75 



APPENDIX, No. III. 



SUBSTANCE OF A LETTER TO CAPTAIN HENRY KATER, 



BEAD BEFORE THE ROYAL SOCIETY, APRIL 24, 1823, 



Giving an Account of some Experiments made by Captain Hall and Mr. Foster with an Invariable Pendulum, 

 during the Voyage to South America, in his Majesty's Ship Conway. 



The following pages contain an account of the 

 experiments made with an invariable pendulum, 

 placed in my hands by the Board of Longitude, at 

 the suggestion of Captain Henry Kater, F.R.S., 

 the philosopher to whom the scientific world is in- 

 debted for this simple method of determining the 

 figure of the earth. The principle, indeed, was 

 known before ; but the practical application, in its 

 present form, is due entirely to his skill and in- 

 genuity. 



It was a source of considerable regret to Mr. 

 Foster and myself, that we should have visited so 

 many remote places, with such means in our 

 hands, and at last have so few results to produce. 

 The fact, however, is, that the service upon which 

 the ship was employed had no connexion with 

 scientific research ; and it was only at casual in- 

 tervals of active professional employment, that I, 

 at least, could attend at all to inquiries of this 

 nature. These occasional opportunities I owe to 

 the indulgence of Sir Thomas Hardy, Commander- 

 in-chief in South America, to whose encourage- 

 ment, in every pursuit having useful knowledge 

 for its object, I stand essentially indebted. 



In drawing up the account of these experiments, 

 care was taken to state all the attendant circum- 

 stances, and to record in tables every observation 

 in the utmost detail ; so that any person wishing 

 to examine the work, may have the best means 

 possible of estimating their value. These tables, 

 which are too voluminous for the present work, 

 will be found at length in the Philosophical Trans- 

 actions for 1823. 



The methods followed for making the adjust- 

 ments of the instruments, conducting the experi- 

 ments, and deducing the results, were those laid 

 down in Captain Kater's paper on the length of the 

 pendulum at the principal stations of the Trigo- 

 nometrical Survey. We took particular care, for 

 example, always to adjust the diaphragm which is 

 placed in the focus of the eye-piece of the telescope, 

 so that its edges should coincide exactly with those 

 of the extremity of the tail-piece of the pendulum 

 of experiment, according to the precept at page 

 9 of Captain Kater's paper, read before the Royal 

 Society, in June 1819. This adjustment, it may 

 be useful to observe, is rendered more easy and 

 exact, by placing a card, or other white object, at 

 a little distance behind the pendulum, when at 

 rest. I also invariably determined the intervals 

 by observing the moment of disappearance of the 

 white disc behind the pendulum, not only in 

 London, but at all the stations abroad. 



I am particular in stating these two circum- 

 stances, especially the first, from its being so 

 essential to the accuracy of the whole experiment, 

 in all cases where the diameter of the disk and 

 the breadth of the pendulum, though in fact equal, 

 happen to be placed at different distances from 

 the eye, and therefore must appear under different 

 angles ; and not, as in Captain Kater's first" ex- 

 periments, (which had another and perfectly 

 distinct object in view,) where the disk and tail- 

 piece were so proportioned, that both occupied the 

 same apparent angle when seen through the tele- 

 scope. 



We were at first disposed to think it might be 

 better to observe both the times of disappearance 

 and reappearance of the white disc, and to assume 

 the mean as the true instant of the coincidence ; 

 but we found, by repeated trials, that the time of 

 reappearance was liable to greater or less uncer- 

 tainty, according to the degree of light, and other 

 unmanageable circumstances ; and, having satis- 

 fied ourselves that the method of obtaining the 

 intervals by observing the disappearance, was 

 rigorously correct in principle, we adhered to it 

 ever afterwards, as being more simple and infallible 

 in practice. It is meant by this, that in all com- 

 parative experiments, such as these were, the 

 method of disappearances is rigorously accurate. 

 It formed no part of our object to determine the 

 absolute length of the pendulum ; and therefore 

 we considered it needless to encumber ourselves 

 with a troublesome method of observing, when 

 another, perfectly easy and simple, and equally 

 correct, was within reach. To those who have 

 not considered the subject attentively, and who 

 may be desirous to know what difference it caused, 

 it will be satisfactory to learn, that when experi- 

 ments are made, at different places, by observing 

 the disappearances only, the results are strictly 

 comparative, and, in point of fact, give identically 

 the same results with those deduced from observing 

 both the disappearances and the reappearances, 

 and taking the mean for the time of true coin- 

 cidence. This assertion is the result of an actual 

 comparison of the two methods. 



In making these statements, it is not only due 

 to Captain Kater, but may, perhaps, be useful to 

 future observers, to state, that, after many trials 

 of fancied improvements and simplifications of his 

 methods, both in the conduct of the experiments 

 themselves, and in the subsequent com juitat ions, 

 we were finally obliged to acknowledge, in every 

 instance, even where we succeeded, that we had, 



