Mr. John T. Graves on the Theory of Couples. 315 



upon in Lieut.-Col. Sabine's valuable Toronto report con- 

 tained in the last Number of the Phil. Mag. p. 20, 1 beg to 

 refer to my papers in the Phil. Mag. for June and July 1842, 

 in which the Plymouth and Leith observations showed that 

 if the barometer or thermometer he observed four times a day at 

 six-hour intervals^ commencing at any convenient hour, 

 the result of an annual series would all but equal the mean of 

 one or two-hourly observations. These conclusions are con- 

 firmed by Col. Sabine's communication; whence, denoting 

 by h 



4 1 the sums of the observations at 2, 



4/' ... ... ... 4, 



4^" ... 6, 



results the foUowhig Table : — 



London, February 17, 1845. 



P.S. If one of a party of travellers ascending a high moun- 

 tain await at one of the stations the return of the others, his 

 six-hourly observations on the thermometer and barometer 

 would give the ?neaTi daily height of these instruments, and 

 hence the altitude of the station ; whence by the method of 

 differences, the exact altitude of the summit would always be 

 ascertainable. 



XLVI. On a Connectio7i between the General Theory of Nor- 

 mal Couples atid the Theory of Complete Qiiadratic Functions 

 of Two Variables. By John T. Graves, M.A.^ F.R.S., 

 Examiner ifi Laws and Jurisprudence in the University of 

 London.* 



nPHE remarkable researches of Sir W. Hamilton on Qua- 

 ^ terniojis, followed by Prof. De Morgan's very able and 



* Communicated by the Author. The continuation of Sir W. R. Ha- 

 milton's paper on Quaternions will be found in our last Number, p. 220. 



