34)4 Mr Sang on Optimum Surveying, 



since the observed and computed latitudes may be expected to 

 agree tolerably — 



lat A — Lat A ^ (sin lat A — sin Lat A) see Lat A 

 = — (cos lat A — cos Lat A) see Lat A 



these forms may be used as analogous to the other terms of the 

 equation. 



In the very same way the observed longitudes may be intro- 

 duced, along with the probable errors in the timekeepers and 

 lunar tables. 



The above five equations, with the additions just indicated, 

 contain all that is needed for deducing with the greatest possi- 

 ble probability of exactness, the latitudes and longitudes of the 

 stations, and the figure of the earth from the geodetical opera- 

 tions : But a single glance at them is sufficient to convince one 

 that the manipulation of them is matter of no small difficulty. 

 Were it not, indeed, from this circumstance that the oblateness 

 of the earth is small, these equations would be next to unma- 

 nageable. Proceeding, however, by steps, neglecting first 

 o? — /S^, then neglecting its second and higher powers u . s .f , 

 we may render the computations practicable. It is unnecessary 

 for me to proceed here to discuss the method of managing such 

 calculations, as that discussion would form rather a treatise on 

 geodetics, than a general essay on the manner in which a geo- 

 detical survey ought to be conducted. 



A Series of Facts and Observations respecting the Natural 

 Causes of Arborescent or Dendritic Figures in the two di- 

 visions ()f Animal and Vegetable Structures, and in Mineral 

 Formations, By Sir Anthony Carlisle, F. R. S. Com- 

 municated by the Author. 



These ramifying figures are not the special productions of 

 living bodies, because they also occur in mineral formations, 

 and when they are not the impressions of organized structures. 



In some instances of organic nature, arborescent figures de- 

 pend on tubular vessels, as in animals ; but in vegetable struc- 

 tures these figures are composed of solid woody fibres, while the 



