of Variable Qaantities. 13 



Then tbis formula will give the height z of the barometer at 

 any station whose latitude and longitude are x, y, as deduced 

 from the heights at the several observing-stations. The ap- 

 plicability of this interpolation depends, of course, on the 

 assumption that the surface is not contorted between the given 

 ordinates; and if the observatories are numerous enough, this 

 assumption is probably justifiable. 



The application of the formula would in general entail a 

 great detail of arithmetic ; but in the case of the reduction 

 from irregular to regular stations, the great mass of the work 

 might be done once for all. In this case the coordinates of 

 the observing stations x^, y^ ; a-,, y-^ ; &c. are the same day after 

 day, and the coordinates of the fixed stations x, y are constant 

 for each of them. Hence the coefficients of z^, Zi, &c. in the 

 formula may be calculated once for all. 



It would be very laborious and unnecessary to make the 

 heights of the barometer at the equidistant stations depend on 

 all the observatories in the country; and it would be probably 

 quite sufficient to make each one depend on the five or six 

 nearest observatories. The practical rule would then run 

 somewhat in this fashion (the numbers being purely hypothe- 

 tical) : — 



Height of bar at lat. ) =-705 Oxford + -20 Kew 



51° long. 1° W. J + -092 Southampton + -002 Cambridge. 



Every separate point to which the reductions were to be 

 made would require a different set of coefficients, which would 

 depend on the four, five, or six nearest actual observing-sta- 

 tions. 



If the heights of the barometer were taken as the excess 

 above 28 inches, the various heights need not be given to 

 more than three figures ; and as the coeflicients w^ouid pro- 

 bably have also three figures, the multiplications might be 

 very easily made by means of Crelle's Iiechentafeln. By 

 these means the daily observations might be very quickly 

 reduced, and the results of each day's observations w^ould be 

 given by a series of numbers on a map spaced out at regular 

 intervals of latitude and longitude. This would, I think, faci- 

 litate the drawing of the '^isobars," and it would also be more 

 intelligible than are the results as given at irregularly dis- 

 persed stations. 



It may be noticed that the same set of coefficients would 

 also be proper for the reduction of any other meteorological 

 element which could be fairly represented by a surface. The 

 calculation of the coefficients would be rather laborious ; but 

 if there is any real advantage in thus classifying the observa- 



