168 Proceedings of the Royal Society of Victoria. 



From 23rcl June to 18th July it had a losing rate, gradually 

 increasing from P-9 to 3«-0. It was then stopped to form 

 the connection above mentioned, when the pendulum was slightly 

 shortened. From 14th August to 14th September its meam 

 gaining rate was 2* '5 per day, the greatest variation from mean 

 being about 0'-5. 



Reduction of the Observations. 



The instructions contained in General Walker's Memoratida 

 on Petididum Observations for the Melbourne Observatory were 

 followed throughout, excepting some slight variation in form, 

 and in the co-efficient in the formulfe for the arc correction. The 

 notation and formulfe used are as follows, viz : — If 7i is the 

 number of observable coincidences during an interval /, and JV 

 the interval between two consecutive coincidences, then /= 

 (n-\)-N 



I is obtained by subtracting the first three, four, or five 

 from the last corresponding three, foui-, or five observed coinci- 

 dences and taking the mean of the differences. JV being 

 approximately known from observations of two consecutive 

 coincidences n is at once derived, with which the mean value 

 of JV is computed. 



^ = number of sidereal seconds in a mean solar day plus the 

 daily rate of the clock Shelton. 



V^ = uncorrected number of vibrations made by the free 



pendulum in a mean solar day, then Fj =^R - 



The vibration numbers V^ resulting from each swing, were 

 all firstly reduced to the mean temperature 62° Fahr., to 

 26 inches pressure at 32° Fahr., and to infinitely small arc, 

 by the following formulae, viz.: — 



Pressure correction^O-34. — -^ -, =R 



1+0-0023 (r- 32) ^ 



Arc correction = V. (^^) .' { ('« + b)- - J (« -b)- \ =a 



Temperature correction = 0-45(Z'— 62°) = t 



