62 



On AbortioJi in Cows. 



line ; and therefore we conclude tliat their number will vary 

 inversely as the cosecant of the angle of junction. 



We have therefore the length of each of these auxiliaries, and 

 their numher^ varying, the one directly and the other inversely, 

 at the cosecant of the same angle ; and consequently as the one 

 increases the other necessarily diminishes in exactly the same 

 proportion ; and whatever be the angle chosen, the total length 

 to be cut remains the same, so long only, be it always remem- 

 bered, as the perpendicular distances between themselves, and 

 those of their upper ends from the line of the primary drain with 

 which they are connected, remain constant at any certain mea- 

 sure. Or, to express it more concisely in a simple mathematical 

 formula, if I signify their separate lengths, and n their number, 

 while r and r' denote any fixed measures representing the above 

 two distances, and G the angle of junction, then the total length of 



7" X cosec , 0 T 



the auxiliary drains, or n I, will vary as ~, or — a con- 



r X cosec 0 r' 



stant quantity ; and therefore will remain always the same ; and if 



L be taken to express the total length of the deep drains in 



the acre, at 20 yards, or any other assumed distance apart, 



T 



L X - will represent the actual whole length of the shallow 



combined with them, upon this scheme, at whatever angle of 

 junction they may be placed. 



III. — On Abortion in Coios. By J. Barlow, V. S. 

 Edinburgh Veterinary College. 



Prize Essay. 



Abortion (from Aborior, to be barren) is the term used to 

 imply an expulsion of the contents of the gravid uterus of any 

 animal before the usual period of gestation is completed. This 

 period, or time included between the process of fruitful connec- 

 tion of the female with the male and the act of natural parturition 

 or birth of the young, differs in duration in various animals. In 

 the cow the time of gestation is commonly considered to be forty 

 weeks. Much difference, however, is seen to exist in various 

 cows ; it is no unusual circumstance for some to exceed this period 

 by one, two, or even three weeks, and for others to calve ten days 

 or a fortnight before its expiration, all these variations being per- 

 fectly consistent with health both of mother and young. 



M. Tessier, in a report founded on forty years' observ^ation, 

 and presented to the Royal Academy of Paris, says, that in J 131 

 cows which he observed, the longest period of gestation was 321 



