President's Address. 
49 
Until such laws are discovered there will always remain an element of 
uncertainty apart from that due to the initial data affecting all predicted 
phenomena — an uncertainty which can only be removed when the 
phenomena cease to be prospective, and when they can be confronted with 
later as well as with earlier observations. 
The fact, however, that the laws of gravitation yield such a close re- 
presentation of the observed motions within the solar system throughout 
historic time, renders the detection of a departure from these laws a 
question of extreme delicacy, but none the less essential, if prediction is to 
be secured for long periods in advance. 
I have dwelt at length on the importance of a study of these laws — a 
study which at every turn calls for more numerous, and, above all, more 
accurate observations. Even, however, if the laws of gravitation could be 
established as absolute, our capacity for prediction would be limited by the 
accumulation loitJi time of the small sources of uncertainty affecting the 
original observations on which all data for prediction must be based. 
These sources of uncertainty may be minimised by extending our observa- 
tions over a long interval. Such an extension will doubtless be possible 
in the future, and we may be sure that astronomers of future centuries 
will take advantage of the facilities which lapse of time will afford 
them. 
At present, however, though, as I have already indicated, we can to 
some extent retrace the past, opportunities for verifying our theories in the 
light of early records and thereby strengthening our data are few and far 
between, and generally lacking in the necessary elements of precision 
required. 
Exact astronomy in the modern sense only dates back for about a 
century and a half, during which interval, however, most of the data 
usually to be found in almanacs may be considered to be known at any 
instant with a precision that can scarcely be expected to be improved on. 
Where immediate direct observations are not available, these data may be 
derived from considerable numbers of observations taken both before and 
after the actual instant by the mathematical process of " interpolation " 
with a precision scarcely less than if all these observations were made 
actually at the instant under consideration, and the effects of fallibility in 
the actual observations themselves can be reduced to a minimum by 
incorporating as large a number of them as are available. 
What, however, I wish to impress on you is that of necessity predic- 
tion always involves essentially the far more uncertain process of extra- 
polation — a process requiring for similar accuracy far higher precision in 
the initial data employed, more accurate knowledge of the laws by which 
these data may be combined and which is at all times liable to an additional 
source of uncertainty owing to the cumulative effect with time of sources 
4 
