(jO PHILOSOPHICAL TRANSACTIONS. [aNNO 1776. 



places farther towards the right hand, in the decuple scale of numbers; and the 

 number of places by which they must be removed, is the same as the distance of 

 each term from the first term of the series, viz. in the 2d term the figures must 

 be moved 1 place lower, in the 3d term 2, in the 4th term 3, &c. so that the 

 latter series will consist of but about half the number of the terms of the former. 

 Thus then this method may be said to effect the business by one series only, in 

 which there is little more to do, than to divide by the several numbers 1, 3, 5, 7, 

 &c. ; for as to the multiplications by the numbers in the numerators of the terms, 

 after they become large, they are easily performed by barely multiplying by the 

 number 2, and subtracting one number from another: for since every numerator 

 is less by 2 than the double of its denominator, if d denote any denominator 

 (exclusive always of the powers of 10) then the co-efficient of that term is 

 — ~ , or 2 — -7, by which the preceding term is to be multiplied; to do which 



therefore, multiply it by 2, that is double it, and divide that double by the divi- 

 sor d, and subtract the quotient from the said double. 



By a pretty exact estimate, which I have made, of the pi-oportion of the trou- 

 ble or time in computing the circumference by this middle form of the value of 

 a, and by Mr. Machin's theorem, I have found, that the computation by his 

 method requires about i or -^V more time than by mine. And its advantage over 

 any of the series' invented by Euler or others, is still much more considerable. 



XXIX. A very Extraordinary Effect of Lightning on a Bulloch, at S%vanborotv, 



in the Parish of Iford near Lewes in Sussex. In sundry Letters ft om Mr. 



James Lambert, Landscape Painter at Lewes; and one from IVm. Green, 



Esq. at Leives, to Wm. Henly, F. R. S. p. 493. 



The bullock was pyed, white and red. The lightning, as supposed, stripped 

 off all the white hair from his back, but left the red hair without the least in- 

 jury. The bullock did not seem to have been hurt; his skin looked fair and well. 

 A Mr. Rogers said, that he had 2 other bullocks struck in the same manner; 

 one last summer, that was all white, was stripped of his hair like this; though 

 not all over his back, but chiefly on his shoulders; the other, 2 years before, 

 was pyed, and affected much like the present. He thought it could not be the 

 effect of any disease, because the beasts were all in good health before and after 

 this accident happened. He was more inclined to think it was the effect of light- 

 ning, because when he has had cattle disordered, so as to make their hair come 

 off, he has never observed white hair to come off more than red, &c. ; but that 

 it has, if party-coloured, fallen off promiscuously, and generally in patches; 

 and also by slow degrees, and never suddenly, as in the case of these bullocks. 

 Mr. Green says, in the evening of Sunday the 28th of August 17/4, at this 

 place, there was an appearance of a thunder storm, but they heard no report. 



