TBANSACTIONS OF SECTION A. 71 



possess several advantages. In the first place, the student is 

 able to form a mental picture of the physical meaning of every 

 step in the mathematical theory, and he therefore finds it 

 easier to understand the step, to remember it, and give it its 

 proper relative importance. And, again, the expression for 

 specific inductive capacity appears naturally in every equation, 

 as it should do, and its significance is at once comprehended. 

 A student's ideas of this quantity formed from the ordinary 

 definitions of it are often very hazy. 



Lastly, the method offers the student a new standpoint, 

 and a fresh view of his subject ; and the view not only makes 

 clear to him many things which were confused before, but is 

 well adapted for giving hmi an insight into the more modern 

 advances in the Electrical Theorv. 



3. Note on the Gregorian Calendar. 



By A. C. GiFFOKD. 



The length of the tropical year is 365d. 5h. 48m. 45-51sec., 

 or 365-2421934d. (Young's " General Astronomy.") 



The fraction of a day is equivalent to the following con- 

 tinued fraction : — 



The convergents to this fraction give us a series of approximate 

 values, each more accurate than the preceding, and it happens 

 that the fourth suggests a rule for the interpolation of leap- 

 years, which is very simple and yet far naore accurate than 

 the Gregorian one. 



The first four convergents are — 



The first is the value of the fraction used in the Julian 

 calendar. The error amounts to one day in about 128 years. 



Had the second been adopted, the error would have taken 

 1,111 years to amount to one day. 



The third, which was adopted in the Persian method of 

 interpolation, gives a result correct for 4,348 years. 



The fourth is so near the true value that, were it used, 

 the error would not amount to a day for more than 169,000 

 years. 



To adopt this value it would only be necessary to make 

 every year whose number is divisible by 4 a leap-year except 

 those divisible by 128. 



