294 Notices respecting New Books. 



purpose they can be applied until the observations are given, we 

 are at a loss to imagine. Connected with this subject the following 

 piece of information strikes us as curious. For some time the lati- 

 tudes, longitudes and reciprocal bearings are stated to have been 

 calculated from formulre furnished by the Astronomer Royal. These 

 formulae, which of course ai^e only approximative, were found not to 

 be sufficiently exact when applied to some of the large triangles which 

 occur in the Ordnance Survey, and on the occasion of the recent 

 chronometrical measurement of the arc of parallel between Green- 

 wich and Valentia, the Astronomer Royal furnished a new set of for- 

 mulae in order that the geodetic longitude of the latter place might 

 be more rigorously computed. The new formulae, along with others, 

 were subjected to the most rigid tests that tables of logarithms 

 to ten places rendered possible, and the following result is an., 

 nounced : — 



" On trial it was found that none of the approximate pro- 

 cesses given by the various writei's on geodesy were sufficiently 

 exact to reproduce the original assumed latitude, longitude and 

 bearing, on carrying the calculations to the point at which they 

 commenced ; and even the formulee given by the Asti'onomer Royal 

 failed to do so, until it was found that the normal, or radius of cur- 

 vature perpendicular to the meridian for the latitude of the given 

 station, must be used in the determination of that of the second 

 station, and the normal for the latitude of the second in the deter- 

 mination of that of the third, and so on, instead of using any ap- 

 proximate radius. This was ascertained by the non-commissioned 

 officer in charge of the calculations, after repeated attempts had 

 been made, without success, to alter or modify the various approxi- 

 mate processes which had been tried, so as to cause them to repro- 

 duce the assumed data, on continuing the calculations to the original 

 point," &c. 



Far be it from us to disparage a discovery so made ; but we would 

 beg leave to suggest, that if the substitution of the successive normals 

 for the approximate radius be really an improvement on the method, 

 there must be a reason why it is so ; which reason should be given, 

 in order that it may not appear to be the practice in the Ordnance 

 Survey to follow empirical modes of calculation, found by groping 

 to answer in some particular cases. 



With respect to the future progress of the survey Captain YoUond 

 observes, " the present, or at all events the succeeding season will 

 serve for the completion of the observations at all the stations re- 

 quired for giving a connected general triangulation of the United 

 Kingdom, including the Western, Orkney and Shetland Islands, with 

 the necessary data for the comparisons between the astronomical and 

 geodetical determinations ; these will be the more valuable, as the 

 result of the late operations at the Cape of Good Hope, for the mea- 

 surement of an arc of meridian depending on a base measured with 

 the compensation apparatus described in this work, and reducible to 

 the same unit of measure, may ere long be exjoected to be published." — 

 p. vii. No doubt the result of the Cape measurement will be very 



