as observed at Plymouth. 479 



.'. k+h" = 2}l+2B sin 2 t+2b cos 2 t+2E sin 4t+2 e cos 4t (1.) 

 h'-\-h'"= 2 H— 2 B sin 2 1—2 fi cos 2 <+2 E sin 4t+2ecos4i (2.) 



A— A" = 2Asini-2a cos <+2C sin 3^+2ecos3< (3.) 



A'— A"'=2Acos< — 2asini!— 2C cos3i!+2csin3^ (4.) 



h+h'+k"-\-h"'—4:H+'lEs\a4t+4ecos4t (5.) 



h+h"—h'--h"' = 4 B sin 2i!+4-6 cos2 i (6.) 



Now equation (5.) compai'ed with the sums of the homony- 

 mous hours, gives 24 H = + 5. It is however evident that 

 H = the mean height, and as only the deviatioiis are con- 

 ceived here, i t = 0. This error of + 5 is partly owing to 

 the approximate estimation of the distance of the * from the 

 curve in plate v., and it might be suggested that in these gra- 

 phical charts the network of coordinates should sometimes 

 present oblong instead of square divisions, so as to allow of 

 the deviations from the regular curve to be better measurable. 

 Equation (5.) gives mean values of E = — '505, and e = 

 + -125. 



Equation (6.) compared with the suras of the homonymous 

 hours, gives three values for B, and the same number for b. 

 The averages are B = 78*3, b = 35*6. 



Applying the corrected deviations to the separate hours, 

 we obtain 



Grouping separately the hours (1, 5, 7, 11), (2, 4, 8, 10), 

 (3, 6, 9, 12), there result three values for each of the quan- 

 tities A, o, C, c ; the means are 



A = - 0-7, a= + 33-3, C = + 2-9, c = - 3"8. 

 Hence at Plymouth we have in English inches, 

 ^ - H = — 0-00007 sin t + 0*00333 cos t — 0-00783 sin 2 t 

 + 0-00356 cos 2^ + 0-00029 sin 3 ^ — 0-00038 

 cos 3 if— 0-00005 sin 4 i+ 0-00001 cos 4/f. 

 = -00333 sin (^ + 91° 12') + -00860 sin {2t+155° 33') 

 + -00048 sin (3 t + 307° 20') + '00005 sin (4^ 

 + 161° 6'). 

 In the Transactions of the Royal Society of Edinburgh 

 vol. X., Mr. Blackadder proposed a self-registering barome- 

 trical instrument, consisting of several barometers, the open 

 ends of which could be closed by air-tight lids at any re- 

 quired time by means of clock-work. Four barometers ar- 



