran. Capella. Rigel. 73.52.35.98 73. 5i.49.22 - 7-79 7-77 7.92 9 /3 Tauri. 61.33.44.22 6l.33.2l.76 — 3-74 3-72 3.80 10 1 1 a Orionis. Sirius. 82.38. 9.23 82.38.15.94 — 1. 12 1. 15 I.36 12 Castor. 57.42.47.54 57.43.29.94 + 7-07 7.22 7.12 !3 Procyon. 84.18.15.33 84.19. 8.42 + 8.85 8.92 8.63 14 !5 Pollux, a Hydrae. 6l.3i.56.07 61.32.44.98 + 8.1 5 8.04 8.02 16 17 Regulus. a Ursae maj. 77. 7.23.06 77- 9- 745 + 17-4° 17.28 17.23 18 (3 Leonis. 74.22.56.44 74.24.57.91 4- 20.24 20.08 20.04 19 20 y Ursae maj. Spica Virg. 35.15.56.22 35.17.55.15 + 19.82 19.95 19.98 21 » Ursae maj. •39.44.58.37 39.46.47.18 + 18.13 18.16 18.15 22 23 Arcturus. jS Ursae min. 69.50.19.33 69. 52.13.66 + 19.05 19.01 1 8-97 24 a. Cor. Bor. 62.38.55.51 62.40.10.46 + 12.49 12.51 12.45 25 26 27 a Serpentis. Antares. a. Herculis. 82.58.38.81 82.59.49.73 -f 11.82 n-73 11 72 28 a Ophiuchi. 77-I7*4°*39 77.i7.58.23 + 3-31 3.16 3.08 2 9 y Draconis. 38.29. 3.70 38.29. 7.51 + 0.635 0.69 0.67 30 a Lyrae. 51.23. 0.84 5 1.22.42.84 — 3-°° 2.94 3.02 3i a Aquilae. 81.36.59.85 81.36. 5.11 — 9.12 8-93 9.06 32 a Cygni. 45.22.58.30 45 21.42.30 — 12.65 12.47 12.63 33 a Cephei. 28.12.13.90 28. 10.42.74 - 15-19 14.99 !5-°7 34 /3 Cephei. 20.15. 31.41 20.13.57.05 - 15-73 1 5.66 15.68 35 36 37 a Aquarii. aPegasi. a. Andromed. 91. 13. 2I-75 91.1 1.39.40 — 17.06 17.00 17.27 The first and second columns of the above table are taken from two papers of Dr. Brinkley, the one printed in the Irish Transactions, the other in the Philosophical Transactions for 1821. C 513 3 XXIV. On the nature of the function expressive of the law of human mortality , and on a new mode of determining the value of Life Contingencies . In a Letter to Francis Baily, Esq. F.R. S. &c. By Benjamin Gompertz, Esq. F. R. S. Dear Sir, Read June 1 6, 1825. The frequent opportunities I have had of receiving pleasure from your writings and conversation, have induced me to prefer offering to the Royal Society through your medium, this Paper on Life Contingencies, which forms part of a continuation of my original paper on the same subject, published among the valuable papers of the Society, as by passing through your hands it may receive the advantage of your judgment. I am, Dear Sir, yours with esteem, 9 th June 1825. Benjamin Gompertz. CHAPTER I. Article 1. In continuation of Art. 2. of my paper on the valuation of life contingencies, published in the Philosophical Transactions of this learned Society, in which I observed the near agreement with a geometrical series for a short period of time, which must pervade the series which expresses the number of living at ages in arithmetical progression, pro- 514 Mr. Gompertz on the nature of the function ceeding by small intervals of time, whatever the law pf mortality may be, provided the intervals be not greater than certain limits: I now call the reader's attention to a law observable in the tables of mortality, for equal intervals of long periods ; and adopting the notation of my former paper, considering L to express the number of living at the age x, and using x for the characteristic of the common logarithm ; that is, denoting by x (L) the common logarithm of the tv number of persons living at the age of x, whatever x may be, I observe that if x (L) — x (L , ), x (L , ) — x (L , ) x(l+2,„)— x IV+3J. &c- be a11 the same; that is t0 say. if the differences of the logarithms of the living at the ages n, » + m ; n + m, n + 2m ; n + 2m, n + sm; &c. be con- stant, then will the numbers of living corresponding to those ages form a geometrical progression ; this being the funda- mental principle of logarithms. Art. 2. This law of geometrical progression pervades, in an approximate degree, large portions of different tables of mortality ; during which portions the number of persons living at a series of ages in arithmetical progression, will be nearly in geometrical progression ; thus, if we refer to the mortality of Deparcieux, in Mr. Baily's life annuities, we shall have the logarithm of the living at the ages 15, 25, 35, 45, and 55 respectively, 2,9285; 2,88874; 2,84136; 2,79379; 2.72099, for x [Lj ; X jLj ; x |LJ ; &c. and we find X jLj — x ^Lj = , 04738 x jLj — x (Lj = , 04757, and con- sequently these being nearly equal ( and considering that for small portions of time the geometrical progression takes place very nearly ) we observe that in those tables the numbers of expressive of the law of human mortality , &c. 515 living in each yearly increase of age are from 25 to 45 nearly, in geometrical progression. If we refer to Mr. Milne's table of Carlisle, we shall find that according to that table of mortality, the number of living at each successive year, from 92 up to 99, forms very nearly a geometrical progression, whose common ratio is ^ ; thus setting out with 75 for the number of living at 92, and diminishing continu- ally by *, we have to the nearest integer 75, 56, 42, 32, 24, 18, 13, 10, for the living at the respective ages 92, 93, 94, 95, 96, 97, 98,99, which in no part differs from the table by 3-yth part of the living at 92. Art. 3. The near approximation in old age, according to some tables of mortality, leads to an observation, that if the law of mortality were accurately such that after a certain age the number of living corresponding to ages increasing in arithmetical progression, decreased in geometrical progression, it would follow that life annuities, for all ages beyond that period, were of equal value; for if the ratio of the number of persons living from one year to the other be constantly the same, the chance of a person at any proposed age living to a given number of years would be the same, whatever that age might be ; and therefore the present worth of all the payments would be independent of the age, if the annuity were for the whole life ; but according to the mode of cal- culating tables from a limited number of persons at the commencement of the term, and only retaining integer num- bers, a limit is necessarily placed to the tabular, or indicative possibility of life ; and the consequence may be, that the value of life annuities for old age, especially where they are MDCCCXXV. 3 X 51 6 Mr . Gompertz on the nature of the function deferred, should be deemed incorrect, though indeed for im- mediate annuities, where the probability of death is very great, the limit of the table would not be of so much con- sequence, for the present value of the first payment would be nearly the value of the annuity. Such a law of mortality would indeed make it appear that there was no positive limit to a person's age ; but it would be easy, even in the case of the hypothesis, to show that a very limited age might be assumed to which it would be extremely improbable that any one should have been known to attain. For if the mortality were, from the age of 92, such that £ of the persons living at the commencement of each year were to die during that year, which I have observed is nearly the mortality given in the Carlisle tables between the ages 92 and 99 * it would be above one million to one that out of three millions of persons, whom history might name to have reached the age of 92, not one would have attained to the age of 192, notwithstanding the value of life annuities of all ages above 92 would be of the same value. And though the limit to the possible duration of life is a subject not likely ever to be determined, even should it exist, still it appears interesting to dwell on a consequence which would follow, should the mortality of old age be as above described. For, it would follow that the non-appearance on the page of history of a single circumstance of a person having arrived * If from the Northampton tables we take the numbers of living at the age of 88 to be 83, and diminish continually by \ for the living, at each successive age, we should have at the ages 88, 89, 90, 91, 92, the number of living 83; 61.3; 45.9; 34.4; 25.8 ; almost the same as in the Northampton table. 51 7 expressive of the law of human mortality , &c. at a certain limited age, would not be the least proof of a limit of the age of man ; and further, that neither profane history nor modern experience could contradict the possibi- lity of the great age of the patriarchs of the scripture. And that if any argument can be adduced to prove the necessary termination of life, it does not appear likely that the materials for such can in strict logic be gathered from the relation of history, not even should we be enabled to prove (which is extremely likely to be the state of nature) that beyond a certain period the life of man is continually becoming worse. Art. 4. It is possible that death may be the consequence of two generally co-existing causes ; the one, chance, without previous disposition to death or deterioration ; the other, a de- terioration, or an increased inability to withstand destruction. If, for instance, there be a number of diseases to which the young and old were equally liable, and likewise which should be equally destructive whether the patient be young or old, it is evident that the deaths among the young and old by such diseases would be exactly in proportion of the number of young to the old ; provided those numbers were sufficiently great for chance to have its play ; and the inten- sity of mortality might then be said to be constant ; and were there no other diseases but such as those, life of all ages would be of equal value, and the number of living and dying from a certain number living at a given earlier age, would decrease in geometrical progression, as the age in- creased by equal intervals of time ; but if mankind be con- tinually gaining seeds of indisposition, or in other words, an increased liability to death (which appears not to be an un- likely supposition with respect to a great part of life, though 518 Mr. Gompertz on the nature of the function the contrary appears to take place at certain periods) it would follow that the number of living out of a given number of persons at a given age, at equal successive increments of age, would decrease in a greater ratio than the geometrical progression, and then the chances against the knowledge of any one having arrived to certain defined terms of old age might increase in a much faster progression, notwithstanding there might still be no limit to the age of man. Art. 5. If the average exhaustions of a man's power to avoid death were such that at the end of equal infinitely small intervals of time, he lost equal portions of his remain- ing power to oppose destruction which lie had at the com- mencement of those intervals, then at the age x his power to avoid death, or the intensity of his mortality might be denoted by aqx, a and q being constant quantities ; and if Lr be the number of living at the age x, we shall have a Lr x q-x for L the fl uxion of the number of deaths = — (L c) ; a b qx— — -f- > abqx = •— h y p . log. of by. hyp. log. of Lx , and putting the common logarithm of j x square of the hyperbolic loga- rithm of 10 = c, we have c.q* = common logarithm of L JL ; d being a constant quantity, and therefore Lx or the d * number of persons living at the age of x=d.g\q ; g being put for the number whose common logarithm is c. The reader should be aware that I mean £}q * to represent g raised to the power q x and not g * raised to the x power ; which latter I should have expressed by , and which would evidently be equal to gq . I take this opportunity to make this observation, as algebraists are sometimes not sufficiently precise in their notation of exponentials. 519 expressive of the law of human mortality , &c. This equation between the number of the living, and the age, becomes deserving of attention, not in consequence of its hypothetical deduction, which in fact is congruous with many natural effects, as for instance, the exhaustions of the receiver of an air pump by strokes repeated at equal intervals of time, but it is deserving of attention, because it appears corrobo- rated during a long portion of life by experience ; as I derive the same equation from various published tables of mortality during a long period of man’s life, which experience there- fore proves that the hypothesis approximates to the law of mortality during the same portion of life ; and in fact the hypothesis itself was derived from an analysis of the expe- rience here alluded to. Art. 6. But previously to the interpolating the law of mor- tality from tables of experience, I will premise that if, according to our notation, the number of living at the age x be denoted by Lt, , and x be the characteristic of a logarithm, or such that x (LJ may denote the logarithm of that number, that if x (LJ — x (La + r) = m, x (La + — x (La + J = mp, x (L +/+/>3+ . . . . pr ) = , ? i m . ; and therefore if pr = q, and s be put equal to the number whose common logarithm is , we shall have X(L« + J=X(LJ-X(£) x(i -qn) = l(f +x (»)•«"; L La+ n — — x ; and this equation, if for a + n we write L —a x L .r, will give Lr =7 .71 q q ; and consequently if f be put 1 520 Mr. Gompertz on the nature of the function q ■* = d , and TJ = g, the equation will stand Lx = d . g] 1 , and -a m ~a x (£) — x (0 x 9 = 7~~r ; and I observe that when q is affirmative, and x ( e) negative, that x (g) is negative. The ^ Q oc equation 'Lx = d.g\ may he written in general x (L J = X(d) ± the positive number whose common logarithm is {x2 (g) + x x (<§*)} » the upper or under sign to be taken according as the logarithm of g is positive or negative, X2 standing for the cha- racteristic of a second logarithm ; that is, the logarithm of a logarithm, \(q)=±. x A (p), A2 (g) = A2 (0 — a. A (q) — A ( yj- ) — a . \(q)= \ (m) — A ( 1 —p) — a A (°745, a (La + 2r) - A (La + 3r) = ,o9i5, and X (La + 3r) X(La + , ) = ,1228 ; now if these numbers were in geometrical progression, whose ratio is p, we should have respectively m = ,0566 ; mp = ,0745 ; mp2 =,0915 ; mpz= ,1228. No value of p can be assumed which will make these equations accurately true ; but the numbers are such that p may be assumed, so that the equation shall be nearly true ; for resuming the first and last equations we have p2 = —^\ logarithm of p = y (logarithm of 1228 — - logarithm of 566) = ,11213, .% k(q)= ,011213 and p= 1,2944. And to examine how near this is to the thing required, continually to the logarithm of ,0566 namely 2,75282, adding ,11213 which is the logarithm of p, we have respectively for the 521 expressive of the law of human mortality , &c. logarithms of mp , of mp % of mp* the values 2,8649, 2,9771, 1,0892; the numbers corresponding to which are ,07327; ,09486 ; ,1228 ; and consequently m , 7np , mp 2, and mp6 re- spectively equal to ,0566; ,07327; ,09486, and ,1228 which do not differ much from the proposed series ,0566 ; ,07327 ; ,09486, and ,1228 ; and according to our form for interpola- tion, taking m = ,0566 and p = 1,2944 ; we have — = — = —,1922 ; and x(Lj5) agreeably to the Northampton tables, being = 3,7342 we have X ( d)= 3,7342 -f- ,1922 = 3,9264, d = 8441, X2 (7), that is to say, the logarithm of the logarithm of q = X (7--^) — # ^ (7) = T28375 — ,16819 = 1,1156, x(g)=— ,130949= 1,8695, the negative sign being taken because x (g) = X (e ) x q a = 7— . q a, and g = ,7404. And therefore .r being taken between the limits, we are to examine the degree of proximity of the equation Lt = 8441 x 7404 j 1,02 1 or x(Lr), that is, the logarithm of the number of living at the age x =3,9264 — number whose logarithm is (1,11556 + x x .011213), as the logarithm of g is negative. The table constructed according to this formula, which I shall lay before the reader, will enable him to judge of the proximity it has to the Northampton table ; but pre- viously thereto shall show that the same formula, with dif- ferent constants, will serve for the interpolations of other tables. Art. 8. To this end let it be required to interpolate Deparcieux's tables, in Mr. Baily’s life annuities, between the ages 15 and 55. 522 Mr. Gompertz on the nature of the function The logarithms of the living at the age of 15 are 2,92840 differences = ,03966 = x(Vr ■X(L^) 25 2,88874 >04738 I 1 u-l N «< II ■ Kh 5) 35 2,84136 >04757 = X(L 35)- u~\ ^r ! 45 2,19 379 ,07280 = X(L 45)- •X(L5S) 55 2,72099 on the supposi- tion of the possi- bility, though the thing cannot be accurately true. - m Here the three first differences, instead of being nearly in geometrical progression are nearly equal to each other, showing from a remark above, that the living, according to these tables, are nearly in geometrical progression ; and the reader might probably infer that this table will not admit of being expressed by a formula similar to that by which the Northampton table has been expressed between the same limits, but putting, X(L15) = x(L**) = x(Lis) * X(L35) = KL15)~™“?WP X(L45)=X(L15 ^ - X (L 15) - m - mp - - mp *(li5)-*(L35) or its equal m + mp=^ ,08704, and x (L^) — x (L55) or its equal p* x m + pm == ,12037 ; p2 = and the log. of p = — —z L- =,0703997 and p =1,176, = ,04. And to see how these values of m and p will answer for the approximate determi- nation of the logarithms above set down of the numbers of living at the ages 15, 25, 35, 45, and 55, we have the fol- lowing easy calculation by continually adding the logarithm of p — 2,92840 = 2,88874 and we = 2,84136 )> shall have = 2,79379 — 2,72099 expressive of the law of human mortality , &c. 523 Logarithm of m = 2,6020600 Log. of p = 0,0703997 therefore mp =,047039 Log. of mp =2,6724597 mp 4 = ,055317 Log. of f7ipl= 2,7428594 ;«j9s = ,065051 Log. of mp*— 2,8128591 These logarithms of the approximate number of living at the ages 15, 25, 35, 45 and 55, are extremely near those proposed, and the numbers corresponding to these give the number of living at the ages 15, 25, 35, 4 5 and 55, respect- ively, 848; 773,4; <594; 612,3; and 526; differing very little from the table in Mr. Baily’s life annuities ; namely, 848 ; 774; 694; 622 and 52 6. And we have a= 15, r=io, m = ,04; x(m) = 2,60206; 1— = — ,176; xq =z (/>)= — a — a ,00703997; X(g) - 7777 = — , and is negative; X x (^) = X(,04) — 15 x, 00704 — X ( ,176) = 1,25095 ; k(d)= X(LJ — ^=2,9284 +,22727= 3,1557 ;••• X(Lj) = 3,1557 — number whose log. is (1,25095 + ,00704 x), for the logarithm of living in Deparcieux' table in Mr. Baily's annuities, between the limits of age 15 and 55. The table which we shall insert will afford an opportunity of appre- ciating the proximity of this formula to the table. Art. 9. To interpolate the Swedish mortality among males between the ages of 10 and 50, from the table in Mr. Baily's annuities : 3 Y x (Ll5) =2,92840 — m — — ,04 *(LS5) = 2)888+0 — mp = — ,04704 2,84136 — mp7- = — ,05532 2,78604 — mp3 = — ,06505 2,72099 MDCCCXXV. 524 Mr. Gompertz on the nature of the function HereX(Lio) = 3 >779°9* X ( L20^ = 3,746868 to be assumed = X ( L1Q) — m x(L3o) = 3>7°3205 • • = ^ (L10) — m — mp x(L4o) = 3>648i65 • • = X(L10)~ m-mp-mf X^L5q^ = 3,564192 . . — x ( L10) —m — mp — mpz — mp3 Consequently m + mp = X (L:o) X (L3c) — ,075886, and X (L^j — X (L ) = p* x m + mp = ,13901 3 ; therefore ^S = lff55> andAf/>)—> 13 14468 ’ -'-P— !>3535; «=£r+7= — T7r; * (m) = 2,5084775 ; « = , 032244; a=io; r=io; ^>3535 * {.([)— ,01314468 ; k g=m_q'° negative; X X (g) = X(m) —10 X(g) —X (,3535) =2,82861; X ( the fifth term of the differences : take the common ratio — ill and m=, 0256; \(m)= 2,40824. These will give 2^6 X (/>) = , 126; P= 1,3365; a = 10, r= 10, X (?) = ,0126, X («) = ; /. X (g) negative ; \\g = 2,40824 — X(, 3365)— ,126 = 2,75526; and X(d) = X (LI0) + = 3,88631, and accordingly, to interpolate the Carlisle table of mortality for the ages between 10 and 60, we have for any age x, N=s ,88631 — number whose logarithm is (2, 88 126+, 0126 x). Here we have formed a theorem for a larger portion of time than we had previously done. If by the second method the theorem should be required from the data of a larger portion of life, we must take r accordingly larger ; thus if a be taken 10, r — 12, then the interpolation would be formed from an extent of life from 10 to 58 years ; and referring to Mr. Milne's tables, our second method would give X (L*)= 3,89063 — the number whose logarithm is (2,784336 + >° 120948 x)\ this differs a little from the other, which ought to be expected. If the portion between 60 and 100 years of Mr. Milne's Carlisle table be required to be interpolated by our second method, we shall find p = i ,86466 ; X (m) = 1,30812 ; m = ,20329, &c. and we shall have X (LI =3,79657 — the num- ber whose logarithm is (3,74767 + ,02706 x). This last theorem will give the numbers corresponding to the living at 60, 80, and 100, the same as in the table; but for the ages 70 and 90, they will differ by about one year : 526 Mr. Gompertz on the nature of the function the result for the age of 70 agreeing nearly with the living corresponding to the age 71 ; and the result for the age 90, agreeing nearly with the living at the age 89 of the Carlisle tables. Art. 11. Lemma. If according to a certain table of mor- tality, out of a, persons of the age of 10, there will arrive b , c, d, & c. to the age 20, 30, 40, &c.; and if according to the tables of mortality, gathered from the experience of a parti- cular society, the decrements of life between the intervals 10 and 20, 20 and 30, 30 and 40, &c. is to the decrements in the aforesaid table between the same ages, proportioned to the number of living at the commencement of those intervals respectively, as 1 to n, 1 to n', 1 to n", &c. it is required to construct a table of mortality of that society, or such as will give the above data. Solution. According to the first table, the decrements of life from 10 to 20, 20 to 30, 30 to 40, &c. respectively, will be found by multiplying the number of living at the com- mencement of each period by a-I~ , ~T~3 &c., anc* therefore, in the Society proposed, the corresponding decre- ments will be found by multiplying the number of living at those ages by ■ ^ n ; n ' ; n" &c.; and the number of persons who will arrive at the ages 20, 30, 40, &c. will be the numbers respectively living at the ages 10, 20, 30, &c. multiplied respectively by > ~b , — > &c.; hence out of the number a , living at the age 10, there will arrive at the age 10, 20, 30, 40, 50, &c. the numbers 1 . a-\- nb ; 1 — n . a -|- nb x 1 "7 n ° ? 1 . a-f- nb x 1 — n' . b -j- 71 c ^ 1 — n " . c-\- if . d . gcc< anc[ the numbers for b c the intermediate ages must be found by interpolation. 5 27 expressive of the law of human mortality , In the ingenious Mr. Morgan's sixth edition of Price's Annuities, p. 183, vol. i. it is stated, that in the Equitable Assu- rance Society, the deaths have differed from the Northampton tables ; and that from 10 to 20, 20 to 30, 30 to 40, 40 to 50, 50 to 60, and 60 to 80, it appears that the deaths in the Northampton tables were in proportion to the deaths which would be given by the experience of that society respectively, in the ratios of 2 to 1 ; 2 to 1 ; 5 to 3 ; 7 to 5, and 5 to 4. According to this, the decrements in 10 years of those now living at the ages 10, 20, 30, and 40, will be the number living at those ages multiplied respectively by ,0478 ; ,0730 ; ,1024; ,1284 ; and the deaths in twenty years of those now living at the age of 60, would be the number of those living multiplied by ,3163. And also, taking, according to the Northampton table, the living at the age of 10 years equal to 5675, I form a table for the number of persons living at the ages . . 10 20 30 40 5° 60 70 being . . . and the log. of') the number of > persons living J 5675 54°3>5 5010 449 6 39*9 3 1 1 6 * 3,75612 3,73268 3,69984 3,65283 3>593 1 8 349360 * Consequently, if a = 20, r = 10, we have x (L20)= 3,73268 ; * (l4o) = x (L*°) — m — mp = 3,65283 ; X (L6o) = Lzo - m — mp — mp% — m p3 = 3, 49360 ; m. 1 + p = ,07985 ; and mp* x 1 +p = 3,65283 — 3,4936o— ,15923 ; hence X(/>)= 3 x (fsfflf) ==> *49875; and />= 1,412131; x(m)=x(, 07985) — x (2, 41 243) =2, 519874; and m = ,033013 ; X (e) = ■ ~ ■ v v ' ,412131 negative ; \ (g ) is negative ; XX (g) =X?n — x} 412131 — ,0149875 x 20 = 2,6051 ; x(d) = x (l20) — A (<0 = 3.73268 — ,080302 = 3,81s sufficiently near ; and our formula for the 528 Mr. Gompertz on the nature of the function mortality between the ages of 20 and 60, which appears to me to be the experience of the Equitable Society, is X ( L j = 3,813 — the number whose log. is (2.6051 -J- ,0149875 a:). This formula will give At the ages 10 20 30 40 50 60 70 No. of living 57°3>2 5403,5 5007 4496 00 ON N) 3116 * Differs from the"l proposed by J 28,2 0 + 3 0 — 57 0 * In the table of Art. 12, the column marked 1, represents the age ; column marked 2, represents the number of persons living at the corresponding age ; column marked 3, the error to be added to the number of living deduced from the for- mula, to give the number of living of the table for which the formula is constructed ; column marked 4, gives the error in age, or the quantity to be added to the age in column 1, that would give the number of living in the original table, the same as in column 2. It may be proper to observe, that where the error in column 3 and 4 is stated to be o, it is not meant to indicate that a perfect coincidence takes place, but that the difference is too small to be worth noticing. expressive of the law of human mortality , &c. 52 9 Art. 12. x (l) = x (d) — number whose logarithm is (x2(g) + x x q). \r ' Northampton. Deparcieux. Sweden. Carlisle. Formula of supposed experience of the Equitable, Compared with supposed exp. Compared \ Carlisle vith • 1 2 3 4 2 3 4 2 3 4 2 3 i 4 2 3 2 3 4 I 10 1 1 1 2 f3 H 6013 5974 5935 5894 5852^ O — 16 — 22 — 26 — 24I 1 3" 1 — 3 2 7T 3 8 6460 6427 6393 6358 6322 O + 4 + 7 + 1° + 13 0 4- i • 8 + 3 + h + £ 5703 5677 565° 5622 15594 — 28 — r J ; hence, if ^ \ b,c,d ' d- r be put = a , the value of the annuity will be b, c, d /> + if a O I _.1l 4. _* o— fl 1 — a a + ^" + fl3+^ — —a — the upper, with the addition of the two cyphers, give the proportional parts for ,001, 002, 003, ,004, 00 5; and the under, with the two cyphers, shows the proportional parts for ,009, 008, 007, 006 ; and the reason of choosing this arrangement, is the advantage which it offers of proof of correctness ; thus the sum of the higher an lower numbers of each of the above row with the two cyphers = 002752, which is double ,001376, and equal to the whole difference between the successive terms. (I — \ — — j, corres- ponding to log. of axo = 1.7954. In the General Table I, Opposite to T.79 we have . . ,88868 For ,005 we have proportional part . 256 For ,0004 . ditto . . .20 The sum . ,89144 is the answer. 536 Mr. Gompertz on the nature of the function If log. of ap is less than 3,00, then it will be necessary to calculate Xf—fLA by common methods, as the tables do not \ « — 1 / go ower. And generally it will be then sufficient, omitting a P> only t0 calculate the value of — X (a— 1) ; but from this, if more accuracy be required, subtract the number whose common logarithm is (1,6378 -f x (r)p). ^ X (717 ) be Siven> and (a) be required, proceed thus, I —a 10 X ( +i. X(/>)-J- X (77—7^ I have likewise had Table IV. calculated, which is a general table, for the com- mon log. of corresponding to a given value of 537 expressive of the law of human mortality , &?c. commencing with X (a) = T.7 ; 1,701 ; 1,702, &c. with the differences between them. I have not, in this table, had the proportional parts inserted, though it would be attended with advantage, as the table is not meant to be of general use ; but only given to be applied for rough purposes, or where accuracy is not particularly required for calculating at once the value of a life annuity for the whole term of life, or the whole remaining terms of life, after a given term, by con- sidering the present value of each successive payment to form the successive terms of a geometrical progression whose first term and common ratio are each equal to a. And as X (^7— j will represent the log, of the sum of the said geo- metrical progression, it will likewise express approximative^ the logarithm of the value required. For many purposes, a table of -j— , answering to given values of a , would be pre- a — 1 ferable, but not for general purposes. Art. 7. I have already, in Art. 4 and 5, Chap. II, intro- duced the term accommodated ratios, or chances, and endea- voured to explain the methods to be adopted to reap the advantage of the ideas there expressed. Table V, for Carlisle, Deparcieux, and Northampton, are the logarithms of tenth terms of the accommodated ratios, or the logarithms of the accommodated chances for living ten years, calculated ac- cording to a mode laid down in Art. 5, Chap. II ; that is, it expresses for every age, or value of b, the logarithm of when -J— x ( 1 ,05 L + 1,05? L -f &c. . . . 1,05 “f L \ ^b 6 + 1 0+2 b p) is equal toi,05~1e+ 1 ,05"" £2+&c. ... 1,05 T’V0. and to show, by example, how these are calculated, let it be required to find the logarithm of the accommodated chance for living 53 8 Mr. Gompertz on the nature of the function ten years, for the age 20, calculated according to the Carlisle table upon the consideration of interest at 5 per cent. Accord- 1, 05_1 ing to the Carlisle tables, I find X i5 that is, the logarithm of the annuity of one pound on a life of 20, for ten years, at 5 per cent — ,87176, and putting a = 105 •£, by hypothesis X “T) x we shall have X io| a ; that is the logarithm of [a + a* + a*. . . tf,J) = ,87176; that is, A^~a-1-^== ,87i7 6; hence proceed- ing, as shown above, to find from General Table I. ,0) Having given . . ,87176 >. f “~- a'-— 1 We have next lessrz, 86842 corresponding to ... T.75 ,00334 difference ,00302 proportional p art . . ,006 30 . ditto ,0006 2 . . ditto ,00004 .87176 corresponds to . x(a10) r: 1.75664 X (1,05 ,0) rr ,21189 1.96853 for the log. of the accommodated chance to lwve 10 years at the Carlisle mortality. In the same way may the accommodated chance be found for any other term, when general tables for the term are constructed, and from any other base of interest. I may observe, that by using different rates of interest, as a base for determining the accommodated chances, different degrees of accuracy may be obtained. See Art. 5. Chap. II. Art. 8. Table VI. is the logarithm of the accommodated chances £ at every age, b for living one year, where € is of such value that the sum of the geometrical progression — — — -+ &c. ad infinitum, or, which is the same thing, expressive of the law of human mortality , &c. 539 shall be equal to the value of the whole life annuity at T"1 l.OS"1 five per cent, at such age, namely TTjl; consequently x 1 ,05 1.05”1 1,05 1 1,05—1 / l, 05~1 \ ( i + Til ) = Til ; x£ = x(ill)-|-x(i ,05) — x \ 71* * / This table is constructed for Carlisle, Deparcieux, and Northampton, and is to be used in conjunction with Table IV., where only a rough value of the contingency is required ; and though this table applies as the other tables of accom- modated chances, to different rates of interest, still it would be of advantage more particularly here for the greater ap- proximation to have similar tables constructed from the formula x (£)= X ( 1 ll ) + X (r-1) — X \ ill / for different values of r. Art. 9. In calculating the value of life annuities for long periods, by means of adding together the values of portions of those periods, the portions of the distant periods contain factors of the real chance of living to these periods, and likewise of the discounted value of the money of which the payment is not immediate; thus if t be greater than 10, a+10,6+10, c+io r r It will be therefore convenient to have a table of the logarithm of the real chance of living 10, 20, 30 years, &c. and also for other terms ; and some of these are given by Tables VII., VIII., IX. 4 A MDCCCXXV. 540 Mr. Gompertz on the nature of the function Time will not allow me, for the present, to offer more than a very few examples of the method to be employed in calculating by these tables, which are as follow : Example 1 . Required, according to the Carlisle table, the value of a life annuity, for ten years, on the joint lives 30 and 40, at 3 per cent interest. In Table VIII; for Carlisle, log. of accommodated chance for io years, at the age 30 . . rr T.9552 Ditto 40 . . . . = T.9383 Ditto X 1,03 . . . ' =1.8716 Sum . . 7.7651 =x(a*°) In Table I, 7.76 corresponds to . . . .8734 In proportional parts ,005 corresponds to .253 Ditto . . 0001 corresponds to . 5 Consequently 7,765 1 corresponds to . .87604 which is the log. of the required value : the number corres- ponding to this is 7,5169, for the value of the annuity, according to the Carlisle mortality, at 3 per cent, on the joint lives 30 and 40; and by calculation from Mr. Milne's tables, I find the value should be 7,5168 ; the difference of the two is evidently insignificant. In this way I calculated the log. of the value of the life annuity, at the Carlisle mortality, at 3 per cent, for 10 years, for the joint lives o and 10, 10 and 20, 20 and 30, 30 and 40, 40 and 50, 50 and 60, to be ,76580 ; ,90247 ; ,89139 ; ,87604 ; ,86295 ; ,81067 ; and the annuity, or the numbers corresponding to the said logarithms, 5,8318; 7,9874; 7,7874; 7,5169; 7,2937; 6,4665; and, according to calculation from Mr. Milne's tables, I get 5,8595; 7,992; 7,7906; 7,5168; 7,2916; 6,4679. The difference between the two sets is insignificant, except expressive of the law of human mortality , &c. 541 1,05 — 1 perhaps in the values of i5 l°> 10 ; that is, the value of the annuity on the joint life of a child just born, with one of the age of 10, at 3 per cent. Had we divided the period in por- tions, the value might have been obtained as near as we pleased ; or we should likewise have obtained greater accu- racy, had we assumed an accommodated chance deduced at a more appropriate interest than 5 per cent. See Art. 5, Chap. II. Example 2. Let it be required to find the value of a life annuity at 3 per cent, for 10 years, at the Carlisle mortality, for the five lives of the age 20, 30, 40, 45 and 50. In Table VIII. log. of accom. chance for io years at age 20 = T.9685 30=1.9552 Ditto Ditto Ditto Ditto This sought in Table I.; thus, 1,59 giving ,79035 ,009 427 ,0005 23 40=1.9383 • 45 = T-9367 • 50 = 7.9292 -i° - , ^ * 1,05 = 1.8716 x (a *°) = 1.5995 1,03 1 1 gives >79485 the N° to which log. is 6,2352 1,03—* for the value of 1*°> 4* 4* Example 3. Let it be required to find the value of 1 M+10 Carlisle mortality, when b= 10, that is, for the whole joint lives of 10 and 20. By dividing the whole in portions of ten 1,03 years, the operation will stand thus for 10 iL b -f 10. 542 Mr. Gompertz on the nature of the function b — IO b “20 b—3° O II bzz 50 b- 60 0 II *<5 b— 80 Log. of accom. ratio ) 1. 9768 forioyears zz $7.9685 X(i,03_lo)= 1. 8716 I. 9685 1.9552 1.8716 1.9552 1 -9383 1.8716 I-93s3 1 .9292 T.8716 T.9292 1.8318 T.8716 7.8318 7.6689 7.8716 1 .6689 £ • 3 ‘ 34 1.8716 7.31347 from Tab. VIII. 2.6695 5 Carlisle. 1.8716 sum . . = 1. 8 169 ‘•7953 I. 7651 ‘•739‘ "1.6326 ‘•3723 2-8539 3-8545 No* corresponding i to suminTablel. $ *90247 .89139 .87604 .86295 .81067 .69156 .48781 .19146 Log. of ratios for 1 0 years = | M,o3-*° . . = T. 97438 1 .96681 1.87163 T. 94120 I. 92082 T-74325 T. 89520 T. 85854 I. 61488 T. 83292 7.77684 7.48651 7.75123 ‘•59577 1.35814 7.57016 1 . 1 9448 7.22977 7. 16886 2.36767 1.10139 The log. of the present 7 worth of each portion $ ” .70421 .48131 •23‘57 7.90694 7.39670 2.48222 4.82938 And the present worth of each, or the numbers correspond- ing to the last logarithms are arranged below. For first 10 years 7.9886 2nd ditto 5.0607 3d d° 3.0291 4th d° 1.7044 5* d° .8071 6th d° .2492 7 th d° •0303 8th d° .0007 sum 18.8701 which differs but i] As the method by which the logarithms of the present worth of the different portions are found, may not be seen by every reader, I will explain the operation in the third portion ; that is, when the logarithm of the portion first found is anticipated for 20 years. Resume ..... .87604 Table VII. log. of real chance for age ) - , , 10 living 20 years . . . ) Ditto 20 years living . . 1. 92082 *(i>03~10) .... T . 74325 .48131 which gives 18.873. In a similar way, I find the value of the joint lives for ages 20 and 30, at 3 per cent, and Carlisle mortality to be 16.745 ; which, according to Mr. Milne's table, should be 16.749 ; which appears to be an insignificant difference. Example 4. To find, when particular accuracy is not required, according to the formula for the whole of life, 1,03 1 I —I a> a + 10 at the Carlisle mor- the approximate value of tality, when a — 10, 20, 30, &c. call the logarithm of accom- modated ratios for an unlimited time at the age a , Ra standing for the accommodated ratio in Table VI. at the age a. expressive of the law of human mortality , &c. 543 a — 10 20 30 40 50 60 70 80 1 90 Ra 7.99529 7.99455 7.99265 7.98991 7.98546 7.97514 T-9575S 7.92461 7.8666o R , • a+ 10 T-99455 7.99265 7.9899I 7.98546 T-975I4 T-95755 7.92461 7.86660 7.81282 7.98716 7.98716 7.98716 7.98716 7.98716 7.98716 7.98716 7.98716 7.98716 7.97700 7.97436 7.96972 7.96253 7.94776 7.91985 7.86932 T-7?8 37 7.66658 Log. which corresponds to 7.2645 1 1 1.20975 .00631 1.13083 .01062 1.03886 .00641 .88674 .00667 .68817 .00502 b 4- 0 >— 1 00 wo ^4 • 1 757i .00093 1. 21 606 1-HH5 1.04527 .89341 .69319 .45460 .17664 Numbers . . Instead of . 18.387 18.S73 16.446 16.749 13.850 14.449 1 1.099 11.954 7.824 8.729 4- 9339 5- 565 2.8485 3.229 1.5019 1.589 To find the value corresponding to 1.66658, not in the table, find the number corresponding complement of the log. T.6658, which number is 2,159; subtract 1, and find the complement of the log. which is = 1.9359 165, whose num- ber is ,8628. Mr. Milne's table gives .97 9. But as it is not always the same rate of interest which gives the best accommodated ratios, in order to try when, for instance, the interest of money is 3 per cent, what rate of interest should be used in determining the ratios, use the following table:* Interest. 1 .08 1 .07 1 .06 1 .05 1 .04 x (1.08 x 1.03) 1= 7.979 ' x (1.07 1 x 1.03) =7.983 X (1.06 x 1.03) =7.987 / -1 X (1.05 x 1.03)= I .991 x (1.04 1 x 1.03) 7.996 y nearly ; * This is not given as a perfect and unerring rule, but as a method in many cases useful, and which would be perfect for the accommodated ratio of one of the lives, if the other lives followed an exact geometrical ratio throughout; and that the real geometrical ratios were in that case used for them, provided that instead of comparing the said sum with the small table, we take for the base of interest the number whose logarithm is — X (1,03), when the interest is 3 per cent.; and it is to be recollected that the methods is only given as a rough approximation. 544 Mr. Gompertz on the nature of the function Add the logarithm of accommodated ratios, as given in the Table VI. of all the lives but one in question, together, and see which of those rates of interest it nearest agrees with, and use that to calculate the life left, and proceed so for 1,03—' every life ; thus for^*1 3°» 4° ; to find the rate of interest for 30, I observe that R = T.9899 agrees nearest with 6 per cent, in the little table, and R==T. 99265 agrees nearest with 5 per cent., I therefore take 6 per cent, for the age 30, and for the other I take 5 per cent. : proceed thus : Example 5. R if calculated at 6 per cent. 30 r *•993*6 R per table 40r I.98991 A I,05“* . . . = T.98716 1. 97023 1.14558 Proportionate parts .00327 To which logarithm . OO 00 *■* ►M The N° corresponding is I4.088 Instead of . 14449 Example 6. I l4°> $0 Rat 6 per cent. . . 1. 99060 40 - R at 6 per cent. . . 1.98032 50 1.98716 I.96408 I.05336 .00102 1.06438 1 1.598 Example 7. 1\1 50, 60 R at 8 per cent. . 50 R at 6 per cent. . 60 A i,o3_l . Instead of = i.987S9 = *-97599 — 1.98716 *-95°74 •9*357 .00687 .92044 .8318 . .8729 11.954 which log. corresponds . instead of 545 expressive of the law of human mortality , &c. I observe that I have not given any table of the logarithm of the accommodated ratios for an unlimited term, except that calculated with 5 per cent, as a radix ; but by the assist- ance of a table of life annuities, for single life at different rates per cent., this will enable us, independent of certain exceptions, to derive the quantity for the same rates per cent, for any radix at the per cent, contained in the second table ; thus to find R Carlisle mortality, radix 8 per cent. I look to the Carlisle table of single lives at 8 per cent., and I find the value of the annuity on the life of 50 = 8.987, I search the age to which this will correspond at 5 per cent, and I find sufficiently nearly 59,82 for the age corresponding, to which from my table ( with the radix at 5 per cent. ) for the log. of ratios I find 1.97536 ; to this I add log. of ^ ; that is, ,01223, and we get T. 98759! the same as given on the other side. This method is accurately consistent with the defi- nition of accommodated ratios for unlimited periods ; and if this description of accommodated ratios at a certain rate per cent, be given for one table, for which at the same rate per cent, we have the value of single lives, we may find the same description of accommodated ratios for any other table of mortality for which, at the same rate per cent, we have a table of the value of single lives : thus, suppose the logarithm of this description of accommodated ratios be given for the Carlisle table at five per cent., and the same be required for 1,05 -1 60 the Northampton for the age 60, at the same rate ; Northampton = 8,392, this being sought in the Carlisle 54b Mr. Gompertz on the nature of the function 1,05 table for i1 IfL gives x = 62,41 for the corresponding age seek the logarithm of accommodated ratios for an unlimited term, corresponding to this for Carlisle, for the age 6,241, and we have T.9723, agreeing with the table given. Previously to concluding this chapter, I shall add a small table, which will be found very useful in the application of the methods here proposed. n Log. of 1,03 n Log. of 1,035'” Log. of 1, 04"” Log. of 1,045“” Log. of 1,05“” 1 I. 9871628 7.9850597 7.982 9667 7.9808837 7.9788107 2 1.9743256 1 .9701193 t-96593 33 7.9617674 1.9576214 3 1 .9614883 1. 9551790 1 .9489000 i .94265 1 1 *. 9364321 4 1.948651 1 1 .9402386 7.9318666 *• 9235348 1 .9152428 5 1. 9358^9 7.9252983 i‘‘9H*333 1 .9044185 1.8940535 6 1.0229767 1 •9I°3579 1 . 8978000 7.8853023 1 .8728642 7 7.9101394 1 .8954176 7.88076 66 1 .8661860 1 .8516749 8 1.8973022 7.8804772 1*8637333 7.8470697 1 . 8304856 9 1.8844650 7.8655369 1 . 8466999 7.8279534 i .8092963 10 7.8716278 1 .8505965 7.8296666 1 . 8088371 i .7881070 ft IN expressive of the law of human mortality, &c. 547 General Table I. X(a10), X )• * ('-“H 1 9 2 8 3 7 4 6 5 1 9 2 8 I 3 7 4 6 5 \ i J \a"— 1 3.00 ,00163 ,00 0200 °399 °599 0798 0998 3-25 ,05295 ,00 0212 0423 0635 0847 io59 ,00199,6 *796 1 5 97 1 397 1 198 ,002 1 1,7 19°S 1694 1482 1270 3.01 ,0036,2 0200 0401 0601 0801 J002 3.26 ,05506 0212 0424 0637 0849 106 j ,00200,3 1803 1602 1402 1202 ,00212,2 1910 1698 1485 1 273 3.02 ,00563 0201 0401 0602 0802 1003 3*27 >°57i9 0213 0425 0638 0851 1064 ,00200,6 1 805 1 605 1404 1 204 ,0021 2,7 1914 1702 1489 1 276 3*03 ,00763 0201 0402 0603 0804 1005 3.28 >0593* 0213 0426 0640 0853 1066 ,00201,0 1809 1608 1407 1 206 ,00213,2 1919 1706 H92 1279 3 *°4 ,00964 0202 0403 0605, 0806 1008 F 29 ,06144 0214 0427 0641 0855 1069 ,00201,5 1814 1612 141 1 1 209 ,00213,7 1923 1710 M96 1 282 3-05 ,01166 0202 0404 0606 0808 1010 3*30 ,06358 0214 0429 0643 o8£Zu 1072 ,00202,0 1818 1616 1212 ,00214,3 1929 I7I4 1500 ! 1286 3.06 ,01368 0202 °4°5 0607 0810 1012 3*3i ,06572 0215 0430 0644 0859 I074 ,00202,4 1822 1619 1417 1214 ,00214,8 1933 1718 1504 1 289 3-07 ,01570 0203 0406 0608 0811 1014 3-32 ,06787 0215 °43 1 0646 0861 1077 ,00202,8 1825 1622 1420 1217 ,00215,3 i938 1722 J5°7 1292 3.08 >° 1 773 0203 °4°7 0610 0814 1017 3-33 ,07002 0216 0432 0648 0864 1080 ,00203,4 1831 1627 1424 1 220 ,00216,0 *944 1728 1512 1 296 3-09 ,01976 0204 0408 061 1 0815 1019 3 - 34 ,07218 0216 °433 0649 0866 1082 ,00203,8 l834 1630 1427 1223 ,00216,4 1948 *73* 1515 1 298 3 • 10 ,02180 0204 0409 0613 0817 1022 3-35 >07435 0217 °434 0651 0868 1085 ,00204,3 i839 1634 1430 1226 ,00217,0 1 95 3 1736 1S19 1302 3*ii ,02384 0205 H°9 0614 0819 1024 3-36 ,07652 02 1 8 0435 0653 0870 1089 ,00204,7 1 842 1638 H33 1 228 ,00217,5 1958 I74° >523 1 3°5 3.12 ,02589 0205 0410 0616 0821 1026 3 • 37 ,07869 0218 0436 0654 0872 1090 ,00205,2 1847 1642 H36 1231 ,0021 8,0 1 962 1 744 1526 1308 3-i3 ,02794 0206 041 1 0617 0823 1029 3 *38 ,08087 0219 °437 0656 0875 1094 ,00205,7 185 1 1646 H4° I234 ,00218,7 1968 1750 x53 1 *312 3- H ,03000 0206 0412 0618 0824 1031 3-39 ,08306 0219 0438 0658 0877 1096 ,00206, i i855 1649 H43 1237 ,00219,2 1 97 3 1 754 1 534 1 3 1 5 3- *5 ,03206 1 ' 0207 0413 0620 0826 io33 3-40 ,08525 0220 °439 0659 0879 1099 ,00206,5 i859 1654 1446 1239 ,00219,7 *977 1758 M38 1318 3.16 ,00207 0207 0415 0622 0829 I°37 3 -41 ,08745 0220 0441 0661 0882 1102 ,00207,3 1 866 1658 1451 1244 ,00220,4 j984 1763 1 543 1322 3-i7 ,03620 0208 0415 0623 0830 1038 3*42 ,08965 022 1 0442 0663 0884 1 105 ,00207,6 1868 1661 1 45 3 .1246 ,00221,0 1989 1 768 1547 1326 OO *— < • ,03827 0208 0416 0624 0832 1041 3-43 ,091 86 0221 0443 0664 0886 1 107 ,00208,1 *873 1665 H57 1249 ,00221,4 1993 1771 »55i 1328 3* !9 ,04036 0209 0417 0626 o834 1043 3-44 ,09408 0222 0444 06 66 0888 1 1 1 1 ,00208,6 18 77 1669 1460 1252 ,00222,1 1999 17 77 1 5 5 5 1 333 3.2c ,04244 0209 0418 0627 0836 1046 3-45 ,09630 0223 0445 0668 0890 1113 ,00209,1 1882 1673 H64 I255 ,00222,6 2003 1781 1558 1 336 3.21 »°4453 0210 0419 0629 0838 1048 3-46 ,09852 0223 0446 0670 0893 1116 ,00209,6 1886 i677 1467 1258 ,00223,2 2009 1786 1562 1 339 3.22 ,04663 0210 0420 0630 0840 105 1 3-47 ,10076 0224 0448 0671 0895 1119 ,00210,1 1891 1681 1471 1 261 ,00223,8 2014 1790 i567 1 343 j 3-2 3 ,04873 0211 0421 0632 0842 I05 3 3-4^ ,10300 0224 °449 0673 0898 1 122 ,00210,6 189s 1 685 H74 1264 ,00224,4 2020 1 7 95 1571 1346 3.24 ,05084 021 1 0422 0633 0844 1056 3-45 ,10524 0225 0450 0675 0900 1125 ,0021 1, 1 1 1900 1689 J478 l 1 267 ,00225,0 2025 1800 1 575 *35° 4 B MDCCCXX V 548 Mr. Gompertz on the nature of the function General Table I. X fa10), X I • \ a — i ' X(a'°) x(i=£ \ 1 9 2 8 3 7 4 6 5 A(V°) 1 9 1 2 8 3 7 4 6 5 ' a-I_i J V:_J 3-5° >*°749 ,00 0226 0451 0677 0902 1128 3*75 ,16581 ,00 0242 0484 0726 0968 1210 ,00225,6 2030 1805 1579 *354 ,00242,0 2178 1936 1694 1452 3-5i ,10975 0226 0452 0679 0905 * 1 3 * 3-76 ,16823 0243 0485 0728 0971 1214 ,00226,2 2036 1810 *583 *357 ,00242,7 2184 *942 *699 1456 3 • 52 ,1 1201 0227 0454 0680 0907 **34 3-77 ,17065 0244 0487 0731 °974 1218 ,00226,8 2041 1814 1588 1361 >00243,5 2192 1948 1705 1461 3-53 ,11428 0228 0455 0683 0910 1138 3-78 >*7309 0244 0488 °733 0 977 1221 ,00227,5 2048 1820 *593 *365 ,00244,2 2198 *954 *709 1465 3 * 54 ,1*655 0228 0456 0684 0912 1 1 4 z 3-79 >*7553 0245 0490 0735 0980 1225 ,00228,1 2053 1825 *597 1369 ,00244,9 2204 *959 1714 1469 3-55 ,11883 0229 0457 0686 0915 **44 3.80 >17798 0246 °49* 07 37 0982 1228 ,00228,7 2058 1830 1601 *372 ,00245,6 2210 *965 17*9 *474 3*S6 ,121 12 0229 0458 0688 °9*7 1 146 3.81 ,18044 0246 °493 0739 0986 1232 ,00229,2 2063 *834 1604 *375 ,00246,4 2218 *971 1725 1478 3-57 ,12341 0230 0460 0690 0920 * *5 * 3.82 ,18290 0247 °494 0741 0988 1236 ,00230,1 . 2071 1841 161 1 1381 ,00247,1 2224 *977 1730 1482 3»58 ,12571 0231 0461 0692 0922 **53 3-83 >18537 0248 0496 °743 °99* 1239 ,00230,6 2075 1845 1614 *384 ,00247,8 2230 1982 *735 1487 3 • 59 ,12802 0231 0462 0694 0925 1156 3*84 ,18785 0249 °497 0746 °994 *243 ,0023 1,2 2081 1850 1618 *387 ,00248,6 2237 *989 1740 *492 3.60 >*3°33 0232 0464 0696 0928 1 160 3 • 85 ,*9°34 0249 0499 0748 0997 1247 ,00231,9 2087 *855 1623 *39* ,00249,3 2244 *994 *745 1496 3.61 ,13265 0233 0465 0698 0930 1163 3.86 ,19284 0250 0500 0750 1000 125 1 ,00232,5 2093 i860 1628 *395 ,00250,1 2251 20c 1 1751 1501 3.62 >*3497 0233 0466 0699 0932 1165 3 • 87 >*9533 025 1 0502 °753 1004 1255 ,00233,0 2097 1864 1631 *398 ,00250,9 2258 2007 1756 1505 3*63 >13730 0234 0468 0701 °935 1 169 3.88 ,19784 0252 0503 °755 1006 1258 ,00233,8 2104 1870 *637 1403 ,0025 1,6 2264 2013 1761 1510 3-64 >13964 0235 0469 0704 0938 1*74 3*89 >20035 0252 0505 °757 1010 1262 >00234,5 21 1 1 1876 1642 1407 ,00252,4 2272 2019 1767 *5*4 3-65 ,14199 0235 0470 0705 0940 1 176 3-9° ,20288 0253 0506 0760 1013 1266 >00235,1 2 1 16 1881 1646 141 1 ,00253,2 2279 2026 *772 *5*9 3.66 >*4434 0236 0472 0707 °943 **79 3*9* ,20541 0254 0508 0762 1016 1271 ,00235,8 2122 1886 1651 *4*4 ,00254,1 2287 2033 *779 1525 3-67 ,14670 0237 0473 0710 0946 1183 3*92 >20795 0255 0509 0764 1019 1274 ,00236,6 2129 *893 1656 1420 >00254,7 2292 2038 *783 1528 3.68 ,14906 0237 0474 0711 0948 1 186 3-93 ,21050 0256 05 1 1 0767 1023 1279 ,00237,1 2134 1897 1660 1423 ,00255,7 2301 2046 1790 *534 3*69 >*5*43 0238 0476 0714 0952 1190 3-94 ,21306 0256 °5 *3 0769 1025 1282 >00237,9 2141 19°3 1665 1427 ,00256,3 2307 2050 *794 *538 3-7° >*5381 0239 0477 0716 °954 **93 3 *95 ,21562 0257 0514 0772 1029 1286 ,00238,5 2147 1908 1670 *43* ,00257,2 2315 2058 1800 *543 3-7* ,15620 0239 0478 0718 0957 1 196 3*96 ,21819 0258 0516 0774 1032 1290 ,00239,2 2153 *9*4 *674 *435 ,00258,0 2322 2064 1806 *548 3 *72 ,15859 0240 0480 0720 0960 1200 3 * 97 ,22077 0259 0518 0776 *°35 *294 ,00239,9 2159 *9*9 1679 *439 ,00258,8 2329 2070 1812' *553 3-73 ,16099 0241 0481 0722 0962 1 1203 3-98 ,22336 0260 0519 0779 1038 1298 ,00240,6 2165 1925 1684 *444 ,00259,6 2336 2077 1817 1558 3-74 >i6339 0241 0483 0724 0965 1207 3-99 ,22559 0260 0521 0781 1042 1302 ,00241,3 2172 1 1930 1689 1448 ,00260,4 2344 2083 1823 1562 expressive of the law of human mortality , &c. 549 General Table I. X (a10), X \ a - — j 1 9 2 8 3 7 t 5 L (*— a'°i 1 9 2 8 3 7 4 6 5 la L_i / 'a~.!_i i 2.00 ,22856 ,00 0261 0523 0784 1046 1307 2.25 ,29652 ,00 0284 0568 0852 1 1 36 1420 ,00261,4 2353 2091 1830 1568 ,00283,0 2555 2271 J987 1703 | 2.01 ,23117 0262 0524 0786 1048 1310 2.26 ,29936 0285 0570 0855 1 140 1425 ,00262,0 z358 2096 l834 1572 ,00284,9 2564 2279 1994 1709! 2.02 ,23379 0263 0526 0789 1052 1315 2.27 ,30221 0286 0572 0858 1144 1430 ,00263,0 2367 2104 1841 !578 ,00285,9 2573 2287 2001 1715 2.03 ,23642 0264 0528 0791 1055 1319 2 . 28 ,30 5°7 0287 0574 0860 1147 j 1 434 ,00263,8 2374 21 10 i847 i583 ,00286,8 2581 2294 2008 1721 2.04 ,23906 0265 0529 0794 1059 1324 2.29 ,30794 0288 0576 0864 1152 ,1440 ,00264,7 2382 2118 i853 1588 1 ,00287,9 2591 2303 2015 1727 2.C5 ,24171 0266 °53i 0797 1062 1328 2.30 ,3 1081 0289 0578 0867 1156 j 1 445 ,00265,6 2390 2125 1859 J594 ,00288,9 2600 2311 2022 1 733 2.06 ,24036 0266 0533 0799 1065 1332 2.31 ,31370 0290 0580 0870 j 1 160 1450 ,00266,3 2397 2130 1864 1598 ,00289,9 2609 2319 2029 1739 2.07 ,24703 0267 °534 0801 1068 1 3 3 5 2.32 ,31660 0291 0582 0873 1164 1 45 5 ,00267,0 2403 2136 1869 1602 ,00290,9 2618 2327 2036 1745 Ml • O 00 ,24970 0269 °537 0806 io74 1343 2*33 ,3I95I 0292 0584 0876 1 168 1460 ,00268,5 2417 2148 1880 161 1 ,00291,9 2627 2335 2043 1751 2.09 ,25238 0269 °538 0807 1076 1 345 2-34 ,32243 0293 0586 0879 1 172 1465 ,00269,0 2421 2152 1883 1614 ,00293,0 2637 2344 205 1 1758 2 . IO ,25507 0270 °54° 0810 1080 135° 2.35 >32536 0294 0588 0882 1 176 1470 ,00269,9 2429 2159 1889 1619 ,00294,0 2646 2352 2058 1764 2. I I >z5 777 0271 0542 08 1 2 1083 1 354 2.36 ,32830 0295 0590 0885 1 180 H75 ,00270,8 2437 2166 1896 1625 ,00295,0 2655 2360 2065 1770 2.12 ,26048 0272 °543 0815 1087 1 359 2-37 >33125 0296 0592 0888 1 184 1481 ,00271,7 2445 2174 1902 1630 ,00296,1 2665 2369 2073 1 777 2.I3 ,26320 0273 °545 0818 1090 1363 2.38 >3342i 0297 0594 0891 1188 1485 ,00272,6 2453 2181 1908 1636 ,00297,1 2674 2 377 2080 1783 2 . 14 ,26592 0274 °547 0821 io94 1368 2.39 >337i8 0298 0596 0895 1193 M9i ,00273,5 2462 2188 1915 164.I ,00298,2 2684 2386 2087 1789 2.I5 ,26866 0275 °549 0824 1098 1 373 2.40 ,34016 0299 °599 0898 1197 H97 ,00274,6 2471 2197 1922 1648 ,00299,3 2694 2394 2095 1796 2.l6 ,27140 0275 °5 5° 0826 1 101 1376 2.41 >34316 0300 0601 0901 1 201 1 502 ,00275,2 2477 2202 1926 165 1 ,00300,3 2703 2402 2102 1 802 2.I7 ,27415 0276 °553 0829 1 105 1382 2.42 >343j6 0301 0603 0904 1206 1507 ,00276,3 2487 2210 x934 1658 ,00301,4 2713 241 1 21 10 1808 2.18 ,27692 0277 °554 0832 1 109 1386 2.43 >34917 0303 0605 0908 1210 1513 ,00277,2 2495 2218 1940 1663 ,00302,5 2723 2420 2118 1815 2 . 19 ,27969 0278 0556 0834 1112 1391 2.44 ,35220 0304 0607 091 1 1214 1518 ,00278,1 2503 2225 T947 1669 ,00303,6 2732 2429 2125 1822 2.20 ,28247 0279 0558 o837 1 1 16 1396 2-45 >35523 0305 0609 °9H I2I9 1524 ,00279,1 2512 2233 !954 1675 ,00304,7 2742 2438 2133 1828 2.21 ,28526 0280 0560 0840 1 120 1401 2.46 ,35828 0306 0612 °9 1 7 1223 1529 ,00280,1 2521 2241 1961 1681 ,00305,8 2752 2446 2141 1835 2.22 ,28806 0281 0562 o843 1 124 1406 2.47 >36134 0307 0614 0921 1228 1535 ,00281,1 2530 2249 1968 1 1687 >00306,9 2762 2455 2148 I 841 2.23 ,29087 0282 0564 0846 1128 1410 2.48 >36441 0308 0616 0924 1232 1541 ,00281,9 2537 2255 1 97 3 1691 ,00308,1 2773 2465 2157 1 849 2.24 ,29369 0283 0566 0849 1132 I415 2.49 >36749 0309 0618 0928 1237 1546 ,00282,9 2546 2263 1980 i697 ,00309,2 2783 2474 2164 1 855 55 o Mr. Gompertz on the nature of the function General Table I. X ( ax0 ) , A LziL ' a* — i (a‘°) 1 9 2 8 3 7 4 6 5 1 9 2 8 3 7 4 6 5 l a i_i / '■'a i_i ' 2.50 >37058 ,00 0310 0621 0931 1241 x552 2-75 >45 x74 ,00 034x 0682 1022 x363 x7°4 ,00310,3 2794 2482 2172 1862 ,00340,8 3067 2726 2386 2045 2.51 >37368 0312 0623 0935 1246 x5 58 2.76 >455x5 0342 0685 1027 1369 1712 ,00311,5 2804 2492 2181 1869 >00342,3 3081 2738 2396 2054 2.52 ,37680 0313 0625 0938 1250 1563 2.77 >45857 0343 0687 1031 x374 1718 ,00312,6 2813 2501 2188 1876 >°°343>5 3092 2748 2405 2061 2 *53 >37993 0314 0628 0941 1255 1 569 2.78 ,46201 0345 0690 io35 1380 x725 ,00313,8 2824 25 10 2197 1883 ,00345,0 3105 2760 24 x5 2070 2.54 >38306 0315 0630 0945 1260 1 5 75 2.79 ,46546 0346 0692 1038 x384 x73x ,00314,9 2834 2519 2204 1 889 ,00346,1 3H5 2769 2423 2077 2.55 ,38621 0316 0632 0948 1265 1581 2.8c ,46892 0348 0695 I043 x39° x738 ,003 16,1 2845 2529 2213 1897 >oo347>5 3128 2780 2433 2085 2 .56 >38937 03*7 0635 0952 1269 x587 2.81 >47239 0349 0698 io47 1396 x745 >00317,3 2856 2538 2221 x9°4 ,00348,9 3Ho 2791 2442 2093 2.57 >392S5 0319 0637 0956 1274 1 593 2.82 >47588 0350 0700 1051 1410 x75 1 ,00318,5 2867 2548 2230 191 1 ,00350,2 3X52 2802 2451 2101 2.58 >39573 0320 0639 °959 1278 1 598 2.83 >47938 0352 0703 io55 1406 1758 ,00319,6 2876 2557 2237 1918 ,00351,6 3164 2813 2461 2110 2.59 >39^93 0321 0642 0962 1283 1604 2 • 84 ,48290 0353 0706 io59 1412 176s ,00320,8 2887 2566 2246 1925 >00353,0 3i77 2824 2471 21 18 2.60 >402 1 3 0322 0644 0966 1288 1610 2.85 >48643 0354 0709 1o63j X4X7 1772 ,00322,0 2898 2576 2254 1932 >°°354>3 3x89 2834 2486 2126 2.61 >40536 0323 0647 0970 1293 1617 2 . 86 ,48997 0356 0712 1067 x423 1779 >00323,3 2910 2586 2263 x94° >00355,8 3202 2846 2491 2135 2.62 ,40859 0325 0649 0974 1298 1623 2.87 >49353 0357 °7X4 1071 1428 1786 ,00324,5 2921 2596 2272 x947 >00357,1 3214 2857 2500 2143 2.63 >4ii83 0326 065 1 0977 1302 1628 2.88 >497IQ 0359 °7 1 7 1076 x434 x793 ,00325,6 2930 2605 2279 x954 >00358,5 3227 2868 2510 2151 2.64 >4I5°9 0327 0654 0980 1307 i634 2 . 89 ,50069 0360 0720 1080 1440 1800 ,00326,8 2941 2614 2288 1961 ,00360,0 3240 2880 2520 2160 2.65 >4J 836 0328 0657 0985 1313 1642 2.90 ,50429 0361 0723 1084 x446 1 807 ,00328,3 2955 2626 2298 197° >00361,4 3253 2891 253o 2168 2.66 ,42164 0329 0659 0988 i3i8 i647 2.91 ,50790 0363 0725 1088 1451 1814 ,00329,4 2965 2635 2306 1976 ,00362,7 3264 2902 2539 2176 2.67 >42493 0331 0661 0992 1322 i653 2.92 >5 1 1 5 3 0364 0728 IQ93 1 45 7 1821 ,00330,6 2975 2645 23H x984 ,00364,2 3278 29x4 2549 2185 2.68 >42833 0332 0664 0996 1328 1660 2-93 >5I5I7 0366 0731 1097 1462 1828 ,00331,9 2987 2655 2323 1991 ,00365,6 3290 2925 25 59 2194 2.69 >43J56 0333 0666 1000 1 3 3 3 1666 2.94 >5 1 883 0367 0734 I IOI 1468 1836 >00333,2 2999 2666 2332 1999 ,00367,1 3304 2937 2570 2203 2.70 ,43490 0334 0669 1003 x338 1672 2.95 ,52250 0369 0 737 1 106 x474 1843 >00334,4 3OI° 2675 2341 2006 ,00368,5 3 3 1 7 2948 2580 22x1 2.71 ,43824 0336 0671 1007 1343 1679 2.96 ,52618 0370 0740 1 1 10 1480 1850 >oo335>7 3021 2686 2350 2014 ,00369,9 3329 2959 2589 2219 2 . 72 >44159 0337 0674 1 0 1 1 x348 1686 2.97 ,52988 0371 0743 1 1 14 i486 1857 >00337,1 3034 2697 2360 2023 >00371,4 3343 2971 2600 2228 2-73 >44496 0338 0676 1015 1 353 1691 2.98 >5336o 0373 0746 1119 x492 1865 >00338,2 3044 2706 2367 2029 >00372,9 3356 2983 2610 2237 2.74 ,44835 0340 0679 1019 1358 1698 2.99 >53732 0374 0749 112 7 1498 1872 >00339,6 3056 2717 2377| 2038 | ,00374,4 337° 2995 2620 224.6 55 1 expressive of the law of human mortality, &c. General Table I. X ( al°), X f 1 ~ — ). \ a — i ' X (a10) ul~a \ 1 9 2 8 3 7 4 6 5 (a-L.i ) I .00 ,54107 ,00 0376 0752 1127 *503 1879 ,00375,8 3382 3006 2631 2255 I .OI >544^3 03 77 0755 1132 1510 t-s OO 00 ►— « >00377,4 3397 3019 2642 2264 I .02 ,54860 0379 0757 1 136 *5*5 *894 ,00378,7 3408 3030 265 1 2273 I .03 >55239 0380 0761 1 141 1521 1902 • ,00380,3 3423 3042 2662 2282 I .04 >556*9 0382 0764 1 146 1528 1910 ,00381,9 3437 3055 2673 2291 1 .05 ,56001 0383 0767 1 150 *533 *9*7 ,00383,3 345° 3066 2683 2300 I .06 ,56384 0385 0770 **55 *54o *925 ,00384,9 3464 3079 2694 2309 I .07 >56769 0386 0 773 **59 *546 1932 ,00386,4 3478 3091 2705 2318 I .08 >57^6 0388 0776 1 164 *552 *940 ,00388,0 3492 3*04 2716 1 2328 I .09 >57544 0389 0779 1 168 1558 *947 ,00389,4 3505 3**5 2726 2336 T. io >57933 °39* 0782 **73 1564 *955 ,00391,0 35*9 3128 2 737 2346 T . 1 1 ,58324 0393 0785 1 178 *57o 1963 >00392,5 3533 3*4° 2748 2355 1 . 12 >58717 0394 0788 1183 *577 *97* ,00394,2 3548 3*54 27 59 2365 * -*3 >59 1 1 1 0396 0792 1188 *584 1980 >00395,9 3563 3*67 277* -375 I . \L. >59507 0 397 0794 **9* 1588 1986 ,00397,1 3574 3*77 2780 2383 *•*5 >59904 0399 0798 1 196 *595 *994 ,00398,8 3589 3*9° 2792 2 393 1 . 16 >60303 0401 0801 1 202 1602 2003 ,00400,3 3605 3204 2804 2403 *•» 7 ,60703 0402 0804 1 206 1608 201 1 ,00402,1 3619 3217 2815 24*3 1 . 18 ,61 105 0404 0827 1 2 1 1 1615 2019 ,00403,7 3633 3230 2826 2422 1. 19 ,61509 0405 081 1 1216 162 1 2027 ,00405,3 3648 3242 2837 j 2432 T.20 ,61914 °4°7 0814 1221 1628 2035 ,00406,9 3662 3255 2848 2441 I. 21 ,62321 0409 0817 I 226 1634 2043 ,00408,5 3677 3268 2860 J 245* T. 22 ,62729 0410 0820 *230 1640 205 1 ,00410,1 3691 3281 2871 2461 I.23 ,63140 041 2 0824 *235 I 1647 2059 ,0041 1,8 3706 3294 2883 2471 I. 24 >6355* 04*3 0826 *239 1652 2066 ,00413,1 l 37*8 3305 2892 ' 2489 A(a10) 1 1 9 2 8 3 7 4 6 5 l aL.il 1. 25 ,63964 ,00 04*5 0831 1 246 1661 2077 ,00415,3 3748 3322 2907 2492 1 . 26 ,64380 04*7 0833 1250 1667 2084 ,00416,7 375° 3334 29*7 2500 1. 27 ,64796 0418 0837 *255 1674 2092 ,0041 8,4 3766 3347 2929 2510 7.28 ,65215 0420 0840 1 260 1680 2100 ,00420,0 3780 3360 2940 2520 7.29 >65635 0422 0843 1265 1687 2109 ,00421,7 3795 3374 2952 2530 7.30 ,66056 0423 0847 1 270 1693 2117 ,00423,3 3810 3386 2963 2540 *•3* ,66480 0425 0850 1275 1700 2125 ,00425,0 3825 34oo 2975 2550 * .32 ,66905 042/ 0853 1280 *707 2134 ,00426,7 3840 34*4 2987 2560 *•33 >6733* 0428 0857 1285 1714 2143 ,00428,4 3856 3427 2 999 2570 *•34 ,67760 0430 0860 1 290 1720 2151 >00430,1 387* 344* 3°* * 258 1 *•35 ,68190 0432 0863 *295 1727 2159 >00431,7 3885 3454 3022 2590 * .36 ,68622 0434 0868 1302 1736 2170 ,00434,0 39°6 3472 3038 2604 *•37 ,69056 0435 0869 *304 *739 2*74 ,00434,7 39*2 3478 3043 2608 *-00437,0 3933 3496 3059 2622 *•39 ,69927 0439 0877 *3*6 *755 2*94 ,00438,7 3948 35*o 307* 2032 7.40 ,70366 0440 0881 1321 1 762 2202 ,00440,4 3964 3523 3083 2642 1 .41 ,70806 0442 0884 1326 1768 221 1 ,00442,1 3979 3537 3095 2653 7.42 >71249 0444 0888 *33* *775 2219 >00443,8 3994 35 5° 3*07 2663 *•43 ,71692 0445 0890 *335 1780 2225 ,00445,0 4005 3560 3**5 2670 *•44 >/2*37 0448 0896 *344 *792 2240 ,00448,0 4032 00 3*36 2688 *•45 >72585 0449 0898 *347 *796 2246 ,00449,1 4042 3593 3*44 2695 1 .46 >73035 045* 0902 *352 1803 2 2 c 4. ,00450,8 4057 3606 3*56 2705 J T *•47 >73485 0453 0905 *358 1811 2264 ,00452,7 4074 3622 3*69 2716 7.48 >73938 0454 0909 1363 1 8 1 8 2272 ,00454,4 4090 3635 3*8* 2726 *•49 >74393 0456 0912 1368 1824 228 1 ,00456,1 4*05 3649 3*93 2737 55 2 Mr. Gompertz on the nature of the function General Table 1. A (. a'° ), A A(a’°) /i— aIO\ 1 9 2 8 3 7 4 6 5 \(a10) 1 9 2 8 3 7 4 6 5 (a-1— J I.50 ,74.849 ,00 0458 0916 *374 1832 2290 *•75 ,86842 ,00 0504 1007 1511 2015 25 '9 ,00458,0 4122 3664 3206 2748 ,00503,7 4533 4°3° 3526 3022 1.51 ,75307 0460 0920 '379 i839 2299 1 .76 ,87346 0506 1 0 1 1 1517 2022 2528 ,00459,8 4 '38 3678 3219 2759 ,00505,6 455° 4°45 3539 3034 1.52 ,75766 0462 0923 '385 1 846 2308 1.77 ,87851 °5°7 101 5 1522 2030 2537 ,00461,6 4154 3693 3231 2770 ,00507,4 4567 4059 3552 3°44 1 *53 ,76228 0463 0927 1390 1853 23 «7 1 .78 ,88359 °5°9 1019 1528 2038 2547 ,00463,3 4I7° 3706 3243 2780 ,00509,4 4585 4075 3566 3056 1 *54 ,76691 0465 0930 1396 1861 2326 1.79 ,88868 05 1 1 1022 *534 2045 2556 ,00465,2 4187 3722 3256 2791 ,005 I 1,2 4611 4090 3578 3067 '•55 >77'56 0467 0933 1400 1 867 2334 1. 80 ,89379 °5'3 1026 '539 2052 25 66 ,00466,7 4200 3734 3267 2800 >00513,1 4618 4'°5 3592 3 °79 x .56 ,77623 0469 0938 I4°7 1876 2345 1 .81 ,89892 °5'5 1030 '545 2060 *575 ,00469,0 4221 3752 3283 2814 ,00515,0 4635 4120 3605 3°9° 1 *57 ,78092 0470 °94I 141 1 1882 2352 1 .82 ,90407 0517 io34 1550 2067 2584 ,00470,4 4234 3763 3293 2822 ,005 l6,8 4651 4*34 3618 3'oi 1 .58 ,78562 0472 °945 1417 1890 2362 1.83 >90924 °5'9 1038 '556 2075 2594 ,00472,4 4252 3779 3307 2834 ,005 l8,8 4669 4x50 3632 3"3 T.59 >79°35 0474 0948 1422 1896 2371 1 .84 >9' 443 0521 1041 1562 2082 2603 ,00474,1 4267 3793 3 3 1 9 2845 ,00520,6 4685 4165 3644 3124 I.60 ,79509 0476 0952 1428 1904 2380 I.85 ,91964 0523 1045 1568 2090 2613 ,00476,0 4284 3808 3332 2856 ,00522,6 4703 4181 3658 3136 T.61 >79985 0478 0956 H33 191 1 2389 x .86 ,92486 0524 I049 '573 2098 2622 ,00477,8 4300 3832 3345 2867 ,00524,4 4720 4'95 3671 3*46 1. 62 ,80463 0480 °959 '439 1918 2398 1 .87 >93011 0526 1052 1578 2104 2631 ,00479,6 4316 3837 3357 2878 ,00526,1 4735 4209 3683 3'57 1. 63 ,80942 0482 0963 '445 1926 2408 1.88 >93537 0528 x°57 1585 ZI13 2642 ,00481,5 4334 3852 3 3 7 1 2889 ,00528,3 4755 4226 3698 3'7° 7.6 4 ,81424 0483 0967 I45° 1 93 3 24*7 1 .89 ,94065 0530 1060 '59° 2 1 20 2650 ,00483,3 435° 3866 3383 2900 ,00530,0 477° 4240 37*o 3180 1. 65 ,81907 0486 °97I *457 '943 2429 T.90 >94595 0532 1064 1596 2128 2660 ,00485,7 43 7 1 3886 34°° 29*4 ,00532,0 4788 4256 3724 3*92 7.66 >82393 0486 0973 1 45 9 '946 2432 1 .91 >95I27 0534 1068 1601 2'35 2669 ,00486,4 4378 3891 34°5 2918 >00533,8 4804 4270 3737 3203 7.67 ,82879 0489 0978 1466 '955 2444 x .92 ,95661 0536 1072 1607 2143 2679 ,00488,8 4399 39IQ 3422 2933 >00535,8 4822 4286 375' 3215 7.68 ,83368 0492 0983 H75 '967 2459 '•93 ,96197 0538 io75 1613 2150 2683 ,00491,7 4425 3934 3442 2950 ,00537,6 4838 4301 3763 3226 7.69 ,83859 °493 0985 1478 1970 2463 1.94 >96734 0540 1079 1619 2158 2698 ,00492,5 4433 394° 3448 2955 ,00539,6 4826 43' 7 3777 3238 7.7c >84351 °494 0989 '483 1978 2472 '•95 >97274 0541 1083 1624 2 l66 2707 ,00494,4 4450 3955 346i 2966 >0054*>4 4873 433' 3790 3248 7.71 ,84846 0496 °993 1489 1985 2482 1 .96 >97815 0543 1087 1630 2173 2717 ,00496,3 4467 3970 3474 2978 >°°543>3 4890 4346 37°3 3260 7.72 >85342 0498 0996 *494 1992 249 1 1.97 >98359 0545 1090 1636 2l8l 2726 ,00498,1 4483 3985 3487 2989 >°°545>2 4907 4362 37 »6 327' 7 .73 ,85840 0500 1000 1 500 2000 2500 1 .98 ,98904 0547 1094 1642 2189 2736 ,00499,9 4499 3999 3499 2999 ,00547,2 4925 4378 3830 3283 7.74 ,86340 0502 1004 1 506 2008 2510 *•99 >99451 ,00501,9 45 '7 4005 35 1 3 3011 expressive of the law of human mortality , &c. 553 General Table II. X (a7), X / 1 ). \ a — i ' 554 Mr. Gompertz on the nature of the junction General Table II. X (a7),\ (L^L). v \ a —i / ( 1 a 7 \ 1 9 2 8 3 7 4 6 5 X(«7) J*-«7\ 1 9 2 8 3 7 4 6 5 U L_iJ te) 3*5° 1,89283 ,00 0252 0504 0756 1008 1260 3*75 *>95767 ,00 0268 0536 0804 1072 1340 ,00252,0 2268 2016 1764 1512 ,00268,0 2412 2 144 1876 1608 3-5i *>89535 0253 °5°5 07 58 1010 1263 3-76 1,96035 0269 0537 0806 *074 *343 ,00252,6 2273 2021 1768 1516 ,00268,5 2417 2148 1 880 161 1 3-52 1,89787 0253 0506 0759 1012 1266 3-77 *,96303 0269 °539 0808 *077 *347 ,00253,1 2278 2025 1772 1519 ,00269,3 2424 2*54 1885 1616 3-53 i ,90040 0254 °5°7 0761 101 5 1269 3-78 1,96573 0270 °54° 0810 1080 *35° ,00253,7 2283 2030 *7/6 1522 ,00270,0 2430 2160 1 890 1620 3-54 1,90294 0254 0509 0763 1017 1272 3-79 1,96843 0271 °54* 0812 1083 *354 ,00254,3 2289 2034 1780 1526 ,00270,7 2436 2166 *895 1624 3-55 1,90548 0255 0510 0765 1020 1275 3.80 *>97**3 0271 0543 0814 1085 *357 ,00255,0 2295 2040 *785 *530 ,00271,3 2442 2170 *899 1628 3-56 1,90803 0256 05 1 1 0767 1022 1278 3.81 *>97385 0272 0544 0816 1088 * 36* ,00255,5 2300 2044 1789 *533 ,00272,1 2449 2* 77 *9°5 *633 3-57 1,9x059 0256 0512 0769 1025 1281 3.82 *,97657 0273 0546 0819 1092 *365 ,00256,2 2306 2050 *793 *537 ,00272,9 2456 2183 1910 *637 3-58 1 >9*315 0257 0514 0770 1027 1284 3-83 1,97930 0273 °547 0820 *°94 1367 ,00256,8 2311 2054 1798 *54* ,00273,4 2461 2187 *9*4 1640 3-59 1,91572 0257 °5*5 0772 1030 1287 3-84 1,98203 0274 °549 0823 *°97 *372 ,00257,4 23*7 2059 1802 *544 ,00274,3 2469 2*94 1920 1646 3.6° 1,91829 0258 0516 °774 1032 1 290 3 * 85 *>98477 0275 °55° 0825 1 100 *375 ,00258,0 •2322 2064 1 806 1548 ,00275,0 2475 22CO 1925 1650 3.61 1,92087 0259 0517 0776 *035 *294 3.86 *>98752 0276 O552 0827 1103 *379 ,00258,7 2328 2070 1811 1552 ,00275,8 2482 2206 *93* 1655 3.62 1,92346 0259 0518 0778 *°37 1 296 3-87 1,99028 0277 °553 0830 1 106 *383 ,00259,2 2333 2074 1814 *555 ,00276,5 2489 2212 *936 1659 3*63 1,92605 0260 0520 0780 1040 * 3°° 3.88 *,99305 0277 °555 0832 1 109 1387 ,00259,9 2339 2 079 1819 *559 >00277,3 2496 2218 *941 1664 3-64 1,92865 0261 0521 0782 1042 *303 3-89 1,99582 0278 0556 0834 1 1 12 1390 ,00260,6 2345 2085 1824 1564 ,00278,0 2502 2224 *946 1668 3-65 i^,93 1 25 0261 0522 0784 *°45 1306 3-9° 1,99860 0279 0558 0836 * * *5 *394 ,00261,2 235* 2090 1 828 *5 67 ,00278,8 2509 2230 1952 *673 3.66 *>93387 0262 0524 0785 1047 1309 3-9* ,00*39 0280 °559 0839 1118 *398 ,00261,8 2356 2094 i833 *57* ,00279,5 2516 2236 *957 1677 3-67 1,93648 0263 0525 0788 1050 *3*3 3-92 ,004 1 8 0280 0561 084 1 1121 1402 ,00262,5 2363 2100 1838 *575 ,00280,3 2523 2242 1962 1682 3.6S 1 >939 1 1 0263 0526 0790 *°53 1316 3-93 ,00699 0281 0562 0843 1 124 1406 ,00263,2 2369 2106 1842 *579 ,00281,1 2530 2249 1968 1687 3-6$ 1 >94*74 0264 0528 0791 1055 *3*9 3 >94 ,00980 0282 0564 0846 1 1 28 1410 ,00263,8 2374 2110 1847 *583 ,00281,9 2537 2255 *973 1691 3*7C 1,94438 0264 0529 °793 1058 1322 3-95 ,01262 0283 0565 0848 113* 1414 ,00264,4 2380 2115 1851 1586 ,00282,7 2544 2262 *979 1696 3 * 7 ^ 1,94702 0265 0530 0795 1060 1326 3-96 ,0*544 0283 0567 0850 **34 *417 ,00265,1 2386 2121 1856 *59* ,00283,4 2551 2267 1984 1700 3«7S x *>94967 0266 0532 0797 1063 1329 3-97 ,01828 0284 0568 0853 i*37 1421 ,00265,$: 2392 2126 1861 *595 ,00284,2 2558 2274 1989 1705 3*7: *>95233 0267 0533 0800 1066 *333 3-98 ,02112 0285 0570 0855 1140 1425 ,00266,1; 2 399 2132 1 866 *599 ,00285,0 2565 2280 *995 1710 3*7' I- *>955°° 0267 0534 0802 1069 1336 3-95 >02397 0286 0572 0858 **44 ‘430 ,00267,2 2405 2138 1 870 1603 ,00285,9 1 2573 2287 2001 *7*5 555 expressive of the law of human mortality , &c. General Table II. X ( a 7), X Ma7) 1 9 2 8 3 7 4 6 5 Ha?) 1 9 2 8 3 7 4 6 5 [a-1 — 1 ) la-l-ij 2.00 ,02683 ,00 0287 °573 0860 1 x47 1434 2.25 ,10107 ,00 0309 0618 0926 1235 1544 ,00286,7 2580 2294 2007 1720 ,00308,8 2 779 2470 2162 1853 2.01 ,02960 0288 °575 0863 1150 H38 2,26 ,10416 0310 0620 0929 1239 1549 ,00287,5 2588 2300 2013 1725 ,00309,8 2788 2478 2169 1859 2.02 >°3257 0288 0577 0865 1 *53 H42 2.27 ,10726 0311 0621 0932 1243 1554 ,00288,3 2595 2306 2018 »73° ,00310,7 2796 2486 2175 1864 2.03 >°3545 0289 0578 0867 1 1 56 1446 2.28 ,11037 0312 0623 0935 1247 1559 ,00289,1 2602 23 1 3 2024 1 73 5 ,00311,7 2805 2494 2182 1870 2.O4 ,03834 0290 0580 0870 1 160 1450 2.29 ,* 1348 0313 0625 0938 125 1 1564 ,00290,0 2610 2320 2030 I74° ,00312,7 2814 2502 2189 1876 2.O5 ,04124 0291 0582 0872 1163 H54 2.30 ,Il66l 0314 0627 0941 1255 1569 ,00290,8 261 7 2326 2036 1745 ,00313,7 2823 2510 2196 1 882 Ml • O ON ,04415 0292 0583 0875 1167 H59 2.31 ,”975 0315 0629 °944 1258 1573 ,00291,7 2625 23 34 2043 1750 ,00314,6 2831 2517 2202 1888 r^. O IN ,04707 0293 0585 0878 1170 J463 2.32 ,12289 0316 0631 0947 1262 1578 ,00292,5 2 633 234° 2048 *755 ,00315,6 2840 2525 2209 i894 N| • O OO ,04999 0293 0587 0880 ”74 1467 2.33 ,12605 0317 0633 0950 1267 1583 ,00293,4 2641 2347 2054 1760 ,00316,7 2850 2534 2216 1900 2.09 ,05293 0294 0588 0883 11 77 i47i 2-34 ,12921 0318 0635 0953 1271 j589 ,00294,2 2648 2354 2059 1765 ,00317,7 2859 (2542 2224 1906 2 . IO ,05587 0295 0590 0885 1 180 1476 2.35 >13239 0319 0637 0956 1275 1594 ,00295,1 2656 2361 2066 1771 ,00318,7 2868 2550 2231 1912 2. I I ,05882 0296 0592 0888 1 184 1480 2.36 >*3558 0320 0639 °959 1279 1 599 ,00296,0 2664 2368 2072 1776 ,00319,7 2877 2558 2238 1918 2.12 ,06178 0297 °594 0890 1 187 H84 2.37 >i3898 0321 0641 0962 1283 1604 ,00296,8 2671 2374 2078 1781 ,00320,7 2886 2566 2245 1924 2.I3 ,06475 0298 0596 0893 1191 H89 2.38 ,14198 0322 0644 0965 1287 1609 ,00297,8 2680 2382 2085 1787 ,00321,8 2896 2574 2253 1931 2. 14 ,06772 0299 0597 0896 1194 1493 2*39 ,14520 0323 0646 0968 1291 1614 ,00298,6 2687 2389 2090 1792 ,00322,8 2905 2582 2260 *937 •— < IN ,07071 0300 °5 99 0899 1198 H98 2.40 , 14843 0324 0648 0972 1296 1620 ,00299,5 2696 2396 2097 1 797 ,00323,9 2915 2591 2267 19+3 2 . 16 ,07370 0300 0601 0901 1202 1502 2.41 >15167 0325 0650 0975 1300 1 625 ,00300,4 2704 2403 2103 1802 ,00324,9 2924 2599 2274 1949 2.17 ,07671 0301 0603 0904 I2O5 1507 2.42 ,15492 0326 0652 0978 1304 1630 ,00301,3 2712 2410 2109 iSo8 >00325,9 2933 2607 2281 1 95 5 2.18 ,07972 0302 0604 0907 1209 1 5 1 1 2.43 ,15818 0327 0654 0981 1308 1636 ,00302,2 2720 2418 2115 1813 ,00327,1 2944 2617 2290 1963 2. 19 ,08274 0303 0606 0902 1212 1516 2.44 ,16145 0328 0656 0984 1312 1 64 1 ,00303,1 2728 2425 2122 1819 ,00328,1 2953 2625 2297 l969 2.20 >o8577 0304 0608 0912 I2l6 1521 2-45 >i6473 0329 0658 0988 1317 1646 ,00304,1 2 737 2433 2I29 I 825 ,00329,2 2963 2634 2304 1 97 5 2.21 ,08882 0305 0610 O9I5 1220 1525 2.46 ,16802 0330 0661 0991 1321 1652 ,00305,0 2745 2440 2135 1830 >00330,3 2973 2642 2312 1 982 2.22 ,09187 0306 0612 091 8 I 224 iS3° 2-47 >17132 0331 0663 0994 1326 i657 ,00305,9 2753 2447 2141 i835 ,00331,, 4 2983 265 1 2320 1988 2.23 >09493 0307 0614 0921 1228 1 535 2.48 ,17464 0333 0665 0998 1 33° 1663 ,00306,9 2762 2455 2148 1 841 ,00332,5 2993 2660 2328 1 995 2.24 ,09799 0308 06 1 6 0923 1231 1539 2-49 » 1 7796 0334 0667 1001 1 334 1668 ,00307,8 2770 2462 2155 ,847 ,00333,6 3002 2669 2335 2002 4 C MDCCCXXV. 5 56 Mr. Gompertz on the nature of the function General Table II. X (aT), X /T=^). H?) 41-"7) 1 9 2 8 3 7 4 6 5 A(°°334>7 3012 2678 2343 2008 >00364,7 3282 2918 25 53 2188 2.51 , 1 8464 0336 0672 1007 1343 1679 2 .76 >27214 0366 0732 io99 H65 1831 >00335,8 3022 2686 2351 2015 ,00366,2 3296 2930 2563 2197 2.52 ,18880 0337 0674 101 1 *348 1685 2.77 >27581 0367 0735 1102 1470 i837 >00336,9 3032 2695 2358 2021 ,00367,4 3307 2939 2572 2204 2. 53 >I9I37 0338 0676 1014 1352 1691 2.78 ,27948 0369 °737 1106 H75 1 844 >00338,1 3043 2705 2367 2029 ,00368,7 33i8 2950 2581 2212 2.54 jI9475 0339 0678 1018 1 35 7 1696 2.79 >28317 0370 0740 11 10 1480 1851 >00339,2 3053 2714 2374 2035 / ,00370,1 333i 2961 2591 2221 2 '55 ,19815 0340 0681 1021 1362 1702 2.80 ,28687 0370 0743 1 1 14 1485 1857 >00340,4 3064 2723 2383 2042 >00371,3 3343 2970 2599 2228 2.56 ,20155 0342 0683 1025 1366 1708 2.8l ,29058 0373 0746 1 1 18 f49l 1864 ,00341,5 3074 2732 2391 2049 ,00372,8 3355 2982 2610 2237 2.57 ,20496 °343 0685 1028 1371 1714 2 . 82 >2943I 0374 0748 1122 J496 1870 >00342,7 3084 2742 2359 2056 >00373,9 3365 2991 2617 2243 2.58 ,20839 0344 0688 1032 1376 172c 2.83 ,29805 0 375 0751 1 126 1502 18 77 >°°343>9 3095 2751 2407 2063 >00375,4 3379 3003 2628 2252 2.59 ,21 183 0345 0690 ID35 1380 !7Z5 2 , 8^. ,30180 0377 0753 1130 1507 1884 >00345,0 3105 2760 2415 2070 ,00376,7 339° 3014 2637 2260 2.60 ,21528 0346 0692 1039 1385 J73 1 2.85 >30557 0378 0756 1 *34 1512 1891 ,00346,2 3116 2770 2423 2077 ,00378,1 3403 3025 2647 2269 2.61 ,21874 °347 0695 1042 1390 l737 2.86 >30935 °379 °759 113S 1518 1897 ,00347,4 3127 2 779 2432 2084 >00379,4 3415 3035 2656 2276 2.62 ,22222 0349 0697 1046 1 395 J744 2 . 87 >3I3I4 0381 0762 1 142 1523 J9° 4 ,00348,7 3138 2 79° 2441 2092 ,00380,8 3427 3046 2666 2285 2.6; ,22570 0350 0699 I049 1 399 *749 2 . 88 >31695 0382 0764 1 146 1529 191 1 >00349,7 3H7 2798 2448 2098 ,00382,2 3440 3°58 2675 2293 2.64 ,22920 0351 0702 io53 1404 1756 2.89 >32077 0384 0767 U5I 1534 1918 >00351,1 3160 2809 2458 2107 ,00383,6 3452 3069 2685 2302 2.65 ,23271 0352 0705 io57 H°9 1762 2.90 ,32461 0385 0770 H55 1540 J925 >00352,3 3i?i 2818 2466 2113 ,00385,0 3465 3080 2695 2310 2.66 ,23623 °354 0707 1061 >4>4 1768 r~2 .91 >32846 0386 0773 n59 1 545 1932 >oo353>5 3182 2828 2475 2121 ,00386,3 3477 3090 2704 2318 2.67 >23977 °355 0709 1064 14.19 J774 2.92 >33232 0388 0776 11 63 i55i 1 939 >00354,7 3*9Z 2838 2483 2128 >00387,8 349° 3102 2715 2327 2.68 ,24332 0356 0712 1068 M24 1780 2.93 >33620 0389 0778 1168 1 5 5 7 1946 ,00356,0 3204 284b 2492 2136 ,00389,2 3503 3114 2724 2335 2.69 ,24688 0357 0714 1072 1429 1786 2.94 ,34009 0391 0781 1172 1562 1 95 3 ,00357,2 3215 2858 2500 2143 ,00390,6 35 1 5 3I25 2734 2344 2.70 >25045 0358 0717 1075 M34 x792 2.95 ,34400 0392 0784 1 176 1568 i960 >00358,4 3226 2867 2509 2150 ,00392,0 3528 3J36 2744 2352 2.71 >254°3 0360 0719 1079 H39 1799 2.96 >34792 0394 0787 1181 1574 1968 ,00359,7 3237 2878 2518 2158 >00393,5 3542 3‘48 2755 2361 2.72 ,25763 0361 0722 1083 1444 1805 2.97 >35 1 85 0395 0790 1 185 1580 *975 ,00361,0 3249 2888 2527 2166 >00394,9 3554 3 1 59 2764 2369 2.73 ,26124 0362 0724. 1087 H49 181 1 2.98 >3558o 0396 0793 j 189 1585 1982 ,00362,2 3260 2898 2535 2173 ,00396,3 3567 3I7° 2774 2378 2.74 ,26486 0364 0727 1 09 1 *454 1817 2.99 >35976 o398 0796 1193 1591 *989 ,00363,5 3272 2908 2545 2181 >00397,8 358° 3182 2785 2387 557 expressive of the law of human mortality , &c. General Table II. X (a1), X ( \ V • X[a7) 1 9 2 8 3 7 4 6 5 a (a7) 1 9 2 8 3 7 4 6 5 '<2 L_i ) T.oo >36374 ,00 0399 °7 99 1 198 1597 1 997 1. 25 ,4881 1 >00 I °43 8 0876 13H 1752 2190 ,o°399,3 3594 3*94 2795 2396 ,00438,0 3942 35°4 3066 2628 i .01 >36773 0401 q8qi 1 202 1603 2004 1. 26 ,47249 °439 0879 1318 1758 2197 ,00400,7 3606 3206 2805 2404 ,00439,4 3955 3515 3076 2636 1 .02 >37*74 0402 0804 1207 i6og 201 1 1.27 ,47689 0441 0882 1324 1765 2206 ,00402,2 3620 3218 28 1 5 2413 ,00441,2 397i 3530 3088 2647 1.03 >37576 0404 0807 1211 1615 2019 1 . 28 >48130 0443 0886 1329 1772 2215 >00403,7 3633 3230 2826 2422 ,00442,9 3986 3543 3100 2657 T.04 >3798o °4°5 081 1 1216 1622 2027 i-29 >48573 0445 0889 1334 1 77 8 2223 ,00405,4 3649 3243 2838 2432 ,00444,5 4001 3556 3112 2667 I.05 >38385 0406 0813 1219 1626 2032 T.30 >49° 1 7 0446 0892 1339 1785 2231 ,00406,4 3658 3251 2845 2438 ,00446,2 4016 357 0 3123 2677 i .06 >38792 0408 0816 1225 1633 2041 TTJr >49463 0448 0896 1343 i79i 2239 ,00408,2 3674 3266 2857 2449 ,00447,8 4030 3582 3135 2687 1 .07 >39200 0410 0819 1229 1639 2050 1.32 ,49911 0450 0899 1349 1798 2248 ,00409,7 3687 3278 2868 2458 ,00449,5 4046 3596 3H7 2697 1 .08 ,39610 041 1 0822 1234 1645 2056 i-33 ,50361 0451 0902 1353 1804 2256 ,0041 1,2 37°i 329° 2878 2467 ,0045 1,1 4060 3609 3158 2707 i .09 ,4002 i 04i3 0826 1238 1651 2064 i-34 ,50812 °453 0909 1359 1812 2265 ,00412,8 3715 3302 2890 2477 ,00452,9 4076 3623 3*7° 2717 T. 10 >40434 0414 0828 1243 1657 2071 *•35 >51265 °455 0909 1364 1818 2273 ,00414,2 3728 33H 2899 2485 >00454,5 4090 3636 3182 2727 7. 1 1 ,40848 0416 0832 1247 1663 2079 1. 36 ,51719 0456 0912 1369 1825 2281 ,00415,8 3742 3326 291 1 2495 ,00456,2 4106 3650 3i 93 2 737 1.12 ,41264 0417 0835 1 252 1669 2087 1 - 37 >52175 0458 0916 1373 1831 2289 >00417,3 3756 333 8 292 1 2504 ,00457,8 4120 3662 3205 2747 1 - *3 ,41681 0419 0838 I257 1 676 2096 1.38 >52633 0460 °9l9 1379 1839 2299 ,00419,1 3772 3353 2934 2515 >00459,7 4137 3 678 3218 2758 1 . 14 ,42100 0420 0840 1261 1 68 1 2101 i-39 >53093 0461 0923 1384 1 846 2307 ,00420,2 3782 3362 2941 2521 ,00461,4 4i53 3691 3230 2768 * • *5 ,42520 0422 0844 1266 1688 21 10 T.40 >53554 0463 0926 1389 1852 2315 ,00421,9 3797 3375 2953 253i ,00462,9 4166 3703 3240 2 777 1 . 16 >42942 0424 0847 1271 1694 2118 1 .41 >54017 0465 09301 1394 1859 2324 ,00423,6 3812 3389 2965 2542 ,00464,8 4183 37i8 3254 2789 1.17 >43366 0425 0850 1275 1700 2126 1 .42 ,54482 0467 °933 1400 1866 2333 ,00425,1 3826 34oi 2976 2551 ,00466,5 4199 3732 3266 2799 1 . 1 8 >4379* 0427 0854 1280 1707 2134 i-43 ,54948 0468 0936 1404 1 872 2341 ,00426,8 3841 34H 2988 2561 ,00468,1 4213 3745 32 77 2809 1 . 19 ,442 i 8 0428 0856 1284 1712 2141 i-44 >55417 0470 0940 1410 1880 2350 ,00428,1 3853 3425 2997 2569 ,00469,9 4229 3759 3289 2819 7.20 ,44646 0430 0860 1250 1720 2150 i-45 ,55886 | °472 °943 1415 1887 2359 ,00429,9 3869 3439 3009 2579 ,00471 >7 4245 3774 3302 2830 1 . 21 >45°76 0432 0863 1 295 1726 2158 1.46 >56358 0474 °947 1421 1894 2368 ,00431,5 3884 345 2 3021 2589 >00473,6 4262 3789 33i5 2842 1 .22 >455°7 0433 0866 I299 1732 2166 1.47 >56832 °475 0950 1425 1900 2376 >00433,1 3898 3465 3032 2599 >00475,1 4276 3801 33 26 2851 1.23 ,45940 0435 0869 1304 1739 2174 7.48 >57307 0477 0954 1431 1901 2385 ,00434,7 3912 3478 3043 2608 ,00476,9 4292 3815 333 8 2861 7.24 >46375 0436 0873 1309 1745 2182 i-49 >57784 0479 °957 1436 1915 2394 ,00436,3 3927 349° 3054 2618 ,00478,7 4308 3830 335 1 2872 558 Mr. Gompertz on the nature of the function General Table II. A (a7), X \ a — i »(«») 1 9 2 8 3 7 4 6 5 K*7) lw*-fl7\ 1 9 2 8 3 7 4 6 5 a-t_i J Vi-i) 1.50 >58262 ,00 0480 0960 *44* 1921 2401 *•75 ,70810 ,00 0526 1052 1578 2104 2630 >00480,2 4322 3842 3361 2881 ,00526,0 4734 4208 3682 3*56 1.51 ,58742 0482 0964 *447 *929 241 1 1 .76 ,71336 0527 1055 1582 2109 2637 _ ,00482,2 4340 3858 3375 2893 ,00527,3 4746 4218 3691 3*64 1.52 ,59225 0484 0968 1452 1936 2420 *•77 ,7*863 0530 *059 1589 2118 2648 ,00483,9 4355 387* 3387 2903 ,00529,6 4766 4237 3707 3*78 1 *53 ,59709 0486 0971 *457 *943 2429 1 .78 ,72392 °53* 1062 *593 2124 2655 ,00485,7 437* 3886 3400 2914 ,00531,0 4779 4248 37*7 3*86 1.54 ,60194 0487 0975 1462 *95° 2437 *•79 ,72924 °533 1067 1600 2*33 2667 ,00487,4 4387 3899 34*2 2924 >°°533>3 4800 4266 3733 3200 *•55 ,60682 0489 0979 1468 *957 2447 1. 80 >73457 0535 1069 1604 2*39 2674 ,00489,3 4404 39*4 3425 2936 >°°534>7 4812 4278 3743 3208 T.56 ,61171 °49* 0982 *473 1964 2456 1 .81 >73992 0536 1072 1608 2*44 2681 ,00491,1 4420 3929 3438 2947 ,00536,1 4825 4289 3753 3217 *•57 ,61662 °493 0985 1478 *97* 2464 1 .82 >74528 0539 *0 77 1616 2*54 2693 ,00492,7 4434 3942 3449 2956 ,00538,5 4847 4308 377° 3231 T . 5 8 ,62155 °495 0989 *484 *978 2473 1.83 >75067 0541 1081 1622 2163 2704 ,00494,6 445* 3957 3462 2968 ,00540,7 48 66 4326 378s 3244 *•59 ,62649 0496 0993 *489 1986 2482 1 . 84 ,75608 0542 1085 1627 2169 2712 ,00496,4 4468 397* 3475 2978 ,00542,3 4881 4338 3796 3254 T .60 ,63146 0498 09 97 *495 *993 2492 1. 85 ,76150 0544 1088 1632 2176 2721 ,00498,3 4485 3986 3488 2990 >00544,1 4897 4353 3809 3265 1. 61 ,63644 0500 1000 1500 2000 2500 1.86 ,76694 0546 1092 *638 2184 273* ,00500,0 45°° 4000 3500 3000 ,00546,1 49*5 4369 3823 32 77 1 .62 >64*44 0502 1004 *505 2007 2509 1.87 >77240 0548 1096 1644 2192 2741 ,00501,8 45*6 4014 35*3 3°* * ,00548,1 4933 4385 38 37 3289 1.63 ,64646 °5°4 1007 151 1 2015 25*9 i.88 >77788 0550 1100 1650 2200 2750 ,00503,7 4533 4030 3526 3022 ,00550,0 4950 4400 3850 33oo I.64 ,65150 0505 101 1 1516 2021 2527 1.89 >78338 0551 1103 *654 2206 2757 ,00505,3 4548 4042 3537 3°32 >o°5 5* >4 4963 44** 3860 3308 T.65 ,65655 °5°7 101 5 1522 2030 2537 I.90 ,78889 0554 1 108 1661 2215 2769 ,00507,4 4567 4°59 3552 3°44 ,00553,8 4984 443° 3877 3323 i . 66 ,66162 0509 1018 1527 2036 2546 1.91 >79443 1 0556 1 1 1 1 1667 2222 2778 ,00509,1 4582 4°73 3564 3°55 >°°555>5 5000 4444 3889 3333 1 .67 ,66671 0511 1022 *533 2044 2555 i .92 >79999 0 557 1115 1672 2229 2787 ,0051 1,0 4599 4088 3577 3066 ,00557,3 5016 4458 3901 3344 1 .68 ,67182 05*3 1025 1538 2051 2564 *•93 ,80556 0560 1 1 19 *679 2238 2798 ,00512,7 4614 4102 3589 3076 >00559,5 5036 4476 39*7 3357 r .69 ,67695 05* 5 1029 *544 2058 2573 *•94 ,81116 0561 1122 *683 2244 2805 ,00514,6 463* 4**7 3602 3088 ,00561,0 5049 4488 3927 3366 1.70 ,68209 05*7 *°33 *55° 2066 2583 *•95 ,81677 0563 1126 1690 2253 2816 ,00516,5 4649 4*32 3616 3°99 ,00563,2 5069 4506 3942 3379 1.71 ,68726 0518 1036 *554 2072 2591 1. 96 ,82240 0565 1129 *694 2258 2823 ,00518,1 4663 4*45 3627 3089 ,00564,6 5081 45*7 3952 3388 1.72 ,69244 0520 1040 1561 2081 2601 *•97 ,82804 0568 **37 *705 2274 2842 ,00520,2 4682 4162 364* 3*21 ,00568,4 5116 4547 3979 34*9 *•73 ,69764 0522 *044 1566 2088 2610 T.98 >83373 0568 **37 *705 2273 2842 ,00522,0 4698 4176 3654 3*32 ,00568,3 5**5 4546 3978 34*o T.74 ,70286 0524 1047 *57i 2095 2619 *•99 >8394* 1 ,00523,7 47*3 4190 3666 3*42 559 expressive of the law oj human mortality , &c. General Table III. A(tf5), X j-Tj. x(«5); '(£?) 1 9 2 8 3 7 4 6 5 3.00 1,52519 ,00 0266 0533 0 799 1065 *332 ,00266,3 2397 2130 1864 1598 3.01 1,52786 0267 0533 0800 1066 *333 ,00266,5 2399 2132 1 866 *599 3.02 1,53052 0267 0534 0802 1069 1336 ,00267,2 2405 2138 1870 1603 3*03 *>53319 0268 0535 0803 1070 *338 ,00267,5 2408 2140 *873 1605 3 *°4 *>53587 0268 0536 0804 1072 *340 ,00267,9 241 1 2*43 *875 1607 3*®5 *>53855 0268 0537 0805 1073 1342 ,00268,3 2415 2146 1878 1610 3.06 *>54*23 0269 0537 0806 1075 *344 ,00268,7 2418 2 150 1881 1612 3*07 *>54392 0269 0538 0807 1076 1346 ,00269,1 2422 2153 1 8 84 1615 3.08 1,54661 0270 0539 0809 1078 *348 ,00269,5 2426 2156 1887 1617 3*09 1,54930 0270 0540 0810 1080 *35° ,00269,9 2429 2159 1889 1619 3.10 1,55200 0270 °54* 081 1 1081 1352 ,00270,3 2433 2162 1892 1622 3*** *>55470 0271 °54* 0812 1083 *354 ,00270,7 2436 2166 *895 1624 3.12 *>5574* 0271 0542 0814 1085 *356 ,00271,2 244* 2170 1898 1627 3*i3 1,56012 0272 0543 0815 1086 1358 ,00271,6 2444 2*73 1901 1630 3'M- 1,56284 0272 0544 0816 1088 1360 ,00272,0 2448 2176 *904 1632 3 • 1 5 1,56556 0273 0545 0818 1090 *363 ,00272,5 2453 2180 1908 *635 3« 16 1,56828 0273 0546 0819 1092 * 365 ,00272,9 2456 2183 1910 1637 3-i7 1,57101 0273 0547 0820 1093 *367 >00273,3 2460 2186 *9*3 1640 3.18 *>57375 0274 0548 082 1 *°95 *369 ,00273,8 2464 2190 1916 l643 3* *9 1,57648 0274 0548 0823 1097 *57* ,00274,2 2468 2*94 *9*9 *645 3.20 *>57923 0275 0549 0824 *°99 *374 ,00274,7 2472 2198 *923 1648 3*21 *>58197 0275 0550 0825 1 100 *376 ,00275,1 2476 2201 1926 1651 3.22 1,58472 0276 0551 0827 1102 *378 ,00275,6 2480 2205 1929 *654 3*23 1,58748 0276 0552 0828 1 104 1380 ,00276,0 2484 2208 1932 1656 3*24 1,59024 0277 0553 0830 1106 *383 ,00276,5 2489 2212 *936 *659 1 9 00 to 3 7 4 6 5 A ’<2 l—I ) 3-*5 1,59300 ,00 0277 0554 0831 1 108 1385 ,00276,9 2492 2215 *938 1661 3.26 *>59577 0277 0555 0832 1 110 1387 ,00277,4 2497 2219 1942 1664 3*2 7 *>59855 0278 0556 0834 1112 1390 ,00277,9 249* 2223 *945 1667 <-K>l • OO 1,60133 0278 °557 o835 1 1 14 *39* ,00278,4 2507 2227 *949 1670 3-29 1,6041 1 0279 0558 0836 1115 *394 ,00278,8 2509 2230 *952 1673 3-30 1,6 0690 0279 0559 0838 1 1 17 *397 ,00279,3 2514 2234 *955 1676 3-3* i,6oy6g 0280 0560 0839 1 119 *399 ,00279,8 2518 2238 *959 1679 3-32 1,61249 0280 0560 0841 1 121 1401 ,00280,2 2522 2242 1961 1681 3-33 1,61529 0281 0562 0842 1123 *4°4 ,00280,8 2527 2244 1966 1685 3-34 1, 61810 0281 0563 0844 1125 *4°7 ,00281,3 2532 2250 *969 1688 3-35 1,62091 0282 0564 0845 1 127 *4°9 ,00281,8 2536 2254 *973 1691 3-36 1,62373 0282 0564 0847 1129 141 1 ,00282,2 2540 2258 *975 *693 3*37 1,62655 0283 0566 0848 * 131 *4*4 ,00282,8 2545 2262 * 979 *697 3* 38 1,62938 0283 0567 0850 **33 *4*7 ,00283,3 2550 2266 *983 1700 3-39 1,63221 0284 0568 0851 **35 *4*9 ,00283,8 2554 2270 *987 1703 3-4° 1,63505 0284 0569 o853 **37 1422 ,00284,3 2559 2274 1990 1706 3-4* 1,63789 0285 0570 0854 **39 *424 ,00284,8 2561 2278 *994 *7°9 3-42 1,64074 0285 0571 0856 1 141 *427 ,00285,3 2568 2282 *997 1712 3-43 *,64359 0286 0572 0857 1 *43 *429 ,00285,8 2572 2286 2001 *7*5 3*44 1,64645 0286 °573 0859 1 145 *43 2 ,00286,3 2 577 2290 2004 1718 3 • 45 *,6493* 0287 °574 0861 1148 1455 ,00286,9 2582 2295 2008 1721 3-46 1,65218 0287 °575 0862 1 150 *437 ,00287,4 2587 2299 2012 *724 3*47 1,65506 0288 0576 0864 1152 1440 ,00288,0 2592 2304 2016 1728 3*48 *,65794 0289 °577 0866 1154 *443 ,00288,5 2597 2308 2020 *73* 3-49 1,66082 0289 0578 0867 1156 *44? ,00289,0 2601 2312 2023 *734 1 56 o Mr. Gompertz on the nature of the function General Table III. x (a5), A ( Lz^i). V CL — “ I • 1 9 2 8 3 7 4 6 5 H“5) * t1-*5 ) 1 9 1 2 8 3 7 4 6 5 U”— 1 ) Vi-.J 3*5° 1,66371 ,00 0290 0579 0869 1158 1448 3-75 I}73787 ,00 0305 0609 0914 1219 !524 ,00289,6 2606 2317 2027 i738 ,00504,7 2742 2438 2133 1828 3-51 1,66661 0290 0580 0870 1 160 1451 3 -76 1,74091 0305 061 1 0916 1221 I527 ,00290,1 261 1 2321 2031 1741 ,00305,3 2748 2442 2137 1832 3*52 1,6695 1 0291 0581 0872 1163 1454 3-77 1.74393 0306 0612 0918 1224 153° > OO 2^0^^ 2616 2326 2035 1744 ,00306,0 2754 2448 2142 1836 3*53 1,67242 0291 05 8 3 0874 1166 1457 3-78 1,74702 0307 0613 0920 1226 1533 ,00291,4 2623 2331 2040 1748 ,00306,6 2759 2453 2146 1840 3-54 1,67533 0292 °584 0875 1167 1459 3*79 I,75009 0307 0615 0922 1230 1537 ,00291,8 2626 2334 2043 1751 ,00307,4 2767 2459 2152 1844 3-55 1,67825 0292 0585 0 877 1170 1462 3.80 y.753 1 6 0308 0616 0924 1232 I54O ,00292,4 2632 2339 2047 1754 ,00308,0 2772 2464 2156 1848 3*56 T,68i 17 0293 0586 o879 1 172 1465 3.81 1,75624 0309 0618 0926 1235 1544 ,00292,9 2636 2343 2050 1757 ,00308,8 2 779 2470 2162 1853 3-57 1,68410 0294 0587 0881 1175 1469 3 *82 1.75933 0309 0609 0928 1237 1547 ,00293,7 2643 2350 2056 1762 ,00309,3 2784 2474 2165 1856 3*58 1,68704 0294 0588 0882 1 176 i47i 3-83 1,76243 0310 0620 0930 1240 1551 ,00294,1 2647 2333 2059 1765 ,00310,1 2771 248 1 2171 1861 3*59 1,68998 0295 0589 0884 11 79 1474 3-84 1,76553 0311 0622 0932 1243 1554' ,00294,7 2652 2358 2063 1768 ,00310,8 2 797 2486 2176 1865 3.60 1,69293 0295 0591 0886 1181 1477 3 • 85 1,76863 0311 0623 °934 1 246 1557 ,00295,3 2658 2362 2067 1772 ,00311,4 2803 2491 2180 1868 3.61 1,69588 0296 0592 0888 1184 1480 3.86 i,77i75 0312 0624 °937 1249 1561 ,00295,9 2663 2367 2071 1775 ,00312,2 2810 2498 2185 1873 3.62 1,69884 0297 0593 0890 1186 H83 3-87 i,77487 0313 0626 0939 1252 1565 ,00296,5 2669 2372 2076 1779 ,00313,0 2817 2504 2191 1878 3-63 1,70180 0297 0594 0891 1188 i486 3*88 1,77800 0314 0627 0941 1254 1568 ,00297,1 2674 23 77 2080 1783 ,00313,6 2822 2509 2195 1882 3-64 1,70477 0298 0595 0893 1 1 9 1 1489 3-89 1,78113 0314 0629 °943 12 57 1572 ,00297,7 2679 2382 2084 1786 ,00314,3 2829 2514 2200 1886 3-65 *,7°77 5 0298 0597 0895 1194 1492 3*9° 7,78428 0315 0630 0945 1260 1575 ,00298,4 2686 2387 2089 1790 ,00315,0 2835 2520 2205 1890 3.66 I,7io74 0299 °598 0896 1195 1494 3-9i 1,78743 0316 0632 0947 1263 15 79 ,0029,88 2689 2390 2092 1793 ,00315,8 2842 2526 22 1 1 1895 3*67 I,7I372 0300 °599 0899 1 198 i498 3-92 1,79059 0316 0633 0949 1266 1582 ,00299,6 2696 2397 2097 J798 ,00316,4 2848 2531 2215 1898 3.68 1,71672 0300 0600 0901 1201 1501 3*93 1,79375 0317 0635 0952 1 269 1587 ,00300,2 2702 2402 2101 1801 ,00317,3 2856 2538 2221 1904 3‘69 7,7^72 0301 0602 0902 1203 1504 3-94 1,79692 0318 0036 °954 1272 1590 ,00300,8 2707 2406 2106 1805 ,00318,0 2862 2544 2226 1908 3-7° 7,72273 0301 0603 0904 1206 1507 3-95 1, 80010 0319 0637 0956 1275 !594 ,00301,4 2713 241 1 2110 1808 ,00318,7 2868 2550 2231 1912 3*7! i,72574 0302 0604 0906 1 208 1510 3 *96 1,80329 0320 0639 0959 1278 1598 ,00302,0 2718 2416 2114 1812 ,00319,5 2876 2556 2237 1917 3*72 7,72876 0303 0605 0908 1 21 1 i5H 3-97 1,80648 0320 0641 0961 1281 1602 ,00302,7 2724 2422 2119 1816 ,00320,3 2883 2562 2242 1922 3*73 1,73179 0303 0607 0910 1214 1517 3-98 1,80969 0321 0642 0963 1 284 1605 ,00303,4 2731 2427 2124 1 820 ,00321,0 2889 2568 2247 1926 3*74 i,73483 0304 0608 0912 1216 1520 3-99 1,81290 0322 0644 0965 1287 1609 ,00304,0 2736 2432 2128 1824 ,00321,8 2896 2574 2253 1931 expressive of the law of human mortality, &c. 56 1 General Table III. X (a’), A fel.]. \ a — i I *(«*) 1 9 2 8 3 7 4 6 5 W1-"5 1 9 2 8 3 7 4 6 5 la-1.1 [a L_i 2.00 T, 81612 ,00 0323 0645 0968 1290 1613 2. 25 1,89923 ,00 0344 0688 1031 ‘375 1 7‘9 ,00322,5 2903 2580 2258 1 935 ,00343,* 3094 2750 2407 2063 2.01 1,81934 0323 0647 0970 I294 1617 2 . 26 1,90267 0345 0689 ‘034 ‘379 ‘724 ,00323,4 291 1 2587 2264 I94° >°°344>7 3102 2758 24‘3 2068 2.02 1,82257 0324 0648 0973 I297 1621 2 . 27 1,9061 2 0346 0691 1037 ‘383 1729 ,00324,2 2918 2594 2269 1 945 >00345,7 311 1 2766 2420 2074 2.03 1,82582 0325 0650 0975 1300 1625 2.28 1,90958 0347 0693 1040 1386 ‘733 ,00324,9 2924 2599 2274 !949 00346,6 3 1 ‘9 2 773 2426 2080 2.04 1,82907 0326 0652 °977 ‘3°3 1629 2 . 29 1,91304 0348 °6 95 ‘043 1390 ‘738 ,00325,8 2932 2606 2281 1 95 5 • ,00347,6 3128 2781 2433 2086 2.C5 1,83232 0327 0653 098c 1306 1633 2.3O 1,91652 0349 0697 1046 ‘394 ‘743 ,00326,5 2939 2612 2286 ‘959 ,00348,5 3i37 2788 2440 2091 2.06 ‘>83559 0327 0655 0982 ‘3°9 1637 2.3I 1,92000 0349 0699 1048 ‘397 ‘747 ,00327,3 2946 2618 2291 1964 >o°349>3 3M4 2794 2445 2096 2.07 1,83886 0328 0656 0985 ^313 1641 2.32 92349 °35‘ 0701 1052 ‘4°3 ‘754 ,00328,2 2954 2626 2297 ‘969 ,00350,7 3 1 56 2806 245S 2104 2.08 1,84214 0329 0658 0987 1316 l645 2-33 1,92700 °35 1 0703 1054 1406 ‘757 ,00329,0 2961 2632 2303 1974 ,00351,4 3163 2811 2460 2108 2.09 1,84543 °33o 0660 0989 *319 i649 2.34 1,93052 0352 0705 1057 1410 1762 ,00329,8 2968 2638 2309 1979 ,00352,4 3 * 72 2819 2467 21 14 2.10 1,84873 0331 066 1 0992 1322 i6S3 2.35 1,93404 0353 0707 1060 ‘4‘3 ‘767 ,00330,6 2975 2645 23H *984 >00353,3 3180 2826 2473 2120 2 . I I 1,85204 0332 0663 0995 ‘326 1658 2.36 l>93757 0354 0709 1063 1 4‘ 7 1 77 1 ,00331,5 2983 2652 2320 1989 >00354,3 3189 2B34 2480 2126 2.12 ‘>85553 0332 0665 0997 I33° 1662 2-37 1,941 12 0355 0711 1066 1422 ‘ 777 ,00332,4 2992 2659 2327 ‘994 ,00355,4 3*99 2843 2488 2132 2.13 1,85868 0333 066 6 1000 1 3 3 3 1666 2.38 1,94467 0356 0713 1069 1426 1782 >°°333,2 2999 2 666 2332 !999 ,00356,4 3208 2851 2495 2138 2. 14 1,86201 °33 + 0668 1002 ‘33^ 1670 2.39 1,94823 0337 0715 1072 1429 1787 ,00334,0 3006 2672 2338 2004 ,00357,3 3216 2858 2501 2144 2 . 15 1,86535 0335 0670 1005 ‘34° 1675 2.40 1,95181 0358 0717 1075 ‘434 1792 ,00334,9 3014 2679 2344 2009 ,00358,4 3226 2867 2509 2150 2. 16 1,86870 0336 0671 1007 1 343 1679 2.41 ‘>95539 0359 °7‘9 1078 ‘438 ‘797 ,00335 >7 3021 2686 2350 2014 >00359,4 3235 2875 2516 2156 2. 17 1,87205 °337 0673 1010 1346 1683 2.42 1,95898 0360 0721 1081 H42 1 802 ,00336,6 3049 2693 2356 2020 >00^ 60^4 3244 2883 2523 2162 2.18 1,87542 0338 0675 1013 *35° 1688 2-43 1,96259 0361 0723 1084 1446 1 807 >00337,5 3038 2700 2363 2025 ,00361,4 3253 2891 2530 2168 2 . 19 1,87880 0338 0677 1015 ‘354 1692 2.44 1,96620 0362 0725 1087 ‘45° 1812 ,00338,4 3046 2707 2369 ' 2030 ,00362,4 3262 2899 2 537 2174 2 . 20 1,8821 8 °339 0679 1018 1 3 5 7 1697 2.45 1,96983 0363 0727 logo ‘454 1817 ,°°339>3 3054 2714 2375 2036 ,00363,4 3271 2907 2544 2180 2.21 1,88557 0340 0680 1021 1 361 1701 2.46 ‘>97346 0365 0729 1094 1458 1823 ,00340,2 3062 2722 2381 2041 ,00364,6 3281 29 1 7 2552 2188 2.22 1,88897 0341 0682 1023 *364 1705 2 *47 1,97711 0366 0731 1097 1462 1828 ,00341,0 3069 2728 2387 2046 ,00365,6 3290 2925 2559 2 ‘94 2.23 1,89238 0342 0684 1026 1368 1711 2.48 r, 98076 0367 0733 1 100 1467I1 834 ,00342,1 3079 2737 2395 20 53 ,00366,7 33oo 2934 2567 2200 2 • 24 1,89581 0343 06 86 1028 I37I 1 7 1 4 2.49 ‘,98443 0368 0735 1103 ‘47‘ 839 ,00342,8 3085 2742 2400 2°57 ,00367,8 • 1 33 10 2942 2575 2207 562 Mr. Gompertz on the nature of the function General Table III. ' a — I 1 X(aJ)U 1 9 2 8 3 7 4 6 5 x(a5) xC-“S} 'a L_i 7 1 9 2 8 3 7 4 6 5 2.50 1 ,98811 ,00 0369 0738 1 106 H75 i844 2-75 >o8373 ,00 0398 0796 1194 *592 I99° ,00368,8 3319 2950 2582 2213 >°°397,9 3581 3183 2785 2387 2.51 it >99*79 0370 0740 1 109 1480 1850 2.76 ,08771 0399 0799 1 198 1598 1997 ,00369,9 3329 2959 2589 2219 ,00399,4 3595 3 1 95 27^6 2396 2.52 ^ ,99549 0371 0742 1 1 1 3 1484 1 85 5 2*77 ,09170 0401 0801 1202 1602 2003 ,00371,0 3339 2968 2597 2226 ,00400,6 3605 3205 2804 2404 2*53 t, 99920 0372 0744 1 1 16 1488 1861 2.78 ,09571 0402 0803 1205 1607 2009 ,00372,1 3349 29 77 2605 2233 ,00401,7 3615 3214 2812 2410 2.54 ,00293 0373 °747 1 1 20 H93 1867 2.79 ,09972 0403 0806 1 209 1612 2016 >°°373>3 3360 2986 2613 2240 ,00403,1 3628 3225 2822 2419 5.55 ,00666 °374 °749 1123 *497 1872 2.80 ,10376 0404 0809 1213 1618 2022 >°°374,3 3369 2994 2620 2246 ,00404,4 3640 3235 2831 2426 2.56 ,01040 0376 0751 1127 1502 1878 2.81 ,10780 0406 0811 1217 1623 2029 >°°375>5 3380 3004 2629 2253 ,00405,7 3651 3246 2840 2434 2.57 ,01416 0376 °753 1 129 1506 1882 2.82 ,11186 0407 0814 1221 1628 2035 ,00376,4 3388 3011 2635 2258 ,00407,0 3663 3256 2849 2442 2.58 ,00792 0378 0756 1134 1512 1890 2.83 >”593 0408 0817 1225 1633 2042 >00377,9 34° 1 3023 2645 2267 ,00408,3 3675 32 66 2858 2450 2.59 ,02170 0379 0758 1136 I5I5 1894 2.84 ,12001 0410 0819 1229 1638 2048 ,00378,3 34°9 3030 2652 2273 ,00409,5 3686 3276 2867 2457 2.60 ,02549 0380 0760 1 140 1520 1900 2.85 ,12410 041 1 0822 1233 1644 2055 ,00380,0 3420 3040 2660 2280 ,00410,9 3698 3287 2876 2465 2.61 ,02929 0381 0762 1144 1525 1906 2.86 ,12821 0412 0824 1237 1649 2061 ,00381,2 343i 3050 2668 2287 ,00412,2 3710 3298 2885 2473 2.62 ,03310 0382 0765 1147 *53® 1912 2.87 ,13234 0414 0827 1241 1654 2068 ,00382,^ 3442 3059 2677 2294 ,00413,6 3722 3309 2895 2482 2.63 ,03692 °383 0767 1150 1534 1917 2.88 ,13647 041 5 0830 1245 1660 2075 ,00383,4 345 * 3067 2684 2300 ,00414,9 3734 3319 2904 2489 2 ,6i. ,04076 0385 0769 1 1 54 1 5 39 1924 2.89 ,14062 0416 0833 1249 1665 2082 ,00384,7 3462 3078 2693 2308 ,00416,3 3747 333° 2914 2498 2.65 ,04460 0386 0772 1 1 5 7 1 543 19z9 2.90 ,14478 0418 0835 i253 1670 2088 ,00385,8 3472 3086 2701 23*5 ,00417,6 3758 334i 2923 2506 2,66 ,04846 0387 °774 1161 1548 1936 2.91 ,14896 0419 0838 I257 1676 2095 ,00387,1 3484 3097 2710 2323 ,00419,0 377i 3352 2933 25H 2.67 ,05233 0388 0776 1165 1 553 1941 2.92 , 1 53 1 5 0420 0841 1261 1682 2102 ,00388,2 3494 3106 2717 2329 ,00420,4 3784 33 63 2943 2522 2.68 ,05621 0389 °779 1168 1558 *947 2-93 ,15735 0422 0843 1265 1687 2109 ,00389,4 35°5 31 1 5 2726 2336 ,00421,7 3795 3344 2952 2530 2.65 ,06010 0391 0781 1 172 1562 1 95 3 2.94 ,16157 0423 0846 1269 1692 2116 ,00390,6 35x5 31 25 2734 2344 ,00423,1 3808 3385 2962 2539 2.7c ,06401 0392 0784 1176 1 568 i960 2.95 ,16580 0425 0849 1274 1698 2123 ,00391,5 3527 3*35 2743 2351 ,00424,6 3821 3397 2972 2548 2.71 ,06793 0393 0786 1179 1572 j965 2.96 ,17005 0426 0852 12 77 *7° 3 2129 ,00393^ ) 3537 3*44 2751 2358 ,00425,8 3832 3406 2981 2555 2.72 ,07186 °394 0789 1183 1577 1972 2.97 >17430 0427 0855 1282 1719 2i37 ,00394,: 3549 3154 2760 2366 ,00427,3 3846 34i8 2991 2564 2*7' ,075s1 0396 °79I 1187 1582 1978 2.98 ,17858 0429 0857 1286 1 7 1 5 2144 00395,. 3560 3164 2769 2373 ,00428,7 3858 343° 3001 2572 2.7^ (. ,07976 0397 °794 1 190 1587 1984 2.9c ,18286 0430 0860 1290 1720 2151 ,00396, 3 357i 3174 2778 2381 ,00430,1 3871 344i 301 1 2581 5^3 expressive of the law of human mortality , &c. General Table III. X(a'), X | 1 _ f— ) >■(<*’) ’ n-“5) 1 9 2 8 3 7 4 6 5 X(a’) 1 9 2 8 3 7 4 6 5 U~— */ 'a'L-i ) T.oo ,18717 ,00 0432 0863 1295 1726 2158 T .25 ,29950 ,00 0469 0939 1408 1877 2347 ,00431,6 3884 3453 3021 2590 ,00469,3 4224 3754 3285 2816 T.oi #19148 0433 0866 1299 1732 2165 1. 26 ,304x9 0471 0942 *4*3 x 884 2355 >00433,0 3897 3464 3031 2598 ,00470,9 4238 3767 3206 2825 2363 T.02 ,19581 0434 0869 1304 1738 2175 T.27 ,30890 0473 0945 1418 1890 >oc>434,5 391 1 3476 3042 2607 ,00472,5 4253 3780 3308 2835 T.03 ,20016 0435 0871 1306 1742 2177 T. 28 >3 1 363 0474 0948 1422 1 896 2371 >°°435>4 39*9 3483 3048 2612 ,00474,1 4267 3793 33*9 2845 7.04 ,2045 1 0438 0875 13 1 3 1750 2188 1. 29 ,3*837 0476 0951 1427 *9 3 2379 ,00437,6 3938 3401 3063 2626 ,00475,7 4281 3806 3330 2854 7.05 ,20889 0439 0877 1316 * 755 2194 1. 30 ,323*2 0477 0955 *432 1909 2387 ,00438,7 3948 35io 3071 2632 ,00477,3 4296 381c. 334* 2864 7.o6 ,21328 0440 0880 1 321 1 761 2201 *•31 >32790 0479 0958 *437 j 916 2395 ,00440,2 3962 3522 3081 2641 ,00479,0 43*o 383* 3352 2873 7.07 ,21768 0442 0883 1325 1 767 2209 7.32 ,33269 0481 0961 1442 1 922 2403 ,00441,7 . 3975 3534 3092 2650 ,00480,6 4325 3845 3364 2884 7.o8 ,22209 0443 0886 1330 1773 22X6 *•33 >33749 0482 0964 *447 *929 241 1 ,00443,2 3989 3546 3102 2659 ,00482,2 4340 3858 337 5 2893 7 .09 ,22653 0445 0889 *334 1 7 79 2224 *•34 >34232 0484 0968 1452 *936 2420 >00444,7 4002 3558 3'<3 2668 ,00483,9 4355 3871 3387 2903 * 7.10 ,23097 0446 0892 1338 1784 223I *•35 >347*5 0486 0971 *457 1942 2428 ,00446, 1 40*5 3569 3123 2677 ,00485,5 4370 3884 3399 29*3 1 . 1 1 >23543 0448 0895 *343 *79 1 224O 7.36 ,35201 0487 0974 1462 '94 9 2436 >00447,7 4029 3582 3134 2686 ,00487,2 4385 3'9« 34*o 2923 1 . 12 >2399* 0449 0898 1348 *797 2246 *•37 ,35688 0489 0978 1466 *935 2444 ,00449,2 4043 3594 3*44 2695 ,00488,8 4399 39‘° 3422 2933 * • *3 ,24440 0451 0992 1 353 1 804 2255 1.38 >36*77 0490 0981 *47* 1902 2452 ,00450,9 4058 3607 3*56 2705 ,00490,4 4**4 3923 3433 2942 7. 14 ,24891 0452 0904 1356 1 808 2260 *•39 ,36676 0492 0984 *476 1968 2461 ,00452,0 1 4068 3616 3164 27 1 2 ,00492,1 4429 3937 3445 . 2953 7.i5 >25343 0454 0907 1361 1815 2269 1.40 >37*59 0494 0988 1 48 1 *975 2469 >00453,7 4083 3630 3176 2722 ,00493,8 4444- 3950 3457 2963 x . 16 >25797 0455 09 1 1 366 1821 22 77 7.41 >3 76 ^ 3 0496 0991 *4*7 1982 2477 ,oo455>3 4098 3642 3l87 2732 >00495,5 4460 3964 3469 2973 1. 17 ,26252 045 7 0914 1 37° 1827 2284 7.42 ,38149 0497 c 994 1492 *989 2486 ,00456,8 41 1 1 3654 3198 2741 >00497,2 4475 3988 3480 2983 f . 1 8 ,26709 0458 0917 1 3 7 5 1 833 2292 *•43 ,38646 0499 0998 *497 1996 2495 ,00458,3 4125 3 666 3208 2750 ,00498,9 4490 399* 3492 2993 1 .19 ,27167 0460 0920 1380 1840 2300 *•44 >39*45 0501 1001 1502 2002 2503 ,00459,9 4139 3679 3219 2759 ,00500,6 4505 4005 3504 3004. 7.20 ,27627 0461 0923 1384 1846 2307 *•45 >39645 0502 1004 1507 2009 25 1 1 ,00461,4 4153 3691 3230 2768 ,00502,2 4520 4018 35*5 3013 X .21 ,28089 0463 0926 *389 x8j2 23*5 7.46 ,40148 °5°4 1...08 1512 2016 2520 ,00463,0 4167 3704 3241 2778 ,00594,0 4536 4032 3528 3024 7.22 ,28551 0465 0929 1 394 1858 2323 *•47 ,4065 2 0506 101 1 *5*7 2023 2529 ,00464,6 4181 3717 3252 2788 ,00505,7 455* 4046 3540 3034 7.23 ,29016 04 66 0932 1 398 1864 233* 7.48 >4**57 0507 101 5 1522 2^30 2537 ,00466,1 4x94 3729 3263 2 797 ,00507,4 4567 4059 3552 3044 7.24 ,29482 0468 0935 *4°3 1871 2339 *•49 ,4x665 0509 1018 1527 2036 2546 ,00467,7 4209 3742 3274 2806 ,00509,0 4582 4073 3564 3055 4 D MDCCCXXV. 564 Mr, Gompertz on the nature of the junction General Table III. X ( a’), X I ' 1 a — i Ma5)' K('-aS\ 1 1 9 2 8 3 7 4 6 5 MflS) >(*-«5'| 1 9 2 8 3 7 1 4 6 1, U -*) V G"1-!/ I.50 >42174 ,00 05 1 1 1022 *532 2043 2554 *•75 >5547* ,00 0555 1 1 10 1666 2221 2776 ,005 10,8 4597 4086 3576 3065 >00555,2 4997 4442 3886 333* 1 • 5 1 ,42684 05*3 1025 *538 2050 2563 i .76 ,56026 0 557 1 1 14 1671 2228 2785 ,00512,5 4613 4100 3588 3075 ,00556,9 5012 4455 3898 334* 1.52 >43 *97 0514 1028 *543 2057 2571 * 77 >56583 0559 hi 7 1676 2234 2 793 ,00514,2 4628 4114 3599 3085 ,00558,6 5027 4469 39*o 3352 1 *53 >437 1 1 0516 1032 1548 2064 2581 1 .78 >57*42 0561 1 121 1682 2243 2804 ,005 16, i 4645 4129 3613 3097 ,00560,7 5046 4486 3925 3364 1 *54 ,44227 0518 1036 *553 2071 2589 *•79 >57702 0562 1 125 1687 2250 28 1 2 ,00517,8 4660 4142 3625 3107 ,00562,4 5062 4499 3937 3374 t-55 >44745 0520 I039 *559 2078 2598 1. 80 ,58265 0564 1128 1693 2257 282 1 ,00519,5 4676 4*56 3637 3**7 ,00564,2 5078 45*4 3949 338s i .56 ,45264 0521 1042 1564 2085 2606 1 . 81 ,58829 05 66 1132 1698 2264 2830 ,00521,2 4691 4170 3648 3*27 >00565,9 5093 4527 3961 3395 *•57 >45786 0523 1046 1569 2092 2615 1 .82 >59395 0568 1136 *703 2271 2839 ,00523,0 4707 4184 3661 3*38 ,00567,8 5110 4542 3975 3407 1 .58 ,46309 0525 *°49 *574 2099 2624 1.83 >59963 0570 **39 *700 2279 2849 ,00524,7 4722 4198 3673 3H8 ,00569,7 5*27 4558 3988 34*8 T.59 >46833 0527 *053 1580 2106 2633 1 .84 >60532 0572 **43 *7*5 2286 2858 ,00526,5 4739 4212 3686 3*59 >00571,5 5*44 4572 4001 3429 T.60 >47360 0528 1057 ■585 2113 2642 T.85 ,61104 0573 **47 1720 2293 2867 ,00528,3 4755 4226 3698 3170 >00573,3 5 160 4586 4013 344° 1. 61 ,47888 0530 1060 1590 2120 2650 1.86 ,61677 0575 1150 *725 2300 2876 ,00530,0 4770 4240 3710 3180 >00575,1 4*76 4601 4026 345* x .62 ,48418 0532 1064 *595 2127 2659 1 .87 ,62252 0 577 1154 *73* 2308 2885 ,00531,8 4786 4254 3723 3*9* ,00577,0 5*93 4616 4039 3462 1.63 ,48950 0534 1067 1601 2134 2668 1.88 ,62829 0579 1158 1736 23*5 2894 >00533,6 4802 4269 3735 3202 ,00578,8 5210 4630 4052 3473 1.64 >49484 0535 1071 1606 2141 2677 1 .89 ,63408 0581 1162 1742 2323 2904 >co535>3 4818 4282 3747 3212 ,00580,8 5227 4646 4066 3485 T.65 ,50019 0537 1074 1 6 1 1 2148 2688 1.90 ,63989 0583 1165 1748 2330 29*3 >00537,1 4834 4297 3760 3223 ,00582,5 5243 4660 4078 3495 T.66 >5°556 0539 1078 1617 2156 2695 1 .91 ,64572 0584 1 169 *753 2338 2922 ,00538,9 4850 43 1 1 3772 3233 ,00584,4 5260 4675 4091 35o6 T.67 >5*095 0541 1081 1622 2163 2704 1 .92 ,65156 0586 1172 *759 2345 2931 ,00540,7 48 66 4326 3785 3244 ,00586,2 5276 4690 4*03 35*7 T.68 >51636 °543 1085 1628 2170 2713 *•93 >65742 0588 1176 1764 2352 2940 ,00542,5 4883 434° 3798 3255 ,00587,9 529* 4713 4**5 3527 1. 69 ,52178 0544 1089 *633 2177 2722 *•94 >66330 0590 1180 *77 0 2360 2950 ,00544,3 4899 4354 3810 3266 ,00590,0 53*o 4720 4*3o 354° T .70 ,52722 0546 1092 1638 2184 2731 *•95 ,66920 0592 1183 *775 2367 2959 ,00546,1 49*5 4369 3823 32 77 ,00591,7 5325 4734 4142 3550 *•7* >53269 0548 1096 i643 2191 2739 1 .96 ,67512 0594 1187 1781 2374 2968 ,00547,8 4920 4382 3835 3287 >00593,5 5342 4748 4*55 3561 1. 72 ,53816 0550 1099 1649 2199 2749 1.97 ,68105 0595 1 1 9 1 1786 2382 2 977 >00549,7 4947 4398 3848 3298 ,00595,4 5359 4763 4168 3572 *•73 >54366 0552 1103 1655 2206 2758 1 .98 ,68701 0597 * *95 1791 2389 2987 ,00551,5 4964 4412 386! 3309 >00597,3 5376 4778 4181 3584 7.74 ,54918 0553 1 107 1660 2213 2767 1.99 ,69298 >o0553>3 l 4980 4426 3873 332° 565 expressive of the law of human mortality , &c. General Table IV. For the whole of life. — X (arL l). X (a) - -X(a — 1 ) I.700 ,00206 ,00201 1 .701 ,00407 ,00201 T.702 ,00608 ,00202 1.703 ,00810 ,00202 1.704 ,01012 ,00203 T.705 ,01214 ,00203 1 .706 ,01418 ,00203 1.707 ,01621 ,00204 i .708 ,01825 ,00205 1 .709 ,02030 ,00205 1.710 ,02235 ,00205 1 .71 1 ,02440 ,00206 1. 712 ,02646 ,00207 1 *7*3 ,02853 ,00207 1. 714 ,03060 ,00207 7.715 ,03267 ,00208 7.716 ,03476 ,00208 1.717 ,03684 ,00209 i .718 ,03893 ,00210 7.719 ,04103 ,00210 7.720 .04313 ,0021 1 1 .721 ,04524 ,0021 1 7.722 .04735 ,00212 **723 ,04947 ,00212 7.724 >°5I59 ,00213 X (a) - x (a~— 1 ) 7.725 .05372 ,00213 7.726 .o5585 ,00214 1.727 .05799 ,00215 7.728 ,06014 ,00215 7.729 ,06229 ,00216 "1*730 ,06445 ,00216 1*731 ,06661 ,00217 i*7 32 ,06878 ,00217 i*733 .07095 ,00219 i*734 .073H ,00218 t*735 .07532 ,00219 i*736 ,07751 ,00220 i*737 .07971 ,0022 1 i-738 ,08192 ,00221 i*739 ,08413 ,00221 7.740 ,08634 ,00223 1*741 ,08857 ,00223 1.742 ,09080 ,00223 i*743 ,09303 ,00224 1*744 ,09527 ,00225 i*745 ,09752 ,00226 7.746 ,09978 ,00226 i*747 ,10204 ,00227 7.748 ,10431 ,00227 i*749 ,10658 ,00228 X(a) 7.750 ,10886 ,00229 1 *75 1 ,11115 ,00330 1.752 .11345 ,00230 i*753 .11575 ,00231 i*754 , I I 806 ,00232 T*755 ,12037 ,00233 1.756 ,12270 ,00233 1*757 ,12503 ,00234 1.758 ,12736 ,00235 i*759 ,12971 ,00235 7.760 ,13206 7.761 ,00236 ,13442 7.762 ,00237 ,13679 ,00237 1.763 ,13916 ,00238 7.764 ,14154 ,00239 1.765 7.766 ,14393 ,00240 ,14633 ,00240 1*767 ,14873 ,00241 i .768 ,15114 ,00242 1.769 ,15356 ,00243 1*77° ,15599 ,00244 i*77i ,15843 *00244. i*772 ,16087 ,00245 i*773 ,16333 ,00246 1*774 ,16579 ,00247 X (a) -X(a — 1) i*775 ,16826 ,00247 i*776 ,17073 ,00248 1*777 ,17322 ,00249 1.778 ,17571 ,00250 1.779 ,17822 ,0025 1 1.780 ,18073 ,00252 1.781 ,18325 ,00253 1 .782 ,18578 ,00254 1*783 ,18832 ,00254 1.784 ,19086 ,00256 I.785 ,19342 ,00257 1 .786 » 1 9599 ,00258 1.787 ,19856 ,02259 1 .788 ,201 15 ,00259 1*789 ,20374 ,00260 1*79° ,20634 ,00261 i*79i ,20896 ,00262 1*792 ,21158 ,00263 i*793 ,21421 ,00264 1*794 ,21685 ,00265 i*795 ,21951 ,00266 1*796 ,22217 ,00267 i*797 ,22484 ,00268 T.798 ,22753 ,00269 i*799 ,23022 ,00270 X (a) -X(a_— 1) 1. 800 ,23292 ,00271 1. 801 ,23564 ,00272 1. 802 ,23836 ,00274 1.803 ,241 10 ,06275 i .804 ,24385 ,00270 T.805 ,24661 ,00277 1 .806 ,24938 ,00278 1. 807 ,25216 ,00279 1 .808 ,25495 ,00281 1. 809 ,25776 ,00281 1. 810 ,26057 ,00283 1 .8 1 1 ,26340 ,00284 T.812 ,26624 ,00285 1.813 ,26909 ,00287 1.814 ,27196 ,00287 1. 815 ,27483 ,00289 1 .816 ,27772 ,00291 1.817 ,28063 ,00291 1 .818 ,28354 ,00293 1.819 ,28647 ,00294 1. 820 ,28941 ,00295 1 .821 ,29236 ,00297 1 . 822 ,29533 ,00298 1.823 ,29831 ,00299 1 .824 ,3°i3° 1 ,00301 x(a) U(o-a-i) T.825 T. 826 1.827 T. 828 1. 829 ,3°43i ,00302 ,30733 ,00304 ,31037 ,00305 ,31342 ,00307 ,31649 ,00308 1.830 ,31957 ,00309 1. 831 ,32266 ,00311 1.832 ,32577 ,00313 00 • ,32890 ,00314 OO • ,33204 ,00315 I-835 ,33519 ,003 1 7 I. 836 ,33836 ,00319 1.837 ,34155 ,00320 1*838 ,34475 ,00322 I. 839 ,34797 ,00324 1.840 ,35121 ,00325 T.841 ,35446 ,00327 I .842 ,35773 ,00329 to 00 • ,36102 ,00331 1 .844 ,36433 ,00332 1.845 ,36765 ,00334 1 .846 ,37099 ,00336 1*847 ,37435 ,00338 1 .848 ,37773 ,00339 1 .849 ,38112 ,00342 5^6 Mr. Gompertz on the nature of the function General Table IV. For the whole of life. — x(a”Ti). X (a) - -X(cf-Li) X ( a ) -X(a .Li) 1 X(«) -X(a _Li) \(a) -X(38454 7.875 ,47688 7.900 ,58683 7.925 ,72468 7.950 >91357 1-975 1,22728 ,00343 ,00401 ,00488 >00635 ,00929 ,01824 1.851 >38797 1 .876 ,48088 1 .901 >59171 7.926 >73i°3 “.951 ,92286 T.976 1,24552 ,00345 ,00405 >00493 ,00642 ,00946 ,01899 7.852 >39H2 1.877 >48493 7.902 ,59664 7.927 >73745 7.952 ,93232 i.977 1,26451 ,00348 ,00407 ,00497 ,00650 ,00966 ,01980 t-8S3 ,39490 7.878 ,48900 1.903 ,60161 7.928 >74395 i-953 ,94198 1.978 1,28431 ,00349 ,00410 ,00502 ,00659 ,00984 - ,02071 1.854 >39839 1.879 >49310 1 .904 ,60663 i .929 >75°54 “1.954 ,95182 1-979 1,30502 ,00351 ,00412 ,00507 ,00668 ,01006 ,02170 7.855 ,40190 7.88o >49722 7.905 ,61170 i.93o ,75722 i-955 ,96188 7.980 1,32672 >00353 ,00416 ,0051 1 ,00676 ,01027 ,02278 1 .856 >40543 1 .881 >50138 1 .906 ,61681 i-93i ,76398 7.956 >972i5 7.981 1,34950 >003.55 ,00419 ,00516 ,00685 ,01049 ,02398 1.857 ,40899 1 .882 >5°557 1.907 ,62197 “ 1-932 >77083 1-957 ,98264 7.982 i>37348 >00357 ,00422 ,00521 ,00695 ,01073 ,02583 1 .858 ,41256 1.883 >5°979 1 .908 ,62718 i-933 >77778 1.958 >99337 7.983 1,39881 ,00360 ,00425 ,00527 ,00704 ,01097 ,02683 1 -859 ,41616 1 . 884 >5 H°4 1 .909 ,63245 i-934 ,78482 1.959 1,00434 1 .984 1,42564 ,00362 ,00428 ,00531 ,00715 ,01123 ,02853 7.86o ,41978 7.885 >51832 7.910 ,63776 i-935 >79197 7.960 1,01557 1.985 i>454i7 ,00364 ,0043 1 ,00537 ,00724 ,01150 >03047 1 .861 ,42342 1.886 >52263 1.911 >64313 7.936 >79921 1 .961 1,02707 1 .986 1,48464 ,00366 >00435 ,00543 >00735 ,01179 ,03269 1 .862 ,,42708 1 . 887 ,52698 1.912 ,64856 i-937 ,80656 1 .962 1,03886 1.987 i>5i733 ,00368 ,00438 ,00548 ,00746 ,01209 ,03526 1.863 ,44076 1.888 >53136 1.913 ,65404 1.938 ,81402 1.963 1,05095 1 .988 J>5 5259 ,00371 ,00442 ,00554 ,00758 0,01241 ,03829 1 .864 >43447 1 .889 >53578 1.914 >65958 1-939 ,82160 1 .964 1,06336 1 .989 1,59088 ,00373 ,00445 >00559 ,00769 ,01274 ,04189 7.865 ,43820 7.890 ,54023 T-9i5 ,66517 7.940 ,82929 7.965 1,07610 7.990 1,63277 ,00376 ,00449 ,00566 ,00781 ,01309 ,04626 1 .866 44196 1 .891 >54472 1 .916 >67083 1.941 ,83710 1 .966 1,08919 1.991 1,67903 ,00378 ,00452 ,00572 ,00793 ,01348 >05163 1 .867 >44574 1 .892 >54924 i-9i7 >67655 1.942 >84303 1.967 1,10267 1.992 1,73069 ,00380 ,00456 ,00578 ,00807 ,01387 ,05849 1 . 868 >44954 1.893 >5538o 1.918 ,68233 i-943 ,85310 1 .968 1, 1 1654 1*993 1,78918 ,00383 ,00460 ,00584 ,00820 ,01429 >06745 1 . 869 >45337 1 .894 >55840 i-9i9 ,68817 i-944 ,86130 1 .969 1,13083 1.994 1 ,85663 ,00385 ,00464 ,00591 ,00833 >01475 ,07968 0 00 >45722 7.895 ,56304 7.920 ,69408 1-945 ,86963 i.97o i>i4558 7.995 1,93631 ,00388 ,00467 ,00598 ,00848 ,01523 ,09741 I .871 ,461 10 i .896 ,56771 1 .921 ,70006 1 .946 ,8781 1 i.97i 1,16081 1 .996 2,03372 ,00390 ,00472 ,00695 ,00863 ,01574 >12544 CO • Iw ,46500 1 -897 >57243 1 .922 ,7061 1 1.947 ,88674 1.972 1,17655 1*997 2,15916 .00393 ,00476 ,006*1 ,00878 ,01530 >'7459 00 • I** ,46893 1 .898 >57719 1-923 ,71222 1 .948 >89552 1*973 1,19285 1 .998 2>33575 ,00396 ,00479 ,00620 ,00894 ,01690 >3°' 53 1.874 ,47289 1 .899 ,58198 1 .924 ,71842 1.949 ,90446 1-974 1,20975 1.999 2,63728 ,00399 ,00485 ,00626 ,00911 >°i753 56‘7 expressive of the law of human mortality , &c. TABLE V. — Logarithms of the accommodated chances of living io years, deduced from the value of an annuity for io years, at 5 per cent, from the actual tables of mortality, and considered equal to a geometrical series of ten terms, of which the common ratio is the same as the first term, and the tenth term the accommodated chance ; and to find the accommodated chance for 5, 7 years, &c. without a table calculated for the purpose, it may be considered sufficient to multiply by ,5 ; ,7, &c. the accommodated ratio in this table when extreme accuracy be not required. Age. Carlisle. Deparcieux. Northampton. O 1,6892 1 1,6763 — 1,7044 2 1,8699 — 1,8356 3 1’9159 1,9166 1,8790 4 1,9401 1 ,93 5 1,9081 5 1,9586 1,941 1 1,9220 6 1,9686 1,9486 1,9369 7 1 ’97 3 7 r»9544 1,9476 8 1,9764 i,9592 1,9550 9 i,9773 1,9637 1,9586 10 1,9768 1,9669 1,9592 1 1 1,9754 1,9679 1,9582 1 2 1,9742 1,9669 1,9566 13 1,9729 1,9658 1,9546 14 1,9716 1,9704 1,952 1 15 1,9704 1,9628 1,9490 16 1,9698 1,9609 1,9455 17 1,9694 1,9600 1,9419 18 1,9693 1,9586 1,9388 19 1,9690 i,9574 1,9358 20 1,9685 i,9559 1,9337 21 1,9679 i,9554 1,9321 22 1,9670 i,9549 i,93U 23 1,9659 i,9544 1,9298 24 1,9644 i,954o 1,9289 25 1,9628 i,9534 1,9277 26 1 ’95 73 i,953i 1,9264 27 i’959i £,9524 1,9257 28 i,957o 1,9521 1,9238 29 i’9556 1,9518 1,9226 30 1,9552 £,95H 1,921 1 3i £,9548 £,9514 1,9196 3* £,9540 1,9514 1,9180 33 1,9528 £,9515 1,9164 34 *,9513 i,95i7 1,9146 35 1,9485 1,9522 1,9126 36 £,9477 1,9528 1,9104 37 £,9452 £,9534 1,9083 38 £’94-37 £,9527 1,8057 39 1,9406 1,9517 1,9031 40 1,9383 1,9506 1,9001 4i i,9372 1,9488 1,8973 4* *,9365 1,9466 1,8943 43 1,9365 1,9438 1,8915 44 1,9366 1,9403 1,8882 45 1, 9367 1,9361 1 ,8848 46 1,9366 1,9308 1,8810 47 1,9358 1,9263 1,8767 48 i,935i 1,9200 1,8740 49 1,9328 1,9158 1,8631 50 1,9292 1,9098 1,8621 5i 1 i,9233 1,9027 1,8571 Age. Carlisle. Deparcieux. Northampton. 52 53 54 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 96 97 98 99 1,917* 1,9098 I,9oi3 1,8915 1,8803 T,868o £>8513 £>8435 1,8318 £,8243 £,8171 1,8090 I»7974 1,7860 £,7703 £,75°6 £,7107 £,7° 05 £,6689 £,6319 £>5936 £>5563 £,5269 £,4940 £,4642 £’4344 £,4007 £>3538 £>3i34 £,2582 £,2043 £,1765 £,0727 £’9939 2,9166 2,8490 2,8055 £>7537 2,6695 2,6658 £’73*3 2,8031 £’8355 2,8107 £,8279 £,7589 £,6695 £,5111 1,9006 £’8957 1,8901 £,8853 £,8799 £,8732 £,8673 1,8601 1,8511 £,8398 £,8264 1,8120 £,7946 £.7735 £,7510 £,7270 £,7017 £,6754 £,6480 1 ,6167 £,5841 £,5500 £’ 5 1 1 9 £’47n £,4218 £,3684 £’3^34 £,2497 £,1876 £,1214 £,0609 2,9688 2,8536 £,7199 £’5736 £’4*54 £jI943 3,9129 3*5265 3,0266 4,3694 5,2971 £,8523 £,8471 £,8417 £’8357 £,8294 1,8228 £,8156 £,8081 £,7998 £,7908 £,7811 1,7699 £’7576 £’743i £,7267 £,7083 £,6879 £,6651 £,6402 £,6126 £,5823 £>5^87 £’5ii7 £’47*3 £,4308 1,3846 £’33°7 £,2644 £,1900 £,1101 £,0234 2,9341 £’8592 2,7813 2,7003 2,6149 2,5369 2,4179 2,24 1 4 3.9356 3’5037 4’7375 ?’5769 7,0496 100 101 102 103 £,1629 3,5689 4’3245 6,0595 % 568 Mr. Gompertz on the nature of the function TABLE VI, — Accommodated annual ratio for an unlimited period for every age a l,05_t 1,05'* \r—\ i If _ ^ o + x 1,05. -1 ^ r Carlisle, ^rDeparcieux. ? f Northampton. a ^ V Carlisle. r Deparcieux. ^ Northampton. 0 T98665 — — 52 1,98390 1,98216 *,97950 I T99121 — 1,98517 53 1,98305 1,98240 1,97878 2 *>99313 — 1,98997 54 1,98212 1,98156 1,97802 3 1,99458 *>99399 1,99151 55 *,981 12 1,98073 *>97721 4 1,99528 *,99446 1,99244 56 1,98005 1,97982 *>97635 5 1,99577 *>99473 1,99284 57 1,97887 1,97882 *>97542 6 1,99599 *>99493 1,99324 58 1,97763 1,97780 *>97445 7 1,99606 *,99505 1,99346 59 *>97637 1,97668 *>9734i 8 1,99606 *>995*3 ‘>99357 60 *>975*4 *>97545 1,97230 9 1,99600 *>995*9 *>99354 61 1,97400 1,97408 1,97* * * 10 1,99529 *>995*9 1,99341 62 1,97281 *>97254 1,96983 1 1 1,99576 *,99514 1,99323 63 *>97154 1,97093 *>96843 12 *>99563 1,99503 1,99304 64 1,97014 1,96912 1,96693 13 *,99549 ‘>9949* 1,99284 65 1,96858 1,96707 1,96526 *4 *>99535 1,99478 1,99262 66 1,96685 *,96489 1,96346 *5 1,99522 *>99464 1,99240 67 1,96491 1,96250 1,96150 16 1, 99509 *>99450 *>99ZI3 68 1,96273 1,96009 1,95936 *7 1,99487 *,99438 1,99190 69 1,96029 *>95750 *>95703 18 *>99484 *,99425 1,99167 70 *>95755 1,95480 1,95448 19 1,99471 *,99413 *>99145 7* ‘>95440 1,95181 *>95 *7* 20 *>99455 1,99398 1,99124 72 1,951 1 1 *,94870 1,94869 21 *>99442 1,99388 1 .99106 73 *,94784 *>94542 *>9454* 22 *,99425 *>99375 1,99088 74 *>94467 1,94180 1,94186 23 1,99408 *>99364 1,99070 75 1,94185 *>9379° 1,938*2 24 *>9939° *,99350 1,99051 76 1,93888 *>9333° *,93423 25 1,99370 *>99338 *>99030 77 *>9359* 1,92833 *,92994 26 *>99349 ‘>99323 *,99009 78 1,93265 *>923*4 1,92503 27 1,99328 *,99308 1,98988 79 1,92863 *>9*7*5 1,91916 28 1,99306 *,99293 1,98965 80 1,92461 1,91 124 1,91246 29 1,99290 *,99277 1,98943 81 1,91891 *>9°493 1,90509 3° 1,99265 *,99259 *,98917 82 1,91491 1,89856 *,89697 31 *,99245 *,99241 1,98892 83 *>90939 1,89069 *,88844. 32 1,99224 *>99223 1,98865 84 *,90344 1,88005 1,881 10 33 1,99201 1,99202 1 ,98837 85 *,89657 1,86782 1,87361 34 1,99176 *,99181 1,98808 86 1,88978 1,85416 1,86599 35 *,99149 *,99158 ‘,98777 87 1 ,88369 1,8401 1 1,85803 36 1,991 10 *,99134 *>98745 88 1,87972 1,81788 1,85069 37 38 1,99090 1,99058 £,99109 1,99077 1,98811 1,98675 89 90 1,87481 1,86660 1,78941 1,75223 £,85454 1,82243 39 1,99025 *,99043 *>98637 9* 1,86560 1,70265 *>79303 40 1,98991 1,99006 *,98597 92 T..87056 1,63694 1,74992 4i 1,98958 1,98967 *,98556 93 1,87595 *>52971 1,67376 42 43 1,98924 1,98890 *,98924 1,98878 *>985 1 3 1,98469 94 95 1,87840 1,87967 — *>55753 *,30505 44 1,98853 *,98828 1,98423 96 *>77774 — 45 1,98814 *>98771 *>98375 97 *>77*40 — - - — > 46 *>98771 *,98714 1,98323 98 I>76333 — ■ 47 *>98725 *,98655 1,98270 99 1,84829 — — 48 1,98673 1,98590 1 ,98209 100 T, 81282 - - — 49 1,98612 1,98526 1,98148 101 *>75663 — 5° 1,98546 1,98456 1,98083 102 1,65421 * — 51 1,98471 1,98386 1,98017 103 1,40266 expressive of the law of human mortality , &c. 569 TABLE VII. — Logarithm of Carlisle chance of living 5 years at every age a. a X chance. a X chance. a X chance. a X chance. a X chance. 0 7,83232 20 1,98469 40 1,96915 60 1,91826 80 1,66927 1 1,89709 21 *,98457 4* 1,96836 61 1,91483 81 *,64194 2 1,92823 22 1,98439 42 1,96790 62 1,91 1 80 82 1,61095 3 *>95354 23 1,98405 43 1,96780 63 1,90864 83 1,57*00 4 *,96747 24 *>98333 44 1,96808 64 1,90492 84 1,53422 5 1,97792 25 1,98213 45 1,96857 65 1,90067 85 1,50393 6 *>98376 26 1,98091 46 1,96918 66 1,89586 86 1,45652 7 1,98703 27 1,97967 47 1,96941 67 1,88838 87 1,40377 8 1,98869 28 1,97863 48 1,96915 68 1,87746 88 1,36691 9 1,98930 29 1,97804 49 1,96818 69 1,86279 89 *,34438 10 1,9891 1 30 *,97789 5° 1,96676 70 1,84362 90 1,32483 1 1 1,98836 3* *,97783 5* *,96477 7* 1,82305 9* *,34054 1 2 1,98754 32 *,97767 52 1,96269 72 1,80220 92 1,38021 *3 1,98670 33 1,97736 53 1,96017 73 1,78348 93 *>4*373 *4 1,98593 34 1,97687 54 1,95660 74 1,76877 94 *>43933 *5 1,98528 35 1,976* 1 55 *>95*55 75 *,75508 95 *>477*2 16 1,98490 36 *,97490 56 1,9446* 76 1,74231 96 *>48337 *7 1,98479 37 *>97349 57 *,93711 77 *,727*2 97 1,44370 18 1,98476 38 1,97*94 58 *,92973 78 1,71062 98 1, 33099 19 : 1,98472 39 *,97044 59 *,92343 79 1,68963 Logarithm of the Carlisle chance of living 10 years at every age a. 0 1,81023 *9 1 ,96805 38 *>93973 57 1,84891 76 1 1 ,88086 20 1,96682 39 *,93851 58 1,83836 77 2 1,91526 21 1,96548 40 *,93772 59 1,82835 78 3 1,94223 22 1,96406 4* *>93754 60 1,81893 79 4 *,95677 23 1,96268 42 *>9373* 61 1,81070 80 5 1,96702 24 1,96136 43 *,93694 62 1,80018 81 6 1. 97213 25 1,96002 44 1,93626 63 1,78610 82 7 *>97457 26 1,95873 45 *>93533 64 1,76771 83 S 1,97540 2 7 *>95734 46 i,93395 65 *,74430 84 9 1,97523 28 *>9S598 47 1,93211 65 *,7*891 85 10 *,97438 29 *,95490 48 1,92932 67 1,69058 86 1 1 1,97326 30 1,95400 49 1,92478 68 1,66094 87 12 *,97233 3* 1,95273 5° 1,91 830 69 *,63157 88 *3 1,97146 32 1,95116 5* 1,90938 70 1,59870 89 *4 1,07065 33 *,94929 52 1,89980 7* *,56536 9° *5 1,96996 34 1,94730 53 1,88990 72 1,52932 9* 16 1,96947 35 1,94526 54 1,88003 73 i,494* * 92 *7 1,969 1 8 36 1,94326 55 1,86981 74 1,4584° 93 58 1,96881 37 1,94*38 56 1,85944 75 1,42434 £,38425 *>33807 £,28163 £,22385 £>*7320 £,09846 £>01472 £>9379* 2,87860 2,82876 2,79706 2,78398 2,78064 2,78371 2,80195 2,82391 2,82391 2>74473 570 Mr. Gompertz on the nature of the function T ABLE VII. — continued. Logarithm of the Carlisle chance of living 1 5 years for every age a a X chance. a X chance. a X chance. a X chance. a X chance. 0 1-79934 18 *,94744 36 1,91244 54 7,78495 72 7,14027 1 1,86922 *9 1,94609 37 1,91080 55 1,77048 73 7,0651 1 2 3 1,90280 1,92893 20 21 *,9447* 1^94331 38 39 1,90888 7,90669 56 57 £>75530 *-73729 74 75 2,99263 2,92827 4 1,94270 22 *,94*73 40 1,90448 58 1,7*582 76 2,84078 5 1,95230 23 1 ,94004 4i 1.9023 1 59 1,691 14 77 2,74184 6 1,95702 24 1,93823 42 1,90000 60 1,66256 78 2,64853 7 1,95936 25 L936i3 43 1,89712 61 *,63375 79 2,56821 8 1,96015 26 *,93364 44 1,89284 62 1,60238 80 2,49803 9 i,9S99S 27 1 93082 45 1,88687 63 1,56958 81 2,4390° 10 *,959°7 28 1,92792 46 1,87856 64 1,53648 82 2’39494 1 1 1,95784 29 1,92534 47 1,86922 65 *-49937 83 2,35164 12 1,95672 30 1,92316 48 1,85905 66 1,46123 84 2,3*794 *3 *-9555 1 3* 1,92108 49 1,84.820 67 *,41770 85 2,30588 *4 *-95397 32 1, 91905 50 1,83656 68 *,37*57 86 2,28043 ■5 1,95209 33 1,91709 5 1 1,82421 69 1,32120 87 2,22768 16 1,95038 34 1,9^38 52 7,8i 160 70 7,26797 S8 2,1 1 163 *7 1,94885 35 *,9*383 53 *,79853 71 1,20730 Logarithm of the Carlisle chance of living 20 years for every age a. 0 7,78462 *7 1,92652 34 1,88356 5* 1,72007 68 2,94257 1 7,85412 18 1,92479 35 1,88059 52 1,69998 69 2,85542 2 1,88759 *9 1,92295 36 1,87721 53 1-67599 70 2,77190 3 [_£, 9*369 20 1,92082 37 *,87349 54 *-64744 7* 2,66383 4 1,92742 21 1,91821 38 1,86906 55 1,6 1410 72 2,54404 5 1,93699 22 1,91521 39 1,86329 56 *,57835 73 2,43202 6 1,94160 23 *,9**97 40 1,85602 57 *-53949 74 2,33701 7 *,94376 24 1,90866 4* 1,84692 58 *-4993° 75 2,25311 8 1,94421 25 1,90528 42 1,83711 59 1-45991 76 2,18132 9 1,94328 26 7,90199 43 1,82684 60 *-41763 77 2,12205 10 1,94120 27 1,89872 45 1,81628 61 1,37606 78 2,06227 1 1 7,93874 28 1,89572 45 1,80513 62 1,32950 79 2,00757 12 1,93639 29 1,89342 46 *-79339 63 1,28021 80 3,975*5 *3 *-934*4 30 1,89172 45 1,78101 64 1,2261 1 81 3-92237 *4 1,93201 3i 7,89027 48 7,76768 65 1,16864 82 3,83863 *5 7,92999 32 7,88847 49 7,753*2 66 1,10317 83 3-68263 16 1,92821 33 7,88624 50 1 *-73723 67 1,02866 6 71 expressive of the law of human mortality , &c. TABLE VII continued. Logarithm of the Carlisle chance of living 25 years at every age a. a X chance. a x chance. a x chance. a x chance. a x chance. 0 1,76930 16 1,90311 32 7,85 1 16 48 1,64514 64 2,76034 1 1,83969 17 1,90001 33 7,84641 49 1,61591 65 2,67257 2 1,87198 18 1,89673 34 7,84016 5° 1,58086 66 2,55969 3 1,89774 *9 *,89339 35 7,83213 5* *,543* 67 2,43242 4 I,9I°75 20 1,88997 36 1,82182 52 1,502 1 8 68 2,30948 5 1,91912 21 1,88657 37 7,8io6o 53 1,45948 69 2,19980 6 1,9225 1 22 1,8831 1 38 7,79878 54 1,41651 70 2,09673 7 *>92342 23 1,87977 39 1,78672 55 1 ,36918 7* 2,00437 8 1,92283 24 1,87674 40 1,77428 5 6 1,32067 72 3,92425 9 *,92*3* 25 ‘,873*5 4i C76i75 57 1,26661 73 3,84575 10 1,91909 26 1,87117 42 1,7489* 58 1,20993 74 3>77634 1 1 1 ,9 1 65 7 27 1,868 1 3 43 *,73548 59 1,14954 75 3,73023 12 1,91406 28 1,86487 44 1 ,72 1 20 60 1,08690 76 3,66469 ‘3 1,91 150 29 1,86159 45 1,70581 61 1,01800 77 3,56575 H 1,90888 30 7,85848 46 1 ,68926 62 2,94045 78 3,39326 *5 1,90610 3i 7,85504 47 1,66940 63 2,85 121 • Logarithm of the Carlisle chance of living 30 years at every age a. 0 ‘,75*43 ‘5 ‘,87525 3° 1,81003 45 ‘,54943 60 2,59083 1 1,81960 16 1,87146 3* 7,79964 46 1,5*231 61 2,47452 2 1,85164 ‘7 1,86790 32 1,78827 47 1,47160 62 2,34422 3 1,87637 18 1,86453 33 7,77614 48 7,42863 63 2,2181 1 4 1,88879 *9 1,86147 34 1,76358 49 7,38467 64 2,10472 5 1,89701 20 1,85854 35 1,75039 5° ‘,33594 55 3,99740 6 I» 9°°33 21 *,85575 36 *,73665 5* 1,28544 66 3,90023 7 1,90109 22 *,85253 37 1,72240 52 1,22930 67 3,8 1 264 8 1,90019 23 1,84892 38 1,70742 53 1,17010 68 3,72321 9 1,898 1 8 24 1,84492 39 1,69164 54 1,10614 69 3,639*3 10 1,89520 25 1 ,84061 40 1,67496 55 1,03845 70 3,57385 1 1 1 >89147 26 1,83594 4* 1,65701 56 2,96261 7* 3,48774 12 1,88755 27 1,83083 42 1,63729 57 2,87756 72 3,36795 *3 1,88344 28 1,82504 43 1,61294 58 2,78093 73 3> ‘7674 *4 *,87931 29 1,81819 44 1,58399 59 2,68376 Logarithm of the Carlisle chance of living 35 years for every age a. 0 ‘,72933 *4 1,84739 28 *,75476 42 *,43949 56 2, 4*9*3 1 ‘,79743 ‘5 1 ,84382 29 1,74162 43 1,39642 57 2,28133 2 1,82932 16 1,84065 30 1,72829 44 1,35277 58 2.14784 3 ‘,85373 *7 ‘,83732 3* 1,71448 45 *,3045* 59 2,Oz8 1 5 4 1 ,86565 18 * ,83368 32 1,70007 46 1,25462 bo 3,91566 5 1,87312 *9 1,82964 33 1,68477 47 1,19872 61 3,81 506 6 1,87523 20 1,82530 34 1,66850 48 1,13925 62 3,72443 7 1,87458 21 1,82052 35 1,65 106 49 ‘,07432 63 3 63185 8 1,87213 22 1,81522 36 1,63251 5° 1,00520 64 3,54405 9 1,86861 23 1 ,80909 3? 1,61078 5* 2,92738 65 3,47452 10 1,86435 24 1,80152 38 1,58488 52 2,84025 66 3,58360 1 1 1,85983 25 1,79216 39 *»>5443 53 2,741 10 67 3,25033 12 1,85544 26 1,78055 40 1,5 1858 54 2,64036 68 3,05420 *3 1,85123 27 1,76794 4* r 1,48066 55 2,54237 4 E MDCCCXXV. 572 Mr. Gompertz on the nature of the function TABLE VII. — continued. Logarithm of the Carlisle cha nee of living 40 years for every age a. a X chance. a X chance. a X chance. a X chance. a X chance. 0 1,70544 *3 1,82038 26 1,69538 39 1,32320 52 2,24402 1 ^77233 *4 *>81557 27 1,67973 40 1,27366 53 2,10801 2 1,80280 1 5 1,81057 28 1,66340 4* 1,22298 54 3,98474 3 1,82567 16 1,80542 29 1,64654 42 1,16661 55 3,86721 4 1,83609 *7 I,8oooi 3° 1,62896 43 1,10705 56 3,75967 5 1,84227 1 8 *>79385 3* 1,61034 44 1,04240 57 3,66154 6 L84359 *9 1,78624 32 1,58845 45 2,97377 58 3,56i57 7 1,84247 20 1,77684 33 1,56223 46 2,89656 59 3,46748 8 1,83992 21 1,76513 34 *>53*30 47 2,80967 60 3,39278 9 1,83669 22 *>75233 35 1,49469 48 2,71025 61 3,29843 10 1,83292 23 1,73882 36 *>45556 49 2,60854 62 3,16813 1 1 1,82901 24 *>72494 37 1,41298 5° 2,50913 63 4,96284 12 1,82486 25 1,71042 38 1,36836 5* 2,38390 Logarithm of the Carlisle chance of living 45 years for every age a. 0 1,67459 12 *,78755 24 1,62987 36 1,19787 48 2,07716 1 1,74068 *3 *,78055 25 1,61 109 37 1,14010 49 3,95292 2 1,77070 *4 1,77217 26 1,59125 38 1,07899 50 3,83396 3 1,79346 *5 1,76212 27 1,56812 39 1,01283 5* 3,72444 4 1,80417 1 6 1,75002 28 1,54086 40 2,94292 52 3,62423 5 1,81084 *7 1,73712 29 *>5°933 4* 2,86492 53 3,52174 6 1,81277 18 *,72357 30 1,47258 42 2,77756 54 3,42408 7 1,81190 *9 1,70967 3* *>43339 43 2,67805 55 3,34433 8 1,80907 20 1,69510 32 1,39065 44 2,57662 56 3,24304 9 1,80487 21 1,67996 33 *>3457* 45 2,47770 57 3,10524 10 1,79968 22 1,66412 34 1,30007 46 2,35308 58 4 89256 11 *>79378 23 1,64745 35 1,24977 47 2,21344 Logarithm of the Carlisle chance of living 50 years for every age a. 0 1,643 16 1 1 *,73839 22 *,5525* 33 1,05634 44 3,92100 1 1,70987 12 1,72466 23 1,5249* 34 2,98970 45 3,80253 2 1,740*1 *3 1,71028 24 1,49266 35 2,91903 46 3,69362 3 1 ,76261 *4 1,69560 25 *>4547* 36 2,83982 47 3>59365 4 5 *,77234 1,77760 *5 16 1,68038 1,66486 26 27 1,4*430 1,37032 37 38 2,75*05 2,65000 48 49 3,49089 3,39225 6 *,77754 *7 1,64892 28 *,32434 39 2,54705 5o 3,31109 7 *,77458 18 1,63222 29 1,27810 40 2,44685 5* 3,20781 8 1,76925 *9 1,61459 30 1,22766 4* 2,32144 52 3,06793 9 1,76147 20 *,59577 3* *,*757° 42 2,18133 53 4,85274 JO * >75 1 23 21 *,57582 32 *>**777 43 2,04495 , 373 expressive of the law oj human mortality , &c. TABLE VII. — continued. Logarithm of the Carlisle chance of living 55 years for every age a. a X chance. a X chance. a X chance. a X chance. a x chance. 0 1,60991 10 1,66949 20 1,4394° 3° 2,89693 40 3,77i68 1 1,67464 1 1 1,65322 21 1,39887 3* 2,81764 4* 3,66198 2 1,70281 12 1,63646 22 i,3547i 32 2,72872 42 3,56*55 3 1,72278 *3 1,61892 23 1,30840 33 2,62734 43 3,45869 4 1,72894 *4 1,6005 1 24 T, 26143 34 2,52392 44 3,36033 5 1,72914 15 1,58105 25 1,20979 35 2,42296 45 3,27966 6 1,72215 16 1,56072 26 1,15661 36 2,29634 46 3,17699 7 1,71 169 17 t>5373° 27 i',09743 37 2,15482 47 3>°3735 8 1,69897 18 1,50967 28 *,03497 38 2,01689 48 4,82189 9 1,68490 i9 1 ’4773^ 29 2,96773 39 3,89H4 Logarithm of the Carlisle chance of living 60 years for every age a. 0 1,56146 9 1,58982 18 i,293*5 27 2,70839 36 3,63689 1 1,61925 10 1,57016 *9 1,24615 28 2,60597 37 3,535°3 2 1,63992 1 1 1,54908 20 1,19448 29 2,50196 38 3,43063 3 1,65251 12 *,52484 21 1,141 19 3° 2,40086 39 3,33077 4 1,65237 *3 *,49638 22 1,08183 3* 2,27417 40 3,24881 5 *,64740 *4 *,4633* 23 1,01902 32 2,13249 4* 3,14535 6 1,63698 *5 1,42467 24 2,95 106 33 3,99425 42 3,00524 7 1,62349 16 *,38377 25 2,87906 34 3,86830 43 4,78968 8 1,60761 *7 *,3395° 26 2,79855 35 3,74779 Logarithm of the Carlisle chance of living 65 years for every age a. 0 1,47972 8 1,48507 16 1,12608 24 2,48528 32 3,51270 1 1,53408 9 1,45261 *7 T,o6562 25 2,38298 33 3,40798 2 1,55*7* 10 1,41378 18 1,00378 26 2,25507 34 3,30763 3 *,56115 1 1 1,37213 *9 2,93578 27 2,1 1216 35 3,2249a 4 *,55729 12 1,32704 20 2,86374 28 3,97288 36 3,12025 5 1,54807 *3 1,27986 21 2,78313 29 3,84634 37 4,97873 6 1,53285 *4 1,23208 22 2,69278 3° 3,72569 38 4,76162 7 *,5**87 *5 ‘,*7975 23 2,59002 3* 3,6*47* Logarithm of the Carlisle chance of living 70 years for every age a. 0 1,38039 7 *,3*407 *4 2,92171 21 2,23965 28 3,38661 1 1,42994 8 1,26855 *5 2,84902 22 2,09655 29 3,28567 2 1,44010 9 1,22138 16 2,76802 23 3,95693 3° 3,20281 3 1,43861 10 1, 16886 *7 2,67757 24 3,82967 3* 3,09808 4 1,42003 1 1 1,11445 18 2,57478 25 3,70782 32 4,95640 5 1,39170 12 1,05416 *9 2,47001 26 3,5956i 33 4*73897 6 1,3559° *3 2,99049 20 2,36767 27 3,49237 574 Mr. Gompertz on the nature of the function TABLE VII. — continued. Logarithm of the Carlisle chance of living 75 years for every age a. a X chance. a X chance. a X chance. a X chance. a X chance. 0 1,22402 6 1,09821 12 2,665 1 1 18 3»94i69 24 3,26900 1 1,25299 7 1,041 19 13 2,56149 *9 3.81439 25 3,18494 2 1,24230 8 2,97918 H 2.45593 20 3,6925° 26 3,07898 3 1,22209 9 2,91 IOI 15 2,35295 21 3,58019 27 4,93607 4 T. 18885 10 2,83813 16 2,22455 22 3,47676 28 4,7 1 760 5 1,14678 1 1 2,75639 *7 2,08134 23 3,37066 Logarithm of the Carlisle chance of living 80 years for every age a. 0 2,97909 5 2,81604 10 2,34206 15 3,67778 20 3,1696 1 2,99530 6 2,74015 1 1 2,21291 16 3,56508 21 3,0635 2 2,96941 7 2,65214 1 2 2,06888 •7 3,46i55 22 4,9204 3 2,93272 8 2,55018 13 3,92839 18 3,35542 23 4,7016 4 2,87848 9 2,44523 H 3,80031 *9 3,25372 Logarithm of the Carlisle chance of living 85 years for every age a. 0 2,64836 4 2,41271 8 3,9!7°8 1 2 3,449°9 16 3,04845 1 2,63724 5 2,31997 9 3,78962 13 3,34213 *7 4,90525 2 2,58037 6 2,19667 10 3,66689 3,23965 18 4,68641 3 2,50372 7 2,05591 1 1 3,55345 *5 3,15490 Logarithm of the Carlisle chance of living 90 years for every age a. 0 2,15229 3 3,87062 6 3,5372i 9 3,22895 12 4,89279 1 2,09377 4 3,757°9 7 3,43612 10 3,I44°I 1 3 4,67312 2 3,984H 5 3,64480 8 3,33082 1 1 3,03682 Logarithm of the Carlisle chance of living 95 years for every age a. 0 3,47712 2 3,36435 4 3,19642 • 6 3,02058 8 4,66 1 8 1 1 3,4343* 3 3,28436 5 3,12193 7 4,87982 Logarithm of the Carlisle chance of living 100 years for every age a. 4,95424 4,91768 4,80805 4.6I535 expressive of the law of human mortality , &c. 575 TABLE VIII. — Logarithm of Deparcieux chance of living for every age a. a 10 years. 20 years. 30 years. 40 years. 50 years. 60 years. 70 years. 80 years. 90 years. 0 1 2 3 1,93450 1,89763 1,85*26 1,80346 *>73957 1,62634 *,39967 2,85 1 26 3>3°*°3 4 1,94469 1,90644 *>s5957 1,81 *88 1,74401 1,62495 1,37684 2,78408 3,0*323 5 ^95159 *>91193 1,86455 1,81698 *,74418 1,61979 *>34747 2,70443 6 1,95683 *>9*575 1,86784 1,82040 1,74248 1,61130 1,31482 2,61 130 7 1,96027 *,91825 *,86981 1,82177 1,73928 1,59968 *,27663 2,50098 8 1,96282 1,9*985 *,87*5* 1,82222 *,734*o 1,58512 1,2323 1 2,38721 9 *,96495 1,92101 1,87278 1,82146 1,72821 *,56781 1,18415 2,25473 lO 1,96614 1,92122 1,87309 1,81970 *,721 10 1,54688 1,12740 2,09691 1 1 1,96582 1,92042 1,87239 1,81612 1,71269 *>52337 1,06380 3>9°458 IZ 1,96448 1,91860 1,87069 1,81067 1,70296 *>49545 2,99190 3,66454 >3 *,96313 1,91676 1,86896 1,80507 1,69*84 *>465*7 2,91676 3,36653 *4 *,96175 1,91488 1,86719 *>79932 1,68026 1,432*5 2,83939 3,06854 *5 *,96034 1,91296 1,8(3539 1,79259 1,66820 *,39588 2,75284 *6 *,95892 1,91 1 01 *>86357 1,78565 *>65447 *>35799 2,65447 *7 *,95798 *>9°954 1,86150 1,77901 *,63941 1,3*636 2,54071 1 8 *,95703 1,90869 1,85940 *,77*28 1,62230 1,26949 2,42439 *9 * ,95606 *,90783 1,85651 1,76326 1,60286 1,21920 2,28978 20 *,955°8 1,90695 *>85356 1,75496 1,58074 1,16126 2,13077 21 *,95460 1,90657 *,85030 *,74687 *>55755 L09798 3,93876 22 *> 95 4*2 1,90621 1,84619 1,73848 1,53097 1,02742 3,70006 23 *,95363 1,90583 1,84194 1,72871 1,50204 2,95363 3>40340 24 *>953*3 1,90544 *>83757 1,71851 1,47040 2,87764 3,10679 25 1,95262 *>90505 1,83225 1,70786 *>43554 2,79250 26 1,95209 *,90465 1,82673 L69555 1,39907 2,69555 27 *,95156 1,90352 *,82103 1,68143 1,35838 2,58273 28 l_i,95 166 1,90237 1,81425 7,66527 1,3 1 246 2,46736 29 *>95*77 1,90045 1,80720 7,64680 1,263 14 2>33372 3° *>95 1 87 1 ,89848 i,79988 7,62566 T, 2061 8 2,17569 3* 1,95*97 1,89570 1,79227 7,60295 *">*4338 3,984*6 32 1,95209 1 ,89207 1,78436 *>57685 1,07330 3>74594 33 1,95220 1,8883 1 1,77508 1 ,54841 1,00000 3>44977 34 *>95z3* 1,88444 1,76538 T75T727 2,92451 3, *5366 35 1,95243 1,87963 i>75524 1,48292 2,83988 36 1,95256 1,87464 1,74346 7,44698 2,74346 37 *,95196 1,86947 1,72987 7,40682 2,63 117 38 *>95°7* 1 ,86259 *>7*36i 7,36080 2,51570 39 1,94868 *>85543 1,69503 *>31*37 2,38195 4° 1,94661 *,84801 *>67379 1,25431 2,22382 41 *>94373 1,84030 1 ,65098 1,19*4* 2.032 1 g 42 1,93998 1,83227 1,62476 7,12*21 3>79385 43 *,9361 1 1,82288 1,59621 7,04780 3 >497 5 7 44 *>932*3 *,8*307 1,50495 2,97220 3,20135 45 1,92720 1 ,8028 1 *>53049 2,88745 46 1,92208 1,79090 1,49442 2,79090 • 47 *>9*75* *>7779* 1,45486 2,67921 48 1,91 188 1 ,76290 1 ,4*009 2,56499 49 1,90675 *,74635 1,36269 2,43327 5° T,9oi 40 1,727*8 *,30770 2,27721 5 1 1,89657 1,70725 1,24768 2,08846 52 1,89229 1,68478 T,*8i23 3>85387 [ continued . 576 Mr. Gompertz on the nature of the function TABLE VIII. continued. — Logarithm of Deparcieux chance of living for every age a. a 10 years. 20 years. 30 years. 40 years. 50 years. 60 years. 70 years. 80 years. 90 years 53 54 55 56 57 58 59 60 61 62 63 64 66 67 68 69 70 7 1 72 73 74 75 76 77 78 79 80 81 82 83 84 V 1,88677 1,88094 1,87561 1 ,86882 1,86040 1,85 102 1,83960 1,82578 i, 81068 1,79249 *>77333 1,75189 1,72768 1,70352 1,67695 1,64719 1,61634 1,58052 1,54043 i*49645 L45159 1,40724 1,35696 1,29648 1,22435 1,15490 1,07058 2,96951 2,84078 2,67264 2,44977 2,22915 T,66oio 1,63283 1,60329 i>57234 i*53735 1,49821 1*45594 1 ,40630 7,35 1 1 1 1,28894 1,22492 7*159*3 1,08464 T, 00000 2,90130 2,80209 2,68692 2,55003 2,38121 2,16909 3*9°i36 3*63^39 T,i 1 169 1,04007 2,96025 2,86882 2,76170 2,65311 2,52652 2,37581 2,191 89 3,96158 3,67469 3,38828 3*56146 3,26922 ! rv expressive of the law oj human mortality , &c. TABLE IX. — Logarithm of the Northampton chance for living at every age a. 577 a 10 years. 20 years. 30 years. 40 years. 50 years. 60 years. 70 years. 80 years. 90 years. o 1,68764 1*64396 1*57564 1*49417 7,38958 7,24287 7,02428 2,60484 3*59643 i 1,81295 1*76713 1,69746 1,61431 1,50640 i*35435 1,12443 2,67151 3*59446 2 1,88378 *>83536 1,76454 1,67952 7,56809 1,41046 1,16788 2,67677 3,51790 3 1,91089 1,85979 1,78780 1,70070 1,58568 1,42229 1,16522 2,62961 3*37283 4 1,92894 1,87511 1,80190 1,71263 1*59383 1,42421 1,15070 2*55993 3*14495 5 1*93843 1,88180 1*80733 1,71581 i*593oo 1,41691 1*12431 2*47370 4,80625 6 r>94739 1,88788 1,81211 1*71823 1,591 18 7,40806 1*09339 2*37854 7 1 ,95 322 1,89101 1,81390 i*7i755 1,58601 7*39522 1,05661 2,27263 . 8 1,95660 1,89203 1*81352 i*7H59 1*57827 i*379°9 1,01505 2,15453 9 *>95739 1,89080 1,81084 1*70923 1,56781 1*3594° 2,96901 2*03386 lO L95632 1,88800 1,80653 1*70194 1*55523 1*33664 2,91720 3*90879 1 1 *,95418 1,8845 1 1,80136 i*69345 1*54140 1*31148 2*85856 3,78151 12 L95158 1,88076 i*79574 1,68431 1,52668 0 >— « 00 N 2*79299 3*63412 *3 1,94890 1,87691 1,78981 1*67479 1,51140 1*25433 2,71872 3*46i94 *4 1,94617 1,87296 1,78369 1,66489 1*49527 1*221 76 2,63099 3,21602 ,S 1*94337 1,86890 i*77738 1,65457 1,47848 7,18588 2,53527 4,86782 16 i, 94049 1,86472 1,77084 1*64379 1,46067 1*14600 2,43H5 1 7 i*93779 1,86068 1*76433 1,63279 1,44200 1,10339 2,31941 1 8 i*93543 1,85692 i*75799 1 ,62167 1,42249 1*05845 2,19793 19 i*9334i 1*85345 1*75184 1,61042 1,40201 i>oi 162 2,07647 20 1,93168 1,85021 1,74562 1*59891 1,38032 2,96088 3*95247 21 1*93033 1,84718 1,73927 1*58722 i*3573o 2*90438 3*82733 22 1,92918 1,84417 1,73274 i*575H i*33253 2,84141 3,68255 23 1,92801 1,84091 i*72589 1,56250 1*30543 2,76982 3*51304 24 1,92679 1,83752 1,71872 i,549io 1*27559 2,68482 3*26984 25 i>92553 1,83401 1,71 120 i*535n 1*24251 2*59i9i 4,92445 26 1,92423 1*83035 1,70330 1,52018 1,20551 2,4906 6 27 1,92289 1,82654 1,69500 1,50421 1,16560 2,38162 28 1,92149 1,82256 1,68624 1,48706 1,12302 2,26250 29 1,92004 1,81 843 1,67701 1,46860 1,07821 2,14306 3° i’9*853 1*81394 1,66723 1,44864 1,02920 2,02079 31 1,91685 1,80894 1,65689 1*42697 2,97405 3,89700 32 1*91498 1*80355 1,64592 1*40334 2,91223 3,75336 33 1,91 290 1,79788 1,63449 i*37742 2,84181 3,58503 34 1*91073 1,79193 1,6223 1 1,34880 2,75802 3,34305 35 36 1,90848 1,9061 2 1*78567 1*77907 1,60958 i*59595 7,31698 7,28128 2,66637 2,56643 4,99892 37 1,90365 1,7721 1 1,58132 1,24271 2*45873 38 1,90107 1*76475 1*56557 1,20153 2,34101 39 1*89839 i>75697 1,54856 1,15817 2,22302 40 1,89541 1,74870 1,5301 * 1,1 1067 2,10226 41 1,89209 1,74004 1,51012 7,05720 3*98015 42 1,88857 1*73094 1,48836 2*99725 3*83838 43 1,88498 1,72159 1,46452 2,92891 3,67213 44 1,88 1 20 1,71158 1*43*07 2,84730 3*43232 45 1*87719 1,701 10 1,40850 2*75789 3*09044 46 1,87295 1,68983 1,375*6 2,6603 1 47 1,86846 1,67767 i*339o6 2,55508 48 1,86368 1,66450 1 ,30046 2*43994 49 1,85858 1,65017 1,25978 2,32463 50 1*85329 1,63470 1,21526 2.20685 1 5i 1,84795 1,6 1 803 1,165 1 1 2,08806 I 52 1*84237 1*59979 1,10868 3*9498i [continued. 578 Mr. Gompertz on the nature of the function TABLE IX. continued.— Logarithm of the Northampton chance for living at every age a. mm - a io years. 20 years. 30 years. 40 years. 50 years. 60 years. 70 years. 80 years. 90 years. 53 7,83661 *>57954 **04393 3*787*5 54 1,83038 *,55687 2,96610 3*55 * *2 55 1,82391 **53i3i 2,88070 3*21325 56 i, 81688 1,50221 2,78736 57 1,80921 1,47060 2,68662 58 7,80082 7,43678 2,57626 59 7*79*59 1,40120 2,46605 60 1,78141 **36197 2,35356 61 1,77008 1, 3*7*6 2,2401 1 62 *>75742 1,2663 1 2,10744 63 1,74293 1,20732 3*95°54 64 1,72649 **13572 3,72074 65 1,70740 1,05679 3*38934 66 **68533 2,97048 1 67 1,66139 2,87741 68 7,63596 2*77544 69 1,60961 2,67446 70 7,58056 2,57215 71 1,54708 2,47003 72 1,50889 2,35002 73 7,46439 2,20761 74 1,40923 3*99425 75 *>34939 3*68194 76 1,28515 77 1,21602 78 *>*3948 79 1,06485 80 2,99159 81 2,92295 82 2,84113 83 2,74322 84 2,58502 85 2>33255 1 579 expressive of the law of human mortality , &c. How the value of particular assurances may be deter- mined from the value of annuities, is shown in my Paper in the Philosophical Transactions for the year 1820, many of the cases of which are solved by methods essentially the same as those which have been long adopted ; but when such assurances are but for terms, which are not of great extension, very near approximations may be had by using a geometrical progression, without confining the arithmeti- cal operations to the same route, since the chance of extinc- tion of the joint lives of the present age a , b , c , &c. taking place between the period commencing with the time n-\-t — 1, and finishing with the time n -f- t, from the present, is = t- 1 : a, b,c. Sec. \ -f t : a, b, c, &c.) b, c, Sec. j it follows that if r be the present value of unity, to be received certain in % the time 1, and \ +t.t ;a,b,c.&c .= ^-1 "> whatever t may be, that ™ L a, b, c. Sec. or the assurance of unity to be received at the first of the equal periods 1, from the com- mencement of the time n*-> 1 to the expiration of the time m, which shall happen after the extinction of the joint lives, ji — 1 1 flj by c » See* • 1 A. ft — l . U,) Vy r n / * I, . N IS equal to — r x r x (1 — 7 r) -f r x (tt — 7 r9) 4- rl^-TT3) r-x(7Tm-nZi v*1-*)} =( i^7r)x^-TQ^>c-&c-x v a, b , c, Sec. \ rJL. ~ rn"t 1 -9,” if T v” + 3 r” -tt™ -*-l} = T x ! 71-1 ^ -L. |r+irr^ffr+irrtt,.rif ) c. < r i-iraM&cJ OT- 1 1 „ r c,&c.+ r * ti:Uc,fcc. f ==(1 r* Sec. If the assurance be not deferred, n will be equal to 1, and r Nw'l 1 I we shall have, according to the hypothesis, » b c> &c- = r r ( 1 — tr). rx « a,b,c:sf—; and also = ^ . mlfl* b>c> &c- If ^ be MDCCCXXV. 4 F 580 Mr. Gompertz on the nature of the function taken equal to 1 ,we shall have from the equation L +t_ra b Cj& and this would be the real n-i: a,b,c, Sec. value which should be taken for n r, if the geometrical pro- gression coincided perfectly with the fact ; and it would be indifferent whether we made it equal to ”+t,a> 6,c,&c , or ^ 7i-i +t:a,b,c,8cc. II * Q }) C Sc C • -p-:- ’ — - , as the two would be the same ; but this not 7i-l :a, b, c. Sec. being the case, there will be a preference ; and generally, if not always, nr should be taken an intermediate value between the two ; and when the term is not very long, it will answer a good purpose to take it about the middle between them, inclining generally, though perhaps not always, rather nearer the last than the first, as the first terms are generally of more consequence than the last. If the said assurance be not deferred, and instead of being paid for immediately, be to be paid for by equal periodic payments, at an unite of time from each other, up to the time m—i inclusive, and the first payment be to be made immediately, then will the present value of such periodic payment be Jhr’ b>c’ &c^ anc[ consequently each payment, from what is shown above, is r r equal to m ajf> c> jgi. -r 3.— b’ c’ &c- = ( i — 7 r). r. From whence we may draw an inference worthy of remark, namely ; when an assurance of joint lives is meant to commence immedi- ately, and to continue for a term of t years, which is not large, and to be paid for by t annual payments, that those payments will not differ much with the increase of the time t , provided, as I have said, that t be not large, and the ages 581 expressive of the law of human mortality , & c. be not at the extremes of life, a consequence which follows from the near agreement to a geometrical progression which takes place in the number of living at each small equal in- crement of time ; that is to say, from the near coincidence r 71 • b y C y & C. • i 71 *"f“ t l CL% l)y Cf &C. i • • p of n-ua, b, c&c. Wlth n-f.a.b, c, &cT > or the sma11 variation of 7T for the different values of t : and also, that when the number of years for which an assurance continues be not very long, and the ages be not at the extremes of life, the annual pre- miums will not differ widely from the premiums to be paid for an assurance of one year of a life older than the proposed life by about half the term : thus, according to the North- ampton table, at three per cent, to assure 100 /. at the Age .... *5 20 30 40 50 60 For 7 years, the annual premium by the com- mon modes of calculation ► c£i..2.. I I I.. 9.. 5 1.. 14.. 1 1 2.. 4.. 1 CO o’ 4- 7- 1 And the premium for one year assurance for an age 3 years older . . . > i~3» 3 i.. 9.. 8 1..15.. 0 2.4.. 6 3.. I.. O 4.. 7.. 8 the difference of which is very small. — As another example, let Age .... 10 20 30 40 5° 60 For 10 years, the annual' premium will be, by com- mon modes of calculation > £o..ig.. 2 1. .9.. 1 1.. 15.. 8 2.. 5.. 8 3- 3-- 4 4.. 12.. 6 Premium for one year as- I < • 1 6 • • q. 2.. 6.. 8 surance, age 5 years older j 0..17..1 1 1.. 10.. 7 3- 5- 1 4.-15.. 2 Here, except at the age to, the excess is rather more in the approximation than in the first set of examples ; but it should be recollected, that we took the exact middle, instead of inclining to the early age. 582 Mr. Gompertz on the nature of the function According to the Carlisle table of mortality at 3 per cent, to assure 100/. at the Age .... For 7 years, the annual ' premium, by common modes of calculation . For one year, the premium For 10 years, the annual ] premium, by common l modes of calculation . For one year, at an age"l 5 years older ... . j 10 20 30 40 5° £0 10 5 0 13 10 0 19 10 00 111 0 010 5 0 13 9 0192 186 1 12 1 0 11 3 0 14 7 104 1 7 7 1 14 11 012 0 0142 0 19 11 190 1 14 10 60 3 *3 8 3 XS 9 3 17 8 3 l9 9 Moreover, because™ T 1 la, ft, c, 1 vrt V — - Sec. , or the single premium for the assurance of unity, on the joint lives a , 6, c, &c. for m years, is =«. 1 L a,b,c. Sec. 1 a, b, c. Sec. 0)2, b, c, Sec. , . T ' m m l L— r -J- 1 — — * I. m : a, b, c, & c. m 0 \a>b,c,Sec. *111 : a, b, c, 8ec. m ^ » ^ r "’-1 ’ \ 7 f (i-A-ml u,b,c, Sec. * a,b,Cj&. c. ^a,b,c,Sec. T if this be divided by we shall have the annual r r premium for such assurance ; that is,”- c’ &c ~m-^-b,c,~z=z I— m: a, b, c,Sec. »* L a\ hL-i-&cz' — _ — 1 + r . The said annual premium maybe ex- pressed by 1 0 m - 1 a, b, c. Sec. ( 1— m,a,b,c,8ec. J* , ( 1 |a-i, 6-1, c-i, &c _ a-i, 6-1, c-i,&c.^ _ , —j— — •/ • X— -j— — a> b, c, Sec. ’ a, b, c, Sec. / This last mode is well adapted to logarithms in the use of our general tables ; and this method, supposing the annuities were accurately determinable by our general tables, would be accurate. The last formula is derived from that imme- r & & diately before, in consequence of — - — - — being identical r Y1 L \ \a -I, ft -1, c -1, Sec. a— 1, ft— 1, c — 1, &c. with X 7 (If Uf Cf 583 expressive of the law of human mortality , &c. Example. To find the annual premium to assure a life, at the age a years, for 10 years, according to the Carlisle mortality, and three per cent, interest. a — 20 3° 40 50 60 70 Log. of the accommoda. ' chance for living i o yrs. at the age a— i,Tab.V. X 1,03- = T.9690 1. 8716 7.9556 7.8716 7 . 9406 7.8716 7.9328 7.8716 1-8435 7.8716 7.7005 7.8716 Sum . . • — 1 . 8406 7.8272 7.8122 7.8044 7.7151 7.5721 ‘Corresponding . . . To this we get from Ta. I. r 1 •9H43 3i . 90407 362 10 .89892 103 10 •89379 205 21 .84846 248 5 .78092 94 5 1 \a — 1 A jo ■■ - L . — •9H74 .90779 .90005 . 89605 .S5099 .78191 Therefore, A^r^T.Vtl.) T. 96682 7.95400 1-93772 7.91830 7.81893 1.59873 *A i,03-I°— T. 87163 7.87163 7.87163 7.87163 7.87163 7.87163 Sum == the log. . • • T. 83845 7 .82563 7.80935 7.78993 7.69056 7.47036 The N° corresponding — .68937 .66932 . 64469 .61650 .49041 .29536 Its complement to unity • 3 io63 .33068 •35531 •3835° .50959 .70464 The log. of the last r . — I. 49224 7*5 !94! 7.55061 1-58377 7.70722 7.84797 1 Complement of A 10 L a-i — T. 08526 7.09221 7.09995 7.10395 7 . 14901 7.21809 a ^ JL ♦ • • • • • ii ■ T. 99694 7.99571 7.99481 7.99402 7.98754 7.97813 X r • • • • • — I. 98716 7.98716 7.98716 7.98716 7.98716 7.98716 Sum = logarithm . • • 2.56160 i. 59449 2.63253 2.66890 2.83093 7.03135 Number corresponding — 1,03— 1 . . . rn .03644 — .0291 3 •03931 — •o29i3 .04291 — 02913 .04666 — 02913 .06775 — 02913 .10749 — 02913 Ann. premium for an 1 _ assurance of \l. . J ~~ Ditto for 100/. . . . .00732 £o..i4..8 .01018 I •• o»# .01378 1.. 7.. 7 •oi753 1..15.. 1 .03862 3-1 •• 3 .07836^ 7*« 1 ^ > for annual premiums. The reader has here an opportunity of comparing the results from my tables, with those above calculated by Mr. Milne’s Carlisle tables. — I may probably be able at a future period to add examples, which I regret time will not at present permit. L 5^4 1 Errata in Mr. Gompertz s Paper in Part II. of Philosophical Transactions for 1820. Page Line 2 2° \ for * a-\-y put ‘ c + a:’ — lines ii and 20, dele ' ny in the denominator. r Jl I Oy l)y C 221 21 the second symbol should be 223 4 before ‘ chance’ insert ‘ value of the.’ 224 2 and 5 in the symbol, before the second a , insert a comma — line 15, insert ‘ :’ before a"— five lines from the bottom, for ‘ c’ put * C ’—line 2 from the bottom, for ‘ proved ’ read ‘ provided.’ 226 1 3 in the 2d and 3d symbol, put ‘ n ’ for < m ’—and in the 4th, put ‘ p’ for • y 9 — in the first symbol in the bottom line, put < n’ for * m and for the 3d symbol p n m 227 6 for < will ’ read ‘ will be ’—line 7, in symbol, write ‘ * ’ for < and for * r ’ write ‘ r ’ line 14, put ‘ » ’ in the lower angle in the right of the r symbol, thus £ m 228 1, 3, 4, and \ \,fe or — where there is nothing in the lower angle, write 229 9, under the first A put ‘ b ’ for * a ’ — line 2 from the bottom, between ‘ : and -2 ’ put ‘+’. 23 1 2 from bottom, put a dash over the second T. 232 12 for ‘ n’ put *m’ — line 13, for * M.r ’ put ‘ M\ 233 8 for ‘ 9457 ’ put 1 4597 ’. 236 7 for ‘ F’ put * E ’ — line 11, for * a & c ’ put ‘ b ’. 240 8 in the second formula, for ‘ r + 1 ’ put * r + s 243 19 /or f form ’ put * from 244 1 1 ybr f 7 — x ’ read ‘ + x,’ 246 12 for last ‘ p’ put ‘ q’. 247 16 include the last ‘ L’ with the expression of line 17 in * ( )’, 251 11 for ‘ K ’ write ‘ k ’. 255 14 and 15, for ‘ + ’ write ‘ -’. 2c6 2 for ‘ L ’ write * L ’. b « 258 4 from bottom, dash over the first ‘ K 260 7 from bottom, insert ‘ — ’ before * the.’ C 585 3 Page Line 262 i insert « X * before the last * n ’ — line 9, for ( of’ read ‘ if’. 265 1 dele * or last ’ — line 4, for the last ‘ L ’ write ‘ L.’ 269 13 after * there is * insert ‘ only.’ 274 5 for * A ’ read ‘ B ’ — line 8, for the second ‘a’ at top and bottom write ‘ b ’ — line 1 o, /or ‘ A ’ write * B 277 1 and 2, c/e/e last ‘ s ’ in ‘ survives 282 3 transpose the * 3 * and « 2 ’ — line 7, in denominator dele < tt,’ in numerator dele ‘ i — 289 1 after ‘Nr,’ insert ‘ 1 — — line 3, after * become’ insert ‘ — — line 5, at the commencement insert ‘ — — line 8, after ‘ b ’ insert ‘ — , \ 290 1 at the commencement insert * — , ’ — line 2, before c r ’ ‘ — line 3, L_i to c ~ / prefix ‘-f ’ instead of « — — line 6, /or ‘ with ’ ‘without’ L c — line 3 from bottom, in symbol, for ‘ o ’ write ‘ 80 ’ — line 2 from bottom, for ‘ n ’ put ‘ nr \ 291 1 and 2 from bottom, dele dash above ‘ N.’ 294 5 insert * t ’ before the semicolon. . . [ 1 ] PRESENTS RECEIVED BY THE ROYAL SOCIETY, From 18 th November , 1824, to 1 6tli June , 1825. WITH THE NAMES OF THE DONORS. PRESENTS. ACADEMIC et SOCIETATES. Magnce Britanniae, ROYAL INSTITUTION.— A Journal of Science, Lite- rature and the Arts, No. 33 — 37. 8° London. SOCIETY FOR THE ENCOURAGEMENT OF ARTS, MANUFACTURES AND COMMERCE.— Transac- tions of the Society instituted at London for the En- couragement of Arts, Manufactures, and Commerce, Vol. XLII. 8° London, 1824. LINNEAN SOCIETY.— The Transactions of the Linnean Society of London, Vol. XIV. Part IL and III. 40 Lon- don, 1824 and 1825. HORTICULTURAL SOCIETY. Transactions of the Horticultural Society of London, Vol. V. Parts IV. and V. 40 London, 1824. Report of the Garden Committee on the formation and progress of the Garden, drawn up for the information of the Fellows of the Society, as directed by the Bye-Laws, March 31, 1824. 40 London, 1824. GEOLOGICAL SOCIETY. — Transactions of the Geolo- gical Society, established Nov. 13, 1807, 2nd Series, Vol. I. Part II. 40 London, 1824. ASTRONOMICAL SOCIETY.— Memoirs of the Astro- nomical Society of London, Vol. I. Part II. 40 London, 1825. MANCHESTER PHILOSOPHICAL SOCIETY. — Me- moirs of the Literary and Philosophical Society of Man- chester, 2nd Series, Vol. IV. 8° London, 1824. MDCCCXXV. a DONORS. The Managers of the Royal Institution. The Society for Encou- ragement of Arts, Manu- factures and Commerce. The Linnean Society. The Horticultural Society. The Geological Society. The Astronomical Society of London. The Literary and Philoso- phical Society of Man- chester. PRESENTS. DONORS, ACADEMIC et SOCIETATES. ROYAL ASIATIC SOCIETY.— Transactions of the Royal Asiatic Society of Great Britain and Ireland, Vol. I. Part I. 4° London , 1824. Galilee. ACADEMIE ROYALE DES SCIENCES.— M^moires de l’Academie Roy ale des Sciences de l’Institut de France, ann6es^ 1819 et 1820, Tome IV. 40 Paris, 1824. SOCIETE DE GEOGRAPHIE.— Questions proposes aux Voyageurs et a toutes les personnes qui s’intdressent aux progres de la Geographic, premiere Serie. 8° Paris, 1824. Belgii. SOCIETE DE FLORE (DE BRUXELLES.)— Cinquieme Exposition publique. 8° Bruxelles, Juillet, 1824. Sixieme Expo- sition publique. 8° Bruxelles, Fevrier, 1825. Germanice. ACADEMIA LEOPOLDINO-CASSAREA. — Nova Acta Physico-Medica Academic Caesarea Leopoldino-Caro- linae Naturae Curiosorum, Vol. XII. Part I. 40 Bounce, 1824. Russioe. ACADEMIA SCIENTIARUM IMPERIALIS PETRO- POLITANA. — Memoires de l’Academie Imperiale des Sciences de St. Petersbourg, Tome IX. avec l’Histoire de l’Academie pour les annees 1819 et 1820. 40 St. Petersbourg, 1824. Italice. ACADEMIE DES SCIENCES DE TURIN.— Memorie della Reale Accademia delle Scienze di Torino, Vol. XXVII. e XXVIU. 40 Torino, 1823 & 1824. ISTITUTO IMPERIALE REGIO DEL REGNO LOMBARDO VENETO. Memorie dell’ Imperiale Regio Istituto del Regno Lombardo Veneto, Vol I. 1812 — 1813, and Vol. II. 1814—1815. 40 Milano, 1819 — 1821. AMPERE (M.) Precis de la Theorie des Ph^nomenes Elec- tro-Dynamiques. 8° <2 Paris, 1824. ANATOMIA. — A Fasciculus, containing nine Lithogra- phic Anatomical Drawings, from preparations in the Museum of the Army Medical Department at Chatham, fol. London, 1824. ANNALS of Philosophy, New Series, No. 43 to No. 54. 8° London, 1824 and 1825. ASTRONOMIA. — Connaissance des terns ou des Mouve- mens Celestes, a Pusage des Astronomes et des Naviga- teurs pour l’ann. 1827. 8° Paris, 1824. The Royal Asiatic Society. The Royal Academy of Sci- ences at Paris. The Geographical Society of Paris. The Society of Flora, Brus- sels. The Caesarean Academy of Naturalists at Bonne. The Imperial Academy of Sciences of St. Peters- burgh. The Royal Academy of Sci- ences at T urin. The Imperial Lombardo- Venetian Institute. M. Ampere. Sir James Mac Grigor and Sir W. Franklin. John George Children and Richard Phillips. Le Bureau des Longitudes de France. C 3 3 PRESENTS. ASTRONOMIA. Astronomical Observations made at the Radcliffe Observatory at Oxford, from May i, 1824, to May 1825, by and under the direction of the Rev. Abram Robertson, D.D. Sav. Prof. Astron. MS. fol. The Nautical Almanac and Astronomical Ephemeris for the year 1827. 8° London, 1824. AVOGADRO ( Le Chev. amedee) iere et 2eme Memoire sur l’Affinitd des Corps pour le Calorique et sur les Rap- ports d’Affinite qui en rdsultent entre eux. 40 From the Memoirs of the Royal Academy of Sciences of Turin, Vol. XXV III. and XXIX. ( Cat) . amadeo) Nuvove Considerazioni sulle Affinita de’ Corpi pel Calorico calcolate per mezzo de’ loro Calori specifici e de’ loro poteri refringenti alio stato Gazoso. (inserite nel Tomo XIX. degli Atti della Societa Italiana delle Scienze residente in Modena.) 40 Modena, 1822. BERRUTI (secundus joannes maria) De Luce— De Oculi Globo — De Visu — De Metaschematismo — De Epispasticis — De Inflammationibus. 8 9 Augustas, Tauri- norum, 1823. BESSEL (f. w.) Astronomische Beobachtungen auf der Koniglichen Universitats-Sternwarte in Konigsberg — Neunte Abtheilung vom 1 Januar. bis 31 Decern. 1823. fol. Konigsberg, 1824. BOLLES (william) v. Trigonometer. A Description and practical Appli- cation of Bolles’s Trigonometer. 120 1824. BOWDITCH (natiianiel) Modern Astronomy, from the North American Review for April, 1825. 8° Boston, 1825. BROWN (thomas) On Cholera, more especially as it has occurred during late years in British India. 8° Edin- burgh, 1824. CANTU (joannes laurentius) Specimen Chemico-Me- dicum de Mercurii praesentia in Urinis Syphyliticorum, Mercurialem Curationem patientium. 40 Essai Chemico-Medical de l’Existence du lode dans les Eaux Minerales Sulpu- reuses, particulierement dans celles de Castelnovo d’Asti, et des Moyens de la constater. 40 From the 29th Vol. of the Memoirs of the Royal Academy of Sciences at Turin. CATALOGUS. Catalogue of the Library of the Ameri- can Philosophical Society held at Philadelphia, for pro- moting useful Knowledge. 8° Philadelphia, 1824. CHINESE (Books, Manuscript and printed) v. Morrison. — — Hwan Teen Too Shwo, or a literal and pictorial Description of the Circle of the Heavens, edited by Yuen, the present Governor (1824) of the provinces of Kuang Tung and Kuang Se, compiled by him from works formerly written by the Jesuits in China. DONORS. The Trustees under the Will of the late Dr. Rad- cliffe. The Commissioners of the Board of Longitude. Chev. Avogadro. Dr. Berruti. Professor Bessel. Mr. William Bolles. Mr. N. Bowditch. Mr. Thomas Brown. Dr. J. L. Cantu. The American Philosophi- cal Society. JohnReeves,Esq. ofCanton. C 4 3 DONORS. PRESENTS. CHINESE. A Manuscript Dictionary, Chinese and Latin. Dictionary, compiled by order of the Emperor Kang Hee, in 32 volumes (small paper), called Kang HeeTszeTeen. Tsaon Tsze Hwuy, Dictionary of the Running Hand Character. Pih Mei Tao, Portraits and Descriptions of the Hundred illustrious Females. Fa Tee, Rules for forming the Chinese Charac- ter in the best manner. Dr. Morrison’s Translation of the New Testa- ment into Chinese, 8 volumes (large paper.) CHURCHMAN. A respectful Address to the most Rev. the Archbishops and the Right Rev. the Bishops of the United Church of England and Ireland, respecting the necessity of Morning and Afternoon Service on Sunday in every parish Church in His Majesty’s Dominions, with a few Thoughts concerning the residence of the Clergy , by a Churchman. 8° London, 1825. CLARKE (george, Esq.) Essay on the Cause of the Mag- netism of the Needle, with the reason of its being North and South, and its variation ; also other Investigations arising from the same source, proposed for Investiga- tion. 8° Southwark , 1825. DAMOISEAU (M. le Baron de ) Tables de laLune formees par la seule Theorie de l’Attraction, et suivant la divi- sion de la circonference en 400 degres. 40 Paris, 1824. DEGEN (carolus ferdinandus) Tabularum ad facilio- rem et breviorem Probabilitatis Computationem utilium Enneas. 8° Haunice, 1824. DICTIONARIUM (n. Chinese Books.) The Seven Seas, a Dictionary and Grammar of the Persian Language, by His Majesty the King of Oude, in Seven Parts, fol. Printed at His Majesty’s press in the city of Lucknow, 1822. DOEVEREN (hermanus franciscus Van ) De Macro- glossa seu Linguae Enormitate (Dissertatio Medica ln- auguralis) 8° Lugduni Batavorum, 1824. EARLE (henry. Esq ) Practical Observations in Surgery. 8° London, 1823. FLORA BATAVA, No. 66, 67. 40 Amsterdam. FRANKLIN (john, Capt. R.N.J Narrative of a Journey to the Shores of the Polar Sea in the years 1819, 20, 21, and 22 ; with an Appendix on various subjects relating to Science and Natural History, illustrated with plates and maps. 4 ° London, 1823. * GAY LUSSAC (M.) Instructions for the use of the Cente- simal Alcohometer (Alcoometre centesimal), and the Tables which accompany it. 120 Paris, 1824. John Reeves, Esq. of Canton, The Author. George Clarke, Esq. The Board of Longitude of France. C. F. Degen. The Court of Directors of the Hon. Eastlndia Com- pany. Professor Moll. Henry Earle, Esq. H. M. the King of the Ne- therlands. Capt. John Franklin. M. Gay Lussac. C 5 1 PRESENTS. GAZZERA (costanzo) Descrizione del Monumenti Egizi del Regio Museo continent! Applicazione delle Dot- trine del Signor Champollion Minore ad alcuni Monu- menti Geroglifici del Regio Museo Egizio. GOLDINGHAM (john) Report of the Length of the Pendulum at the Equator, by John Goldingham, Esq. from Experiments and Observations made on an Expe- dition fitted out under his direction from the Observa- tory at Madras, by order of the Madras Government, in the year 1821 ; together with a deduction of the Figure of the Earth, by combining the Equator, Madras, and London Experiments ; also the Geographical situation of different places seen on the Expedition, with Plates and Views, fol. no place or date , but printed at Madras in 1824. Results of Meteorological Ob- servations taken at the Madras Observatory under the superintendence of John Goldingham. Esq. MS. fol. Head to the Society 24 th March, 1825. GMELIN (c. g.) m. d. Versuche fiber die Wirkungen des Baryts, Strontians, Chroms, Molybdans, Wolframs, Tellurs, Titans, Osmiums, Platins, Iridiums, Rho- diums, Palladiums, Nickels, Kobalts, Urans, Ceriums, Eisens, und Mangans auf den thierischen Organismus. 8° Tubingen, 1824. GUINAND. Some Account of the late M. Guinand, and of the discovery made by him in the Manufacture of Flint Glass for large Telescopes. 8° London, 1825. HALL (Sir james, Bart.) On the Consolidation of the Strata of the Earth (from the Transactions of the Royal Society of Edinburgh). 4 0 Edinburgh, 1825. HERSCHEL (j. f. w.) On the Absorption of Light by Coloured Media, and on the Colours of the prismatic spectrum exhibited by certain Flames, with an account of a ready Mode determining the absolute dispersive power of any medium by direct Experiment — (from the Transactions of the Royal Society of Edinburgh) 40 Edinburgh, 1823. HILLARY ( Sir william, Bart.) An Appeal to the British Nation on the Humanity and Policy of forming a Nati- onal Institution for the preservation of Lives and Pro- perty from Shipwreck. 8 0 London, 1823. A Plan for the Construc- tion of a Steam Life Boat, also for the Extinguishment of Fire at Sea, Sec. 8° London, 1824. HOLMAN (james) Travels through Russia, Siberia, Poland, Austria, Saxony, Prussia, Hanover, &c. under- taken during the years 1822, 1823, and 1824, while suffering from total blindness, 2 vols. 8° London, 1825. HOSAC (david) m. d. Essays on various subjects of Medical Science, 2 vols. 8° Nexu York, 1824. DONOkS. Professor C. Gazzera. The Court of Directors of the Honble. East India Company. John Goldingham, Esq. Dr. C. G. Gmelin. The Translator. Sir James Hall, Bart. John Frederick William Herschel, Esq. $ Sir William Hillary, Bart. James Holman, Esq. Dr. David Hosac. / DONORS. PRESENTS. IDELER (Dr. ludwig) Handbuch der Mathematischen und Technischen Chronologie. Erster Band. 8° Berlin, 1825. JOMARD. Coup d’oeil rapide sur les progres et l’etat actuel des Decouvertes dans l’lnterieur de l’Afrique (Extrait de la Revue Encyclopedique, 71. cah. T. xxiv) 8° — Extrait d’un Memoire sur la Communication du Nil des Noirs, ou Niger, avec le Nil d’Egypte, contenant des Remarques sur la hauteur et la temperature du lieu ou a peri le Docteur Oudney, dans son voyage a l’ouest du Royaume de Bornou (Lu a l’Academie Royale des Sciences, le 18 Avril, 1825) 8°. KAEMTZ (ludovicus eridericus. Dr.) Dissertatio Mathematico-Physica de Legibus Repulsionum Elec- tricarum Mathematicis, 8° Ilalce, 1823. KIDD (john) m. d. An Introductory Lecture to a Course of Comparative Anatomy, illustrative of Paley’s Natural Theology, 8° Oxford, 1824. KIRCKHOFF (1. r. s.) von. Beknopte Geschiedenis der Koninklyke Akademie van Schoone Kunsten te An- twerpen, tweede Uitgane, 8° Te Antwerpen, 1824. LAGERHJELM (p.), j. h. FORSELLES, & g. s. KALL- STENIUS, Hydrauliska Forsok anstallda vid Fahlu Grufva Aren 1811-1815, 2 vols. 8° Stockholm, 1818. LAPLACE ( Marquis de) Traite de Mecanique Celeste, Livre xiv. 40 Juillet 1824. — « ■- — . — — ■, Livre xv. Decembre, 1824. LINK (iienr. frid.) Elementa Philosophise Botanies, 8° Berolini, 1824. LOCKER (edward hawke. Esq.) Views in Spain from Sketches made in a tour through that Kingdom in 1 8 1 3 . No. 11 and 12. 40 London 1824. LYALL (robert) m. d. An Answer to the Observations on the Character of the Russians, and a detailed His- tory of Moscow, contained in the 61st number of the Quarterly Review, 8° London, 1825. MACMICHAEL (william) m. i>. A Brief Sketch on the progress of Opinion upon the subject of Contagion, with some remarks on Quarantine, 8° London 1825. MAGENDIE (f.) Precis Elementaire de Physiologie, tome i.8°^ Paris, 1825. MANTELL (gideon) The Fossils of the South Downs, or Illustrations of the Geology of Sussex ; the engrav- ings executed by Mrs. Mantell, from drawings by the author. 40 London 1822. MAPS. The Trigonometrical Survey of Great Britain, sheets, 64, 65, 69, 70, 83, 84, 85, and 86. METEOROLOGY ( vide Goldingiiam). Meteorological Table extracted from the Register kept at Kinfauns Castle, N. B. in the year 1824. Dr. Ludwig Ideler. M. Jomard. Dr. L. F. Kaemtz. Dr. John Kidd. Chevalier Kirckhoff. M. Lagerhjelm. Marquis de Laplace. Dr. Henry Frederick Link. Edw. Hawke Locker, Esq. Dr. Robert Lyall. Dr. William MacmichaeL M. F. Magendie. Gideon Mantell, Esq. Major Thomas Colby. Lord Grey. DONORS. C 7 3 PRESENTS. MONTHLY Review, or Literary Journal, enlarged, from June 1824, to April 1825, and Appendix to vol. 104, 5, and 6. 8° London , 1824 and 1825. MOREAU (c;esar) State of the Trade of Great Britain with all parts of the World, from 1698-1822. 1 sheet mounted on canvass. MORRISON (r.) d. d. A Dictionary of the Chinese Lan- guage, in three Parts. Part the 1st, containing Chinese and English, arranged according to the Radicals. — Part 2d, Chinese and English, arranged alphabetically ; and Part 3, English and Chinese, vol. iii. Part 1, and Part 3. 40 London, 1822 and 1823. MORTEMART-BOISSE ( le Baron de) Recherches sur les differentes Races de Betes a Laine de la Grande Bretagne, et particulierement, sur la nouvelle Race du Leicestershire. 8° d Paris, 1824. Notice sur le Troupeau de Moutons Anglais importe en 1774, par Francis Delporte, et sur l’Eta- blissement forme par ses soins a Boulogne-sur-Mer. 8° Paris, 1824. PARRY (charles) Collections from the unpublished Medical Writings of the late Caleb Hillier Parry, M.D. PHILOSOPHICAL Magazine and Journal. 8° No. 315 to 325, London. POISSON (M.) M6moire sur la Theorie du Magnetisme (Lu a PAcaddmie Royale des Sciences le 2 Feb. 1824). 4* POPE (ciiarles). A Lecture on the origin, progress, and present state of Shipping, Navigation, and Commerce. 8° London, 1825. RENSSELAER (van). A Geological and Agricultural Survey of the district adjoining the Erie Canal, in the State of New York, taken under the direction of the honourable Stephen Van Rensselaer. Part 1, containing a description of the Rock formations, together with a geological profile extending from the Atlantic to Lake Erie. 8 0 Albany, 1824. RIVERA (carlo afan de) Considerazioni sul progetto di prosciugare il Lago Fucino e di congiugnere il Mar Tirreno all’ Adriatico per mezzo di un canale di navigazione. 40 Napoli, 1823. ROLANDO (Prof, l.) Osservazioni sul Cervelletto. (Me- morie della Reale Accademia delle Scienze di Torino, tomoxxix). 40 , m . — ■ Recerche Anatomiche sulla Struttura del Midollo Spinale. (Art. tratto del Dizionario Periodico di Medicina.) 8° Torino, 1824. Recherches Anatomiques sur la Moelle Allongee. (Memorie della Reale Accademia delle Scienze di Torino), tom xxix. SCHUBERT (frederic Theodore). Traite d’Astronomie Theorique, Spherique, Rationelle, Physique, 3 vols. 40 St. Petersburg, 1822. George Edw. Griffiths, Esq. M. Caesar Moreau, Vice- Consul of France. The Court of Directors of the Honble. East India Company. Baron de Mortemart-Boisse. Dr. Charles Parry. Richard Phillips, Esq. M. Poisson. Charles Pope, Esq. M. Van Rensselaer. Chev. Carlo Afan de Rivera. Professor Rolando. The Imperial Academy of Sciences at St. Petersburg. PRESENTS. DONORS. SCHUMACHER (h. c.) Astronomische Hulfstafeln fur 1825, 8° Copenhagen. Sammlung von Hulfstafeln Zweites Heft. 8° Copenhagen, 1825. Journal of Observations made for ascertaining the time of the place, in the Observatory which was erected at Helgoland for that purpose, 40 1825. Astronomische Nachrichten, N° 58—72. 4® SCORTIGAGNA (francesco orazio). Memoria Epi- stolare per servire diSchiarimento alia descrizione di un pesce petrificato scavato in altissimo nella vicinanze di Bolca. 8° in Padova, 1807. De Singulari Ichthyolitho Epistola, ad virum Clarissimum Co. Arnaldum Arnaldi 1. Tor- nieri. 8° Patavii, 1817. Schiarimenti relativamente a quanto fu scritto sino qui sopra l’Ittiolito esistente nella pub- lica Biblioteca Bartoliana di Vicenza. 8° Padova, 1824. Descrizione di un Pesce pietrificato di singolare grandezzae spezie esistente in Vicenza presso II R. I. Vicario alle Miniere. 120 Vicenza . SMITH ( Sir james edwaud). Compendium Florae Bri- tannicae, Editio 4. \z° Londini, 1825. SODA (dionigio). La Verita Rettificatrice ritrovata. 8° Napoli, 1816. , La Geometria Piana Rivendicatrice, 8° Napoli, 1822. STANHOPE (joiin spencer. Esq.) Olympia, or Topo- graphy illustrative of the actual state of the Plain of Olympia, and of the Ruins of the City of Elis, folio, London, 1824. STEVENSON (robert) An Account of the Bell Rock Light-House, including the details of the Erection and peculiar Structure of that Edifice; to which is prefixed a Historical View of the Institution, and Progress of the Northern Light Houses. 40 Edinburgh, 1824. TERIANO (georgio) Delle Variazioni del’ Umano Organismo nel corso suo di Vita, Parte I. with a Latin MS. translation. THOMSON (tijomas) m. d. An Attempt to establish the first principles of Chemistry by Experiment, 2 vols. 8° London, 1825. THUNE (ERASMUS GEORGIUS fog) Tentamen circa Trigonometriam Sphaeroidicam. 40 ILaitnice, 1815. TRIGONOMETER (vide Bolles) A brass Trigonometer, the beam 1 foot long, and semicircles \\ inches diameter. WATT (james) Proceedings of the Public Meeting held at Freemasons’ Hall, on the 18th June 1824, for erecting a Monument to the late James Watt. 8° London, 1824. Professor H.C. Schumacher. (Sigr.) Fran. Orazio Scorti- gagna. Sir James Edward Smith. Sig. Dionigio Soda. JohnSpencer Stanhope, Esq. The Commissioners of the Northern Light-Houses. Dr. Georgio Teriano. « Dr. Thomas Thomson. M. Eras. Geor. F. Thune. Mr. William Bolles. Charles H. Turner, Esq. PRESENTS. DONORS. WERNEBURGIUS (j. f. chr.) Curvarum aliquot nuper repertarum Synopsis. 40 Jenae, 1824. WESTON (Rev. Stephen) The Englishman abroad: Part 1. Greece, Latium, Arabia, Persia, Hindostan, and China, with specimens of the Language of those Countries, and two plates. Part 2. Russia, Germany, Italy, France, Spain, and Portugal, with specimens, and a head and tail piece. 8° London, 1824. WHEWELL (william) m. a. An Elementary Treatise on Mechanics, designed for the use of Students in the University, 2d edition. 8° Cambridge, 1824. A Treatisq on Dynamics, containing a considerable collection of Mechanical Problems. 8° Cambridge, 1823. WIGGINS (john) South of Ireland. — Hints to Irish Landlords on the best means of obtaining and increasing their rents, improving their estates, and bettering the condition of the people, by a Land-agent, with an Appendix exemplifying the measures recommended. 8° London, 1824. WILSON (william rae) Travels in Egypt and the Holy Land, 2d edition, with a Journey through Turkey, Greece, the Ionian Isles, Sicily, Spain, &c. 8° London, 1824. THE ZOOLOGICAL Journal, No. 3, 4, and 5. 8° London. M. J. C. F. Werneburg. Revd. Stephen Weston. William Whewell, Esq. John Wiggins, Esq. William Rae Wilson, Esq. Thomas Bell, J. G. Children, James Carle Sowerby, G. B. Sowerby, 3°° 4i 767 4i WbyN 1 Fine. © 4 9 O 3°>535 36 686 36 NW i Foggy. 3 O 3°>5*9 43 734 43 W 1 Foggy. (I 5 9 O 3°>5l6 37 875 37 WNW 1 Foggy. 3 O 3°>443 40 771 40 Cloudy. $ 6 9 O 30,214 37 35 E 1 Cloudy. 3 O 30,125 40 650 40 W 1 Cloudy. S 7 9 O 30,194 34 810 34 SSW 1 Fine. 3 O 30,326 40 800 40 N 1 Cloudy and hazy. n 8 9 O 30,326 35 833 35 S 1 Cloudy. 3 O 30,282 39 794 39 s 1 Fine. 9 9 O 30,22 1 40 857 40 w 1 Fine. 3 O 30,192 44 7°7 44 w 1 Cloudy. h 10 9 O 30,150 43 835 43 SSW 1 Rain. 3 O 30,084 44 781 44 sw 1 Cloudy. © 1 1 9 O 30,260 40 800 39 N 1 Cloudy. 3 O 3°>335 41 743 42 0.105 N 1 Fine. a 12 9 O 3°>479 31' 817 3° NNW 1 Hazy. 3 O 3°>456 35 833 35 w 1 Hazy. s 13 9 O 30,514 29 696 27 w 1 Hazy. 2 30 3°>459 31 9°4 3Z w 1 Fine, rather hazy. $? H 9 O 30.435 27 769 25 w 1 Foggy. 3 O 3o>378 3° 860 3’ WNW i Hazy. V. *5 9 O 30,370 34 785 29 NE 1 Foggy. 3 O 30,340 36 758 37 N 1 Cloudy. S 16 9 O 30,586 34 813 31 N 1 Fine. 3 0 30,588 35 683 36 NW 1 Fine. 4 C S 3 / ! METEOROLOGICAL JOURNAL for January, 1824. I824 January. Time. Barometer corrected. Therm. without. Degree of Moisture _ . by Daniell's Hygrom. Six’s Therm. Rain. Winds. Weather. H. M. Inches. 0 0 Inches. Points. Str. h 17 9 O 3°,554 29 784 M OO tJ|W W I Hazy. 3 O 30,452 35 658 35 NW I Fine, rather hazy. O 18 9 O 30,427 37 844 33 NW I Hazy. 3 0 30,360 39 853 4° NNW I Fine. € l9 9 O 3°>339 39 735 33 NNW I Thick fog. 3 O 30.180 42 842 42 NW I Cloudy. $ 20 8 3° 30,126 38 909 38 N 1 Thick fog. 3 0 30,046 41 849 4i W I F?s- 3 21 9 0 29,719 39 912 39 s 1,2 Fine. 3 0 29,587 44 756 44 Cloudy. U- 22 9 0 29,279 41 904 4i w I Cloudy. 3 0 29,051 45 824 45 O.232 s I Rain. S 33 9 0 28,802 44 805 43 w I Cloudy. 3 0 28,799 46 705 46 1 NW I Cloudy. h 24 9 0 29,728 39 912 36 NW 1 Fine. % 3 0 29,854 44 781 44 NW I Fine. O 25 9 0 29,964 50 790 4i w I Fine. 3 0 30,016 52 738 52f w I Fine. <1 26 9 0 30,142 5° 79 0 49 W by S 1 Cloudy, 2 3° 30,1 12 50 850 5i W I Cloudy. S 27 9 0 29,821 47 868 43 W 1,2 Cloudy. 3 0 29,721 51 79 2 5 1 W 1,2 Rain. 28 9 0 29,565 4° 800 38* 0.185 S by W I Hazy. 3 0 29,517 41 849 4i S 1 Fine. % 29 8 3° 29,820 37 844 36 W I Fine. 3 0 29,865 42 763 42 W by N I Fine. ? 30 9 0 3°»127 33 786 32 W I Hazy. 3 0 30,063 38 758 38 S by E I Fine. 1? 3i 8 0 30,025 39 875 35 S I Fine. 2 3° 29,985 42 71 1 42 S I Fine. \ C 4 3 METEOROLOGICAL JOURNAL for February, 1824. 1824 February. Time. Barom. corrected. Therm. without. Degree of Moisture by Daniell’s Hygrom. Six’s Therm. Rain. Winds. Weather. H. M. Inches. 0 0 0 Inches. Points. Str. O 1 9 0 29,956 35 783 34 SE I Fine and clear. 3 0 29,924 42 658 42 SSE 1 Fine. a 2 9 0 30,061 33 893 33 'E I Hazy. 3 0 30,097 40I 800 4°l E I Fine, rather hazy. $ 3 8 30 3°>i34 34 896 33 E I Hazy. 3 0 30,007 43 785 43s S I Fine. 2 4 9 0 29,719 44 862 41 0.020 W I Cloudy and hazy. 3 0 29,71 8 47 48 E I Fine. 5 9 0 29,871 39 882 37 0.1 10 W I Fine. 2 30 29,912 44 707 44 W I Fine. ? 6 9 0 30,070 36 871 35 W I Fine. 3 0 30,134 41 795 43 SW 1 Cloudy. T? 7 9 0 30,160 49 777 49 sw I Cloudy. 2 3° 30,152 49 783 49 SW I Cloudy. O 8 8 3° 30,229 49 783 47 w 1,2 Cloudy. 3 0 30,297 5 1 792 52 w 1,2 Cloudy. <1 9 9 0 30,403 49 907 48 w 1,2 Cloudy. 2 30 30,402 52 766 52 sw I Cloudy. 5 IO 9 0 30,390 462 824 42 0.041 sw I Cloudy. 3 0 3°, 1 97 5*J 8 79 52 sw I Cloudy. 3 1 1 9 0 30,357 41 740 4° w I Fine. 3 0 30,317 46 63 7 47 NW I Fine. V 12 9 0 30,018 42 868 36f w I Cloudy. 3 0 29>7 33 47 868 47 ssw I Rain. ¥ *3 9 0 29,245 39 882 37 w 1 Fine. 3 0 29,087 45 889 46 w 1 Fine. T? H 9 0 28,906 39 853 38 0.930 ssw I Cloudy. 3 0 29,018 42 842 45 E I Fine. O 15 9 0 29,449 38 849 37 N I Fine. 2 3° 29,503 41 644 4i NNE I Fine. c s j METEOROLOGICAL JOURNAL for February, 1824. 1824 February. Time, Barom. corrected. Therm. without. Degree of Moisture by Daniell’s Hygrom. Six’s Therm. Rain. Winds. Weather. H. M. Inches. O 0 0 Inches. Points. Str. d 16 8 3° 29,603 32 963 28 E I Foggy. 3 0 29>539 38 818 38 E I Fine. i 17 8 3° 29,425 34 862 33 E I Fine. 2 3° 29,323 39 713 39 E I Cloudy. 8 18 9 0 29,294 37 875 33 E I Cloudy and hazy. 3 0 29,332 43 785 44 S I Fine. n J9 9 0 29»393 40 857 36 0.070 E 1,2 Cloudy. 2 3° 29,362 47 68 1 47 E 1,2 Cloudy. ? 20 9 0 29,5°5 41 904 40 E 1,2 Rain. 3 0 29,579 42 79 0 43 E I Rain. T? 21 9 0 29,771 39 854 37 0.250 W I Cloudy. 3 0 29,808 40 857 4i Cloudy. G 22 9 0 29,903 39 97 1 37 E I Fog. 3 0 29, 88} 40 864 41 Fine, rather hazy. d 23 9 0 29,970 4i 93i 40 E 2 Cloudy. 3 0 29,995 4i 1. 000 42 E I Cloudy. i 24 8 30 29,978 40 829 38 E 1,2 Cloudy. 3 0 29,898 42 816 43 E 1 Cloudy. 25 9 0 29,800 37 875 37 NNE I Cloudy. 3 0 29,782 38 818 39 E I Cloudy. % 26 9 0 29,775 37 875 33 N I Cloudy. 2 30 29,702 39 765 40 N I Cloudy. ¥ 27 8 3° 29,617 35 900 35 N I Rain and sleet. 3 0 29,61 1 39 94 1 39 0.060 NE I Rain. I? 28 8 3° 29,813 37 906 34 E I Cloudy, thick fog. 3 0 29,858 4i 712 4i E I Cloudy. O 29 9 0 29,912 38 909 36 N I Cloudy and foggy. 2 30 29,906 39 94 1 39 E I Cloudy. C <5 3 METEOROLOGICAL JOURNAL for March, 1824. Barometer Therm, Degree of Moisture Siy’s Winds. 1824 lime. corrected. without. by Daniell’s Hygrom. Therm. Rain. March. Weather. H. M. Inches. 0 O O Inches. Points. Str. d 1 9 O 29,756 39 794 36 NNW I Fine. 3 O 29,659 43 732 44 N I Rain. S 2 8 3° 29,627 30 635 29 N 2 Fine. 2 3° 29,635 35 35 N I Fine. 2 3 9 0 28,987 33 806 3i W I Cloudy. 3 0 28,938 37 735 40 N 2 Rain and snow. n 4 9 0 29,857 29 730 28 N I Fine. 3 0 29,883 38 620 38 W I Fine. ? 5 9 0 29,554 4£i 777 35 W I Cloudy. 3 0 29,587 48 872 48 N I Cloudy. h 6 9 0 29,820 43 836 4i W I Fine. O 7 3 0 29,801 5i 7°5 51 w I Cloudy. 9 0 29,502 49 907 45 O.02O sw 2 Squally ; violent gusts of 3 0 29,495 52 851 52 w 2 Cloudy. [wind and rain. d 8 9 0 29>153 5i 850 47 { ss w variable. 3 Gale of wind and rain. 3 0 29,197 52 682 52 SW 2 Cloudy. S 9 9 0 29,728 43 760 37 °-3°3 S I Fine ; somewhat hazy. 3 0 29,649 48 777 48 ssw I Cloudy. $ 10 9 0 29,666 4i 861 40 N I Cloudy. 3 0 29>75 1 42 961 44 N I Cloudy. 1 1 1 1 9 0 30,044 38 758 33 SW I Cloudy, thick weather. 3 0 29,801 43 734 46 sw I Rain. $ 12 9 0 29,520 42 709 36 w I Fine. 3 0 29450 4i 813 43 { W var. from WtoN 1,2 Fine. J? 13 9 0 29>333 39 853 35 W I Cloudy. 3 0 29,291 39 765 43 0.170 NW 1 Hail, with thunder. © H 9 0 29,7s0 38 849 31 N I Fine. 3 0 29,971 44 683 45 N I Fine. d 15 9 0 42 737 33 W I Cloudy. 3 0 1 30,025 45 753 47 1 SW I Cloudy. C V 3 METEOROLOGICAL JOURNAL for March, 1824. 1824 March. Time. Barometer corrected. Therm. without. Degree of Moisture by Danieli’s Hygrom. Six’s Therm. Rain. Winds. Weather. H. M. Inches. 0 0 0 Inches. Points. Str. S 16 9 O 29,968 48 0 rl- CO 43 O.016 sw I Cloudy. $ 17 9 O 30A47 46 830 42 w I Cloudy and hazy. 3 O 30,I72 5 1 676 53 w I Fine. V 18 9 O 30,238 48 745 41 w I Cloudy. 3 O 30,208 56 691 56 f w I Fine. ¥ J9 9 O 30,286 51 792 48 w I Cloudy and hazy. 3 O 30,252 55 765 55 w I Cloudy. I? 20 9 0 30,274 432 886 43 w I Thick and hazy. 3 0 30,226 52 636 52 sw I Cloudy. O 21 9 0 29,938 47 868 45 s 1,2 Cloudy. 2 3° 29,787 49 814 49 s 1 Rain. <[ 22 9 0 29,580 44 781 39 O.144 ssw I Rain. 3 0 29,554 4i 877 44 SE 2 Rain. s 23 9 0 29,794 381 939 35 0.128 E I Cloudy ; sleet and snow in 3 0 29^94 43 711 43 E l Fine. [the morning. 5f 24 9 0 29,952 904 38 0.045 NE I Cloudy. 3 0 29,944 44 732 45 N I Cloudy. n 25 9 0 30,072 42 76 3 40 NE 2 Cloudy. 3 0 30,073 44 659 46 NE 2 Cloudy. ¥ 26 9 0 29,990 43 734 39 NE 2 Cloudy. 3 0 29,917 45 2 753 46 N 2 Cloudy. 1? 27 9 0 29,824 4* 849 361 N 1,2 Cloudy. 3 0 29,910 4*1 623 44 N 1,2 Cloudy. 0 28 9 0 29,884 4° 771 35 NE I Cloudy. 3 0 29,909 4*1 623 44 N 1,2 Cloudy ; snow in the fore- « 29 9 0 29,982 37 664 30 W I Cloudy. [noon. 3 0 29,917 45 482 45 NE I Cloudy. $ 3° 9 0 29,707 45 777 38 W I Cloudy. 3 0 29,630 50 574 44 N I Cloudy. $ 3 1 9 0 29,707 34s 966 31 0.027 N I Fine. 3 0 29,721 39 537 39 NNE I Clomdy. C 8 3 METEOROLOGICAL JOURNAL for April, 1824. 1824 April. Time. Barometer corrected. Therm. without. Degree of Moisture Daniell’s ilygrom. Six’s Therm. Rain. Winds. H. M. Inches. 0 0 0 Inches. Points. Str. n 1 9 0 29,905 38 599 28 N I Fine. 3 0 29,774 45 535 45 W 1,2 Cloudy. ? 2 9 0 29,108 44i 805 38 0.248 w 2 Rain. 3 30 29,526 4*1 795 34 N I Cloudy. h 3 9 0 30,022 38 712 3xs NNW I Fine. 3 0 30,057 45 659 45 1 NW I Cloudy. O 4 9 0 30*249 41 740 37 N I Fine, 3 0 3°,3o° 46 534 47 N I Cloudy. d 5 9 0 30,458 41 685 34 NE I Cloudy. 3 0 3o>425 46 483 46 N I Fine. i 6 9 0 30,456 42 711 37 N I Cloudy. 3 0 30,416 48 5*5 48 N I Cloudy. $? 7 9 0 30,162 40 943 38 O.Ol8 NNW I Cloudy. 3 0 30,120 46 659 47 N 2 Cloudy. % 8 9 0 30,264 43 759 38 NE 2 Cloudy. 3 0 30.189 5o 54° 51 N 1,2 Fine. ? 9 9 0 30,049 4iJ 904 41 NE 1,2 Cloudy. 3 0 29,958 48 681 47 NNE I Cloudy. h 10 9 0 29,356 4* 822 40 0.015 W 2 Rain. 3 0 29,412 39 853 44 N 2*3 Squally. O 1 1 9 0 29,346 34 931 34 N 1,2 Snow. 3 0 29>33x 46 551 45 N I Fine. d 12 9 0 29,404 4* 74° 32 0.080 ;NNW I Fine. 3 0 29,488 46 55 1 47 W I Fine. i 13 9 0 29*655 4*J 710 3Z2 w I Fine. 3 0 29*7H 49 536 5° w 1 Fine. $ 14 9 0 29,871 44 707 33 w I Fine. 3 0 29,856 5i 502 53f NW I Cloudy. % *5 9 0 29*837 45 635 36 NE I Fine. 3 0 29,698 5o 470 52 E I Fine. Weather. C 9 3 METEOROLOGICAL JOURNAL for April, 1824. 1824 April. Time. Barometer corrected. Therm. without. Degree of Moisture by Daniell’s Hygrom. Six’s Therm. Rain. Winds. Weather. H. M. Inches. 0 0 Inches. Points. Str. ? 16 9 0 29,292 42 868 40 E 3 Rain. 2 30 29,241 42 921 44 E 2 Rain. h 17 9 0 29,456 43 924 4°i O.495 NE 2 Rain. 3 0 29,578 46 8 97 46 O 108 NE 1,2 Rain. 0 18 9 0 3°>°47 48 723 38 NE I Fine. 3 0 30,132 5!2 599 52 NE I Fine. (I 9 0 30,263 51 580 37 E I Fine. 3 0 30,245 55 538 56 E I Fine. S 20 9 0 30,316 53 45 1 42 E I Fine. 3 0 30,264 61 444 60 SE 1 Fine. $ 21 9 0 30,093 55 57 2 43 E I Fine. 3 0 29,959 60 586 60 SE I Fine. n 22 9 0 29,900 57 669 5i 0.053 W 2.3 Cloudy. 3 0 29,927 61 589 63 W 2 Fine. ? 23 9 0 29,471 56 764 5° 0.038 S 2 Showery. 3 0 29,127 53 874 56 S 1 Rain. h 24 9 0 29,955 53 820 48 0.122 W 1 Fine. O 25 9 0 30,128 53 793 45 SW 1 Cloudy. 3 30 30,030 59 693 60 S 1 Cloudy. d 26 9 0 29,668 57 693 52 s 1 Cloudy. 3 0 29,5! 9 60 672 59 s 1 Cloudy. i 27 9 0 29,79 1 57 646 4 6f w 1 Fine. 3 0 29,867 61 569 62 w 1 Fine. 2 28 9 0 29,916 55 765 53 s 2 Cloudy. 3 0 29,867 56 813 57 s 1 Cloudy. V 29 9 0 29»753 62 673 5i O.OO5 SW 1 Fine. 3 0 29,669 67 555 66| SW 1 Fine. ? 30 9 0 29,632 64 610 55 s 1 Fine. • 3 0 29,676 , 64 535 66 w 2 Fine. # MDCCCXX V. b C 10 3 METEOROLOGICAL JOURNAL for May, 1824. 1824 May. Time. larometer :orrected. , Therm. ^ without. Degree of Moisture by Daniell’s Hygrom. Six’s Therm. Rain. Winds. Weather. H. M. Inches. 0 0 0 Inches. Points. Str. h 1 9 0 29,925 60 650 52 sw 2 Cloudy. 3 O 29,914 63 61 1 64 ssw I "ine. O 2 9 O 29,860 55 840 53 N I 3,ain. 3 O 29,763 57 806 58 O.150 E I Rain. a 3 9 O 29,532 49 946 48 W I Cloudy. 3 0 29,483 59 626 60 N I *ain. z 4 9 0 29,632 5° 700 43 0.1 80 W 2 Cloudy. 3 O 29,714 5^2 618 57 W I Cloudy. 2 5 9 O 29,849 59 737 45 s I Cloudy. 3 O 29,860 60 586 62 w I Cloudy. u 6 9 O 29,891 55 815 5° O.O32 w I Cloudy. 3 0 29,839 62 673 63 w I Fine. ? 7 8 0 29,862 53 901 483 E I Cloudy. 3 O 29,(518 64 572 64 w I Fine. T? 8 9 O 30,160 59 737 49 O.O23 w I Cloudy. 3 0 30,21 1 62 572 64 w I Cloudy. O 9 9 O 30,308 54 817 49 E I Cloudy. 5 O 30,206 58 692 61 E I Fine. a 10 9 0 30,001 60 629 46 NE I Fine. 3 O 29,923 66 5*9 66 ENE I Fine. z 1 1 9 0 29,971 5i 908 48 E I Cloudy and hazy. 3 0 29,929 53 820 53 E 2 Cloudy. 2 12 9 O 29,876 48 814 45 E 1 Rain. 3 O 29,847 5i 712 52 E I Cloudy. K- *3 9 0 29,815 4 Sh 965 43 O.O56 N 1,2 Rain. 3 O 29,728 48 745 49 E 2 Rain. ? H 9 O 29>5'7 47 934 44 O.245 E I Rain. 3 O 29,518 47 t 967 48 N 2 Rain. J? *5 9 0 29,503 44 963 43 N 2 Rain. 3 O z9>453 44t 982 45 O.32I N 2 Rain. 0 16 - 9 O 29,75! 45t 987 42 *•355 N 2 Rain. 3 O 29,881 52 738 53 NNE 1,2 Showery. « C 3 METEOROLOGICAL JOURNAL for May, 1824. 1824 May. Time. Barometer corrected. Therm. without. Degree of Moisture by Daniell's Hygrom. Six’s Therm. Rain. Winds. Weather. H. M. Inches. O 0 Inches. Points. Str. a 1 7 9 O 30,019 52‘2 682 39 0.007 W I Fine. 3 O 29,955 55 639 56 W I Cloudy. $ 18 9 O 29,934 54 7*3 47 w 1,2 Cloudy. 3 0 29/81; 8 56 642 56 w I Cloudy. 2 19 9 O 29,81 1 5 1 821 46 w I Cloudy. 3 O 29,809 50 642 56 w I Cloudy. n 20 9 O 29>7»9 49 516 44 O.Ol8 NW 1 Cloudy. 3 O 29>752 5» 580 54 w I Cloudy. $ 21 9 O 29,878 S°h 580 37 N I Cloudy. 3 O 29,876 55i 420 56 E I Cloudy. h 22 9 O *9,958 47 769 38 N by E I Cloudy and showery. 3 O 29,930 54 539 53f E 2 Cloudy. O 23 9 O 29,905 50 790 43 N I Cloudy. 3 O 29,864 56 569 57 N 1 Cloudy. a 24 9 O 29>9!4 52 879 49 NW I Rain. 3 O 29,929 53 901 54 N byE I Rain. i 25 9 O 3°>I43 52 738 42 N I Cloudy. 2 26 9 O 3°,4I3 57 717 50 O.OO4 N I Cloudy. 3 O 30,455 63* 57 2 64 N I Fine. v 27 9 O 3°»578 62 673 49 1 NW 1 Fine. 3 O 30,573 691 575 70 N I Fine. ? 28 9 O 30,544 64 629 50 W I Fine. 3 P 30,447 71 538 73 S I Fine blue sky. h 29 9 O 30,279 64 651 53 E I Cloudy. O to O 9 O 29,824 61 805 54 E I Cloudy. 3 O 29,792 6if 742 59 E I Cloudy. € 3i 9 O 29,852 60 739 5 1 W I Cloudy. * 3 O 29,865 66 655 67 W I Cloudy. t L 12 D METEOROLOGICAL JOURNAL for June, 1824. 1824 June. Time. Barometer corrected. Therm. without. Degree of Moisture by Daniell’s Hygrom. Six’s Therm. Rain. Wind s. Weather. H. M. Inches. O 0 0 Inches. Points. Str. S 1 9 0 30,129 59 847 54f N 1,2 Cloudy. 3 O 3°>I75 66 678 67 N 2 Fine. 51 2 9 O 30,335 58 905 49 N 1 Cloudy. 3 O 30,276 70 556 70 N 1 Fine. % 3 9 O 30,338 53 901 5° N by E 2 Cloudy. 3 O 30,259 58 578 57 N by E 2 Cloudy. ? 4 9 O 30,329 54 739 5° - E 1 Cloudy. 5 O 30,192 65 572 66 NW I Fine. h 5 9 O 30,232 57 66 9 47 N 2 Cloudy. 3 O 30,176 57 788 6o± N 1 Cloudy. G 6 9 O 30,189 54 870 51 E 1 Cloudy. 3 O 30,143 67 612 67 N 1 Fine and clear. 563 63 650 64 N Cloudy. n 17 8 O 29,796 54 870 52 I 3 O 29,853 60 7H 63 N 1 Fine. ? 18 9 O 3°*°5I 58 5*7 46 N I Fine and clear. 3 O 30,012 60 583 60 N by E 1 Fine. j? !9 9 O 29,681 60 800 49 S I Rain. 3 O 29,642 58 794 59 S I Rain. 0 20 9 3 O O 29>39I 29,403 63 58 837 51 60 S S I I Cloudy. Rain. 1 21 9 O 29,489 65 713 5i S I Cloudy. 3 O 29*505 65 616 66 i 0.505 W I Cloudy. a 22 9 O 29,576 65 676 5° w I Fine. 3 O 29*533 66 61 1 67 s I Fine. 23 9 O 29*3 77 57 937 54 E 2 Rain. 3 O 29*358 63 696 63 0.148 E I Cloudy. n 24 9 O 29*365 55 966 53 o-373 N 2 Cloudy. 2 O 29425 55 935 57 NbyW l Rain. ? 25 9 O 29,687 56 870 52 0.102 W I Cloudy. 3 3° 29*778 60 793 62 w I Cloudy. t? 26 9 0 29,998 65 651 52 w I Fine. 3 0 3°*003 69 537 70 w I Fine. 0 27 9 0 30,001 67 612 52 0.01 5 E I Fine. 3 0 29*943 70 556 7°| N I Fine. d 28 9 0 29,922 67 753 59 S I Cloudy and showery. 2 3° 29,894 70 597 7* S I Fine. 3 29 9 0 29,671 67 826 58 0.072 s I Cloudy and showery. 3 0 29,631 7"2 640 74 s I Cloudy. 5 3° 9 0 29,871 66 749 55 s I Cloudy. 3 0 29,856 68 615 7° s 2 Cloudy. METEOROLOGICAL JOURNAL for July, 1824. Time. Barometer Therm. Degree of Moisture by Daniell’s Hygrom. Six’s Rain. 1824 July. corrected. without. Therm. W JllClbtt Weather. H. M. Inches. 0 0 O Inches. Points. Str. % 1 9 0 29,848 67 612 54 W I Cloudy. 3 0 29,772 69 1 618 71 w I Cloudy. ? 2 8 0 29>557 64 799 58 0.053 w 2 Rain. 1 30 29,562 70 727 70 w 2 Cloudy. h 3 9 0 29,592 65 676 60 0.024 w I Cloudy. 3 0 29,572 64 774 69 w I Rain. j O 4 9 0 29,661 64 723 56 w I Cloudy. 3 0 29>779 66 726 68 O.293 w I Showery. (L 5 9 0 29,980 67 658 5i w I Fair, somewhat cloudy. 3 0 29,944 69 660 70 w I Cloudy. $ 6 9 0 29,874 62 748 56 0.070 SE I Cloudy. 3 0 29,813 63 800 65 s I Cloudy. 5f 7 9 0 29,865 63 855 58 0.023 sw I Cloudy. 3 0 29>797 65 852 65 s 2 Rain. V 8 9 0 29,994 68 729 59 w I Cloudy. 3 0 30,003 74 639 74 w 1 Fine. ¥ 9 9 0 29,947 66 801 62 0.025 w I Cloudy. 3 0 29,865 73 724 75 s I Showery. T? 10 9 0 29,9! 1 69 682 58 N 2 Fine. 3 0 29,930 73 598 74 w I Fine. O 1 1 9 3° 30,073 7i 598 55 w I Fine. 3 0 30,016 74 600 75 w 1,2 Cloudy. a 12 9 0 30,061 6S 878 59 w I Cloudy and thick haze. 3 0 30,006 77 580 78 w 1 Fine, blue sky. $ 13 9 0 30,047 7i 618 57 w I Fine, rather hazy. 3 0 30,080 80 528 81 w I Fine, blue sky. H 9 0 2Q,qo6 77 637 65 w I Fine. [tance. 3 °* 29,907 79 660 81 w I Cloudy, thunder at a dis- 15 9 0 29,899 67 727 0.460 w I Cloudy. 3 0 29,928 74 639 74 w I Cloudy. 9 PM 29,884 73 I 10 27 29,832 69} * C A storm of thunder and \ lightning from 9 till 10. C 15 J METEOROLOGICAL JOURNAL for July, 1824. 1824 July. Time. Barometer corrected. Therm. without. Degree of Moisture by Daniell’s Hygrom. Six’s Therm. Rain. Winds. Weather. H. M. Inches. 0 O 0 Inches. Points. Str. 16 9 O 30,082 71 704 60 W I Cloudy and hazy. 3 O 30,063 72 681 74 W I Cloudy. h *7 9 O 3°, 233 69 537 59 E 1 Fine. 3 O 30,232 74 442 74| N I Fine. O iS 9 O 30,252 68 593 58 N 2 Fine. 3 O 30,286 67 5 92 N by E I Fine, with light showers. a J9 9 O 30,452 66 63c 57 NNE I Fine. 3 O 30,447 7° 473 73 NNE 2 Fine. & 20 9 O 30,394 66 749 56 W I Cloudy. 3 O 30,324 73 523 74 N I Fine. $ 21 9 O 30,250 69 706 58 N I Fine, rather hazy. 3 O 30*234 72 566 74 N by E 2 Cloudy. U 22 9 O 30,260 68 799 61 E I Cloudy and hazy. 3 O 30,228 7 1 598 73 E I Fine. ? 23 9 O 30,177 70 577 59 SE I Fine, but hazy. 3 O 30,099 71 76 SE I Fine. 24 9 O 29,839 70 618 58A W I Fine. 3 O 29,822 74 561 77 NW I Fine. O 2S 9 O 29,859 70 577 57 W 1 Cloudy. 3 O 29,855 72 540 73 w I Cloudy. d 26 9 O 29,854 7i 618 60 E I Cloudy. 3 O 29,795 68 637 7i E I Cloudy. $ 27 9 O 3°>013 61 769 55 0.082 N I Cloudy. 3 O 30,051 65 484 66 W I Cloudy. 2 28 9 O 30,290 68 554 53 W Fine. 3 0 30,274 72 5°4 74 S I Cloudy. n 29 9 O 30,104 68 637 54 E I Cloudy. 3 O 29,970 69 639 72 E I Pine. 30 9 O 29,681 62 ^37 53 N I Cloudy. 3 O 29,604 7i 578 7* N 1 Cloudy. 3i 9 O 29,709 63 800 54 NE I Fine. 3 O 29,654 70 727 72 W I Cloudy. C 16 3 METEOROLOGICAL JOURNAL for August, 1824. » 1824 August. Time. Barometer corrected. Therm. without. Degree of Moisture Daniell’s iHygrom. Six’s Therm. Rain. Winds. Weather. H. M. Inches. 0 0 0 Inches. Points. Str. O 1 9 0 29,687 60 739 58 O. I 18 N I Rain. 3 0 29,787 63 800 64 N I Cloudy. S73 68 615 69 w 1 Fine. n l9 9 O 29,808 63 722 5i w I Fine, rather hazy. 3 O 29,830 64 591 66 w I Fine. 20 9 O 29,850 60 939 58 0.018 E I Dark rainy weather. 3 O 29,863 66 77 6 67 w I Cloudy and dark. b 21 9 O 29,785 64 881 60 w X Rain. 3 O 29>793 66 801 67 w I Cloudy. 0 22 8 3° 30,022 60 850 S5l 0.200 N 1 Cloudy and hazy. 3 0 30,057 63 722 65 NNW I Fine. a 23 8 3° 3°>»32 55 1,000 5o£ N 1 Cloudy and hazy. 3 0 30,117 68 554 70 NE I Fine. $ 24 9 0 30,224 56 902 53 N I Cloudy and hazy. 3 0 3°,2io 65 902 65 NE I Fine, somewhat hazy. 5? 25 9 0 30,330 59 969 55 E I Cloudy and hazy. 3 0 30,298 691 706 70 E I Fine. n 26 9 0 30,37o 64 854 60 N by E 2 Cloudy. 3 0 30,309 68 799 70 E 2 Cloudy. ? 27 9 0 30,290 63 826 55f 0.005 N I Cloudy. 3 0 30,184 68 729 69f E I Cloudy. 1? 28 9 0 30,036 66 776 57 E I Fine. 3 0 29,949 69 682 7i E I Fine and clear. 0 29 9 0 29,925 68 823 53 E I Cloudy and thick haze. 3 0 29,878 75f 702 77 SE 2 Fine and clear. a 30 9 0 29,906 63 1,000 69 ENE I Cloudy. 3 0 29,862 74 773 75 E I Cloudy. s 31 9 0 29,912 65 852 63 N I Hazy and cloudy. 3 0 29,940 7i 773 7i NNW I Fine. MDCCCXXV. c L 18 3 METEOROLOGICAL JOURNAL for September, 1824. 1824 September. Time. Barometer corrected. Therm. without. Decree of Moisture by Daniell’s Hygrom. Six’s Therm. Rain. Winds. Weather. H. M. Inches. O 0 0 Inches. Points. Str. $ 1 9 O 30,018 69 798 61 E 1 Fine. 3 O 29,995 80 528 81 S I Fine. n 2 9 O 30,025 73 749 63 E by S I Fine, somewhat hazy. 3 O 29,989 79 598 80 E by S I Fine and clear. ? 3 9 0 29,966 69 797 65 W I Cloudy and hazy. 3 O 29,924 77 658 78 W I Cloudy, with some drops of h 4 9 0 29,877 68 776 66 O.188 N I Cloudy. [rain. 3 0 29,826 74 543 75 W 2 Fine. O s 9 O 29,768 67 635 57 W I Fine. ( 6 9 O 29,496 64 854 56 s 2 Light rain. 3 0 29,409 69 596 70 s 2 Fine. i 7 9 O 29,508 67 777 58| O.IOI SSE 2 Cloudy. 3 O 29,488 66 776 68 SW I Cloudy and showery. $ 8 9 O 29,380 64 827 58 0.720 w 2 Showery. 3 0 29,464 64 67 3 65 w 1,2 Fine. n 9 9 O 29,667 60 793 52 0.125 w I Cloudy. 3 0 29,687 63 774 7i w I Cloudy. ? 10 9 0 29,747 58 875 54 w I Cloudy. 3 O 29,771 64 844 66 s I Cloudy. h 1 1 9 O 29,656 62 828 56 0.430 s 1 Cloudy. 3 O 29,698 64 774 68 w I Cloudy. 0 12 9 0 29,617 60 821 58 0.227 wsw 3 Rain. 3 O 29,705 64 748 65 w 1,2 Cloudy. <[ 13 9 O 30,069 61 82c 52 0.040 w 2 Fine, but hazy. 3 O 30,090 66 749 67 SW I Fine. s H 9 O 30,030 65 773 57 s 2 Cloudy. 3 O 3°,oi6 67 777 67 s 2 Fine, with thin clouds. 5 15 9 O 30,065 67 826 64 w , 1 Cloudy. 3 O 30,097 7i 725 72 0.014 w I Fine. r 19 3 METEOROLOGICAL JOURNAL for September, 1824. 1824 September. Time. Barometer corrected. Therm. without. Degree of Moisture by Daniell’s Hygrom. Six’s Therm. Rain. Winds. Weather. H. M. Inches. 0 0 0 Inches. Points. Str. % 16 9 0 3°>253 60 821 54 N I Hazy. 3 0 30,228 67 727 68 E I Cloudy. ? 17 9 0 30,166 63 883 59 E I Cloudy and very hazy. 3 0 30,120 70 853 70 E I Fine. h 18 9 0 30,067 63 910 60 I Fine. 3 0 29,923 65 9°4 72 W 1 Hazy. O 19 9 0 29,918 62 943 60 W I Fine. 3 0 29,876 67 826 67 W 1 Cloudy. a 20 9 0 29,840 58 935 56 0.140 W I Cloudy. 3 0 29,846 60 850 61 W I Rain. s 21 9 0 29,841 54 965 5i 0.064 W 1 Rain. 3 0 29,832 58 844 58 W I Rain. 3 22 9 0 30,044 61 853 53 S 1 Fine. 3 0 30,048 63 800 65 N 1 Fine. n 23 9 0 29,925 58 935 55 0.093 N I Rain. 3 0 2g,gi6 63 774 63 N 1 Fine. ? 24 9 0 30,032 60 850 56 00 ;+ 6 N 1 Cloudy. 3 0 30,ozg 62 805 64 N l Cloudy. b 25 9 0 3°>OI4 58 814 56 0.008 W 1 Cloudy. 3 0 29,898 59 737 62 W I Cloudy. O 26 9 0 30,042 45 612 4*1 NNW 1 Fine. 3 0 29,983 5° 73° , 51 NNW I Fine. d 27 9 0 29,590 47 868 43 W I Rain. 3 0 29,507 54 635 54 0.075 w I Fine. S 28 9 0 29,81 2 4i 795 37 w I Fine. 3 0 29,88 1 51 580 5i w I Fine. 3 29 9 0 29,905 46 75° 38 E I Hazy. 4 0 29,852 56 7i5 58 E I Fine. at 3° 9 0 29,616 57 784 49 S I Hazy. 3 0 29>395 58 966 5° E 1 Hazy. C 20 D METEOROLOGICAL JOURNAL for October, 1824. 1824 October. Time. Barometer corrected. Therm, without. Degree of Moisture Daniell’s flygrom. Six’s Therm. Rain. Winds. Weather. H. M. Inches. 0 0 O Inches. Points. Str. ¥ 1 9 0 29,169 59 788 59 E 3 Rain. 3 O 29,074 6 1 825 63 0.310 SSW 2 Fine. h 2 9 O 29*345 57 843 5° S 3 Rain. 3 O 29,432 57 874 62 0.045 S 2 Rain. O 3 9 O 29,757 56 764 5° S 1 Fine. 3 O 29,798 61 672 62 W 1 Fine. a 4 9 O 29,796 56 813 5 1 E 1 Fine. 3 O 29,696 61 742 63 E 1 Cloudy. & 5 9 O 29,613 57 935 56 E 1 Fog and rain. 3 O 29,545 58 884 59 0.069 E 1 Rain. 2 6 9 O 29,43° 59 762 58 E 1 Hazy. 3 O 29,331 60 939 62 0.093 E 1 Rain. n 7 9 O 29,268 62 747 58 0.137 SSW 2 Cloudy. 3 O 29,267 63 800 63 s 1 Cloudy. ? 8 9 O 29,319 61 825 57 0.082 SSW 1 Fine. 3 O 29*317 64 707 65 SSW 1 Fine, rather hazy. h 9 9 O 29*539 59 818 54 w 1 Cloudy. 3 O 29,566 63 722 63 w 1 Cloudy. O 10 9 O 29,538 5° 940 49 E 1 Cloudy. d 1 1 9 O 28,890 55 815 52 °-413 E 1 lain. 3 O 28,923 56 813 57 S 1 Fine. i 12 9 O 28,839 52 967 4-7 CO O o’ N 2 Rain. 3 O 28,924 55 790 55 SE 3 Rain. 3 13 9 O 29*377 40 886 37 NW 1,2 Cloudy. 3 O 29*449 45 588 45 NNE 1 Fine. n 14 9 O 29,578 4i 822 34 0.030 W 1 Hazy. 3 O 29,583 49 639 5° w 1 Hazy, with clouds. s *5 9 O 29,660 40 943 36 WNW 1 Cloudy and foggy. 3 O 29,668 44 805 49 N 1 Rain. h 16 9 O 29,896 37 758 34 0.01 1 NW 1 7ine. 3 O 29,932 42 619 44 NNE 1 Fine. C 21 I! METEOROLOGICAL JOURNAL for October, 1824. 1824 October. Time. Barometer corrected. Therm. without. Degree of Moisture by Daniell's Hygrom. Six’s Therm. Rain. Winds. Weather. H. M. Inches. 0 0 O Inches. Points. Str. O 17 9 0 30,030 35 867 31 NW I Fine. 3 0 29,985 49 660 49i W I Cloudy. a 18 9 0 3°>IS4 39 794 3i 0.024 w I Cloudy. 3 0 30,1 16 40 1,000 41 w I Fine. S *9 9 0 30,126 48£ 872 40 w I Cloudy. 3 0 30,049 54 739 55 w 1,2 Cloudy. 2 20 9 0 30,024 53 766 5° w 1,2 Cloudy. 3 0 30,029 55 739 57 0.003 w I Cloudy. n 21 9 0 30,008 5° 850 46 E 1 Hazy. 3 0 29,967 55 870 56 S I Fine. ? 22 9 0 z9>935 53 874 48 ESE I Cloudy. 3 0 29,856 58 814 59 E I Cloudy. h 23 9 0 29,924 57 843 54 W I Cloudy and hazy. 3 0 29,93° 60 821 61 WNW 1 Fine. O 24 9 0 29,840 55 966 51! E I Cloudy and hazy. 3 0 29,718 60 793 61 SE I Fine. ( I 25 9 0 29,528 58 875 56 S by E 3 Cloudy. 3 0 29,518 59 847 60 0.040 SW 2 Fine. S 26 9 0 29,243 57 874 52 W 2 Cloudy. 3 0 29,278 54 765 58 W 2 Fine. $ 27 9 0 29,504 5i 908 48 W 1 Fine. 3 0 29>57i 56 740 58 W 1 Fine. V 28 9 0 29,657 53 932 48 W 1 Fine. 3 0 29,652 55 933 56 W 1 Cloudy. ¥ 29 9 0 29,671 5Z 935 50 O.023 S 1 Cloudy. 3 0 29,525 53 932 53 0.097 W 2 Cloudy. 30 9 0 29,899 46-1 750 45 NNW 1 Cloudy. 3 0 30,041 58 529 59 N 1 Fine. O 3i 9 0 30,1 10 43 868 39 W 1 Cloudy. 3 0 29,847 5° 850 5° w 2 Rain. C 22 D METEOROLOGICAL JOURNAL for November, 1824. 1824 November. Time. Barometer corrected. Therm. without. Degree of Moisture by Daniell’s Hygrom. Six’s Therm. Rain. Winds. Weather. H. M. Inches. 0 O 0 Inches. Points. Str. < I 1 9 O 29,640 5 1 821 48 0.200 W 1 Cloudy. 3 O 29,602 55 765 55 w 1 Cloudy. S 2 9 O 29,709 54 930 53 w 1 Rain. 3 O 29,519 58 787 59 0.018 WNW 1 Cloudy. 51 3 9 O 29,8oq 46 830 43 w 1 Fine. 3 O 29,788 52 682 52 w 1 Fine. V 4 9 O 29,809 43 835 4i NNW 1 Fine. 3 O 29,796 46 636 47 W byN 1 Fine. ¥ 5 9 O 29,751 42 921 39 W 1 Fine, rather hazy. 3 O 29,810 45 729 46 NW 1 Fine. b 6 9 O 30,135 36 9°3 29 W byN 1 Fine. 2 O 30,095 43 633 43 WSW 1 Fine. O 7 9 O 29,947 52 822 42 W 1 Rain. 3 O 29,907 55 739 56 W by S 1,2 Fine. <1 8 9 O 29,683 54 8i/ 5° S 2 Cloudy. 3 O 29>585 56 841 57 S 1 Cloudy. S 9 9 O 29,971 44 805 42 W 1 Fine. 3 O 30,007 59 47i 60 W 1 Thin clouds. 51 ro 9 O 29,885 55 840 46 0.089 W 1 Cloudy. 3 O 29,784 55 739 56 WSW 1 Cloudy. n 1 1 9 O 29,824 57 787 57 WNW 1 Rain. 3 O 29,768 57 8 99 57 w 1 Rain. ¥ 12 9 O 29,980 47 854 45 0.705 w 1 Fine. 4 O 30,069 48 745 54 w 1 Fine. I? 13 9 O 30,056 46 830 42 w 1 Cloudy. 4 O 29,749 54 870 54 w 2 Cloudy. O H 9 O 29,518 53? 874 46 w 2 Rain. 3 O 29,5 u 5 1 79 2 53 0.177 w 2 Cloudy. a 15 9 O 29,900 43 835 39 w 1 Cloudy. 3 O 29,967 43 759 47 0.007 w 1 Fine. C 23 ] METEOROLOGICAL JOURNAL for November, 1824. 1824 November. Time. Barometer corrected. Therm. without. Degree of Moisture Daniell’s Hygrom. Six’s Therm. Rain. Winds. Weather. H. M. Inches. 0 O 0 Inches. Points. Str. S 16 9 0 30,246 40 771 35 W 1 Cloudy. 3 0 3°>045 49 784 49 S W 2 Cloudy. $ 17 9 0 29,785 5 1 763 49 s w Cloudy. 3 0 29,636 52 822 52 ssw 2 Cloudy. n 18 9 0 29>354 58 814 5 1 sw 2 Rain. 3 0 29,61 8 58 823 52 sw 3 Rain. ? J9 9 0 29,764 49 969 46 ssw 1,2 Cloudy. 3 0 29,681 49 969 5° s 1 Rain. h 20 9 0 29,456 47 901 44 0.220 E 2 Rain. 3 0 29,409 49 876 52 O.392 E 1 Cloudy. O 21 9 0 29,402 5° 940 47 0.253 s 1 Fine. 3 0 29,386 52 940 52 wsw 1 Fine. a 22 9 0 29,409 43 962 41 0-3I5 s 1 Fine. 3 0 29>3SI 47 659 48 SSE 1 Fine. i 23 9 0 28,531 53 712 45 S&SSE 3 Cloudy. 3 0 28,5 12 50 880 53 0.165 SW A most violent gale. 3 24 9 0 28,989 47 769 45 W 1 7ine. 3 0 29,042 48 777 50 w 1,2 Fine. n 25 9 0 29,305 44 927 41 w 1 Cloudy and foggy. 3 0 29,396 48 809 48 w 1 Cloudy. ? 26 9 0 29,678 36 936 35 0.005 w 1 Foggy. 3 0 29,680 40 857 40 w 1 Cloudy. h 27 9 0 29,741 4i 795 38 E 1 Cloudy and hazy. 3 0 29.783 43 785 44 E 1 Cloudy. © 28 9 0 29,669 49 814 40 N 1 Cloudy and hazy. 3 0 29,124 52 850 52* SW 1 Cloudy. d 29 9 0 29,190 49 907 47 O.I98 w 2 Cloudy. 3 0 29.255 5i 676 52 w 1 i Fine. & 3° 9 0 29.473 46 795 4i sw 1 Cloudy. 3 0 29,243 52 804 52 0.4; O ssw 3 J 3.ain. E 24 3 METEOROLOGICAL JOURNAL for December, 1824. 1824 December. Time. Barometer corrected. Therm. without. Degree of Moisture by Daniell’s Hygrom. Six’s Therm. Rain. Winds. Weather. H. M. Inches. 0 0 0 Inches. Points. Str. 3 1 9 0 29,309 44 805 44 sw 2 Cloudy. 3 0 z9>43* 40 743 44 w 1 Fine. % 2 9 0 29,631 36 839 34 w I 7ine. 3 0 29,425 45 753 45 s 2 lain. ? 3 9 0 29,447 37 758 37 w I Fine, rather hazy. 3 0 29,662 39 794 47 w I Fine. h 4 9 0 29,522 37 734 36 O.255 N 1 Rain. 3 0 29,344 4i 932 4* E I Cloudy. O 5 9 0 29,516 39 971 38 °-333 N I Rain. 3 0 29>725 39 941 40 N 1,2 7ine. « 6 9 0 29,828 32 926 3* W I Cloudy and hazy. 3 0 29,643 4* 9°4 4* SW I Fine. & 7 9 0 29,500 38 848 36 o-*45 w 1 ?ine. 2 30 29*555 42 842 42 w 1 Fine. 2 8 9 0 29,863 40 886 35 0.003 w 1 Cloudy and hazy. 3 0 29,781 45 824 45 W by S Cloudy. U 9 9 0 29,707 40 97* 39 0.023 W 1 Cloudy and hazy. 3 0 29*639 43 886 44 W 1 Fine. ? 10 9 0 29,921 33 929 32 0.180 W I Hazy. 3 0 29,990 47 57* 47 W 1 Fine. b 1 1 9 0 30,106 4i 959 32 0.005 W I rlazy, thick weather. 3 0 30,1 10 48 777 48 N by W I Rain. O 12 9 0 30,245 45 824 44 W I Fine. 3 0 30,292 49 826 49 W I Fine. ([ *3 9 0 30,385 46 864 44 W 1 Cloudy. 3 0 30,393 49 876 49 W 1 Hazy. 14 9 0 30,459 45 929 44 W I Cloudy and hazy. 3 0 30,363 46 898 465 SW 2 Cloudy. $ 15 9 0 30,072 44 963 43 w 1 Fine. 3 0 29,963 49 845 49| w I Cloudy. n 16 9 0 29,925 42 763 4* 0.039 N I Fine, rather hazy. 3 0 29,937 43 962 44 NW I Hazy. 1 25 : METEOROLOGICAL JOURNAL for December, 1824. 1824 December. Time. Barometer corrected. Therm. without. Degree of Moisture __ . by Daniell’s Hygrom. Six’s Therm. Rain. Winds. Weather. H. M. Inches. O 0 0 Inches. Points. Str. 17 9 0 30,030 39 971 37 W I Cloudy and hazy. 3 0 30,011 43 962 43 w I Rain. h 18 9 0 30,170 43 924 42 0.070 s I Rain. 3 0 30,125 48 808 48 w 1 Fine. O *9 9 0 30,078 48 968 47 O.OIO w I Cloudy. 3 0 30,024 5i 908 5i w 1,2 Cloudy. d 20 9 0 29,409 5i 821 47 w 2*3 Rain. 3 0 29,491 45 77 6 50 w I Fine. $ 21 9 0 29,416 45 706 40 0.008 sw 3 Cloudy. 3 .0 29,348 5i 879 Si w 2 Cloudy. 2 22 9 0 29,004 5i 734 46 w 3 Cloudy. 3 0 28,81 1 48 702 52 w 3 Fine. n 23 9 0 29*773 34 655 34 0.128 WbyN 1 Fine. 3 0 29,926 37 641 37 W byN 1 Fine. 24 9 0 29,477 44 805 33 0.160 3 Rain. 3 0 29,601 44 805 50 O.140 Rain. h 25 9 0 29,530 5i 792 4i W 2 Cloudy. 3 0 29>493 54 79 1 54 WNw 0 26 9 0 29,816 43 684 43 W 1 Fine. 3 0 29,973 45 682 45 WbyN 1 Fine. d 27 9 0 29,916 47 901 39 WbyS 3 Cloudy. 3 0 29,812 52 822 53 W 2 Cloudy. s 28 9 3° 29,77° 5° 820 49 0 0 o' W 2 Fine. 2 29 9 0 30,061 39 853 39 0.3 10 1 Cloudy. 3 0 30>158 39 882 40 NNE 2 Cloudy. V- 3° 9 0 30,142 46 864 35 0.040 N 2 Rain. 5 0 30,155 46 5i W Fine. ? 3i 9 0 30,184 48 840 44 W 1 Cloudy. 3 0 30,127 5° 880 5i 0.008 w 2 Rain. MDCCCXXV- d C a6 3 1 824. Height of Barometer,* corrected . Height of Ther- mometer without. Degrees of Moisture by Daniell's Hygrometer. Six's thermometer. Rain.t Greatest height. Least height. Mean height. Greatest height. Least height. Mean height. Greatest! height. Least height. Mean height. Greatest height. Least height. Mean height. Inches. Inches. Inches. Deg. Deg. Deg. Deg. Deg. Deg. Deg. Deg. Deg. Inches. January 30,588 28,799 30,053 52 27 40,0 912 650 794 52i 25 39, 1 0,522 February 3°>4°3 28,906 29,807 52 32 41,2 IOOO 637 834 52 28 46,0 1,481 March 30,286 28,938 29,293 55 29 43,4 961 537 763 55 28 41,6 0,853 April 30,458 29,108 29,851 67 34 49,4 943 444 680 66j 28 46,3 1,182 May 30,578 29,453 29,925 7 1 44i 55,4 987 5i9 722 73 42 52,2 2,39* June 30,338 29,220 29,861 72 52 6l,2 IOOO 475 7 12 74 43 57,9 2,183 Ju]y 30,452 29,557 29,977 80 61 69,2 878 442 654 81 51 64,1 1,030 August 30,370 29,492 29,903 75i 55 65,7 IOOO 554 746 77 5°2 63,0 2,092 September 30,253 29,380 29,855 80 41 62,3 966 528 783 81 37 60;2 2,373 October 30A54 28,839 29,627 64 35 53,2 IOOO 529 817 65 31 5D9 1,462 November 30,246 29,042 29,629 59 36 49, 1 969 47i 815 60 29 47,5 3A54 December 30,496 28,870 29,812 54 32 43,9 97 1 57* 837 54 31 43^ 1,972 Whole year 29,799 52,8 763 50,6 20,695 * The quicksilver in the bason of the barometer is ioo feet above the level of low water spring tides at Somerset-place. f The Rain Gage is 114 feet above the same level, and 75 feet above the surround- ing ground.