5o 



REPORT— 1902. 



Tho origin of these limitations is easily found ; the limitation 78 (say), wliich is 

 to be read 'seven himdrjd and eighty something,' is already, at 780, more than 

 8 X 97 = 776, therefore instead of 7 write 8 as the next digit in the quotient. 



Again, these limitations are closely connected with the usual long division 

 process as shown below. It will be noticed that, in general, the digit in the ten's 



97)67001312(690735 



582 



880 

 873 



071 

 000 



713 

 079 



341 



291 



502 

 485 



place of each remainder (before bringing down the next digit of the dividend) is 

 the next digit in the quotient, unless altered by the limitations. [These are put 

 in heavier type for clearness.] 



Mr. Hsmblin Smith noted that the process is true for any factor of such a 

 divisor. Thus to divide by 33, the associated multiplier is 1, and the quotient can 

 be instantly written down; to divide by 7, 14, 49, the multiplier is 2, which 

 recalls the decimal for }. 



The process is capable of even further extension ; as, for instance, to such 

 divisors as 9U7, or 103 with a slight alteration. 



11. A Theorem in Determinmits. By A. A. Robb. 



Dkpartment II. — Physics. 



The following Papers were read : — 



1. Note on the Variation of the Specific Heat of Mercury with Tempera- 

 ture : Experiments by the Continuons-flovi Method of Calorinietry. By 

 HowAKD T. Barnes, M.A.Sc, D.Sc, and H. Lester Cooke, B.A. 



Since the communication to the Royal Society in 1900 of the work of one 

 of the authors on the speciKc heat of water it has been possible to continue the 

 experiments by the continuous-flow method of caJorimetry to the case of mercury. 

 These measurements, which include an interval of temperature between 0" and 

 90° 0., have been carried out with essentially the same apparatus as previously 

 used for water, and with the same electrical standards. The first determinations 

 which were made for mercury by this method were made by Professor Callendar 

 and one of the authors during the summer of 1897, just previous to the Toronto 

 meeting of the British Association. The results then obtained with our prelimi- 

 nary apparatus were entirely revised and recalculated three years later. It was the 

 intention of one of the authors to include them in his paper on the specihc heat 

 of water, since they afforded a most satisfactory verification of the theory of the 

 method. Deeming it advisable, however, to redetermine the value of the specific 

 Jieat, and to e.xtend the exp.erjrnents over as large a range of temperature as possible 



