1820.] Dr. Henry on Urinary Calculi. 107 



Example 22.— To find the increment of the log. x. 

 Per theorem A (log. x) = log. (l + ^) ; then per logarithms A 



See example 11. 



Example 23.— To find the second increment of the log. x. 



Per theorem A» (log. .r) = / (l + j^J) + I (^ - 777,) 



But/ (1 ^. -^j = / . 1 + ^„ - 4 (^j- + i i^.y 



- &c. 



And / (1 - ^,) = / . 1 - ^„- 4 (rf.)- - i (7^)' 



— &c. 



Therefore A' (log.^r) = - \ (j^Y + i (rH^)' + ^ (rf-J* 



+ &c. ^ 



(See Gentleman's Diary for 1818.) 



The young algebraist will observe that the answer to example 

 11, as determined by Taylor's theorem, and that of example 22, 

 are represented by the same series. But the answers to exam- 

 ples 21 and 23 are represented by series which are very different 

 from each other, notwithstanding both are correct, and their lavf 

 of continuation obvious. 



Article IV. 



On Urinary and other Morbid Concrelions. 

 ■ By William Henry, M.D. F.R.S. &c.* 



The analysis of urinary concretions is a subject of chemical 

 research, which has already been investigated with so much 

 ability and success, that it can now be expected to supply little 

 more' than a few scattered facts that may have escaped the 

 industry of former inquirers. My experiments indeed were for 

 the most part made more than 12 years ago ; and such of the 

 results as have not already appeared in an inaugural dissertation 

 on the uric acid, printed in 18U7, were reserved, as 1 there inti- 

 mated, for a larger work on stone and gravel, which at that time 

 1 had it in view to undertake. This, if other impediments had 

 not occurred to its execution, is now completely superseded by 

 an excellent '• Essay on the Chemical History and Medical 

 Treatment of Urinary Calculi," lately published by Dr. Marcet. 



• Read before the Medical aiiH Cliirnrgical Sociitj of London, March 2, 1819. 



