ON THE DeTEKMINATION Ot' GRAVlTy AT SKA. 559 



occasions an error which varies according to the latitude. For equatorial 

 regions the gravity error due to an error of one degree in the course varies 

 per knot from OOOlS when the course is N. or S. to '000012 when it is E. 

 or W. An error of one knot in determining speed produces a gravity 

 error which varies from on a meridian course to '0073 on an E.-W. 

 course. Elsewhere these amounts are to be multiplied by the cosine 

 of the latitude. 



While the average speed of the ship over 24 hours is capable of mea- 

 .surement with considerable accuracy from the dead reckoning, the speed 

 during the five minutes required for an observation is less certain. 



The chief difficulty lies in the uncertainty of the tides, and it would 

 be preferable to anchor the ship before starting the observations ; it 

 is feared that this can only be done on a few occasions, but otherwise, 

 especially in places near the coast, like the Scilly Isles, an appreciable 

 error is involved. There may frequently be an uncertainty of about 

 '015 cm./sec^, which, though unimportant in the present research, may in 

 future work prove a relatively large source of error. 



For high accuracy it is very essential to secure close co-operation 

 between the observer and the executive officers of the ship. 



If the speed of the vessel is ascertained by dead reckoning, ])i telling 

 introduces a small modification of the instantaneous values calculated 

 abo\'e, and tends to diminish them, but the precise amount is incal- 

 culable. 



8. Variation of Gravity with Latitude. 



In Table IV. the deviations of gravity from its value in latitude 45° 

 are shown corrected for the ship's motion in columns headed Aig^, A,g,„ 

 A|g(., according to the aneroid method of reduction. These values, 

 together with the theoretical curve derived from the formula 



y„ = 978030 I 1 + 0005392 sin'^ A — 0-000007 sin^ 2 A | , 



are plotted in figs. 5 (1), 6 (1), 7 (1). The large open circles represent 

 harbour observations, the small circles represent sea observations, of which 

 those which are open are less reliable than those which are black. The 

 aneroid method is clearly capable of showing the general trend of 

 gi'avity with latitude, but we try to push it further: — fig. 5 (1) showed 

 that many of the harbour readings were too high, which threw doubt upon 

 the method of reduction, and led to the trial of the other methods already 

 described and shown graphically in figs. 6 (1) and 7 (1). In none of these 

 is there complete coincidence between the harbour observations and the 

 theoretical curve, though in fig. 6 (1) they lie close to it ; this is therefore 

 the most satisfactory graph, and it shows a defect of gravity between 

 Bombay and Australia. 



The reason why the harbour observations show deviations is not clear ; 

 it may be that the effect of lag upon the mercury barometer is more 

 serious when the ship is at rest, when changes of atmospheric pressure 

 introduce considerable errors, fig. 14, or it may be that there are short 

 period changes in the elastic properties of the aneroid. Though there is no 

 obvious reason why any short period variation should begin and end 

 during a stay in port, the only possible way of improving the curves lay 

 in plotting the station errors against a horizontal scale, — assuming 



