42 



and then dried in a water-oven, to determine the water. The other 

 was macerated in cold water until it became colourless, then mode- 

 rately dried and digested with ether and alcohol to remove fat, and 

 finally dried completely and weighed as fibrin. From the respective 

 weights of the fibrin and the dry clot that of the corpuscles was cal- 

 culated. The following were the results observed in seven different 

 individuals affected with phthisis in different stages of advance- 

 ment : 



Red corpuscles. Fibrin. 



First stage, before the use f Female 129'26 4*52 



of cod-liver oil \Male 116'53 13'57 



First stage, after the use /Female 136'47 5'00 



of cod-liver oil \Male 141'53 4'70 



Third stage, after the use 1 Malg 13g . 74 2>23 



of cod-liver oil J 



Third stage, after the use f Male 139-95 2'31 



of cocoa-nut oil \Male 144*94 4'61 



II. " On a property of Numbers." By the Rev. JAMES BOOTH, 

 LL.D., F.R.S. &c. Received April 6, 1854. 



I know not whether the following property of numbers has been 

 made public. 



A number of six places, consisting of a repetition of a period of 

 any three figures, is divisible by the prime numbers 7, 11 and 13. 

 Thus 376376, 459459, 301301 are so divisible. 



A number N of six places may be thus written : 



N= 100.000 a+ 10.000 b+ 1000 c+ 100 d+ We+f, 



which, when divided by 7, will give a quotient q and a remainder 

 5a+4b+ 6c+ 2d+ 3e?+/. 



Now if d=a, e=b,f=c, this remainder may be written 7(a+b + c), 

 which is divisible by 7, whatever be the values of a, b, c. 



In like manner if a number of six places be divided by 13, the 

 remainder will be 



c+9d+lQe+f; and, as before, if rf=a, e=b,f=c, 



