1The pulsation of the heartbeat felt through the blood vessels; commonly checked to assess one's health.
医者が患者の脈を診た。
The doctor checked the patient's pulse.
手首の脈が速くて少し不安になった。
My wrist pulse was fast, which made me a little uneasy.
運動を始める前に脈拍を測ってください。
Please measure your pulse before starting exercise.
2A vein of ore or mineral deposits — a seam of mineral resources running underground (e.g. 鉱脈, an ore vein).
この地下には豊かな鉱脈が眠っていると言われている。
It is said that rich ore veins lie beneath this ground.
3A chain or range formed by a continuous line of mountains or terrain, such as a mountain range.
ヒマラヤ山脈は世界で最も高い山脈だ。
The Himalayas are the highest mountain range in the world.
遠くに山脈が連なっているのが見える。
In the distance, you can see mountain ranges stretching out.
4Used figuratively to mean a chance or hope, as in "脈がある" (there's still a pulse), meaning there's still a possibility or hope.
交渉にはまだ脈があると思う。
I think there's still a chance in the negotiations.
その企画はまだ脈がありそうだ。
That project still seems to have a chance of succeeding.
5The thread or line of an argument or piece of writing — the logical flow running through a discussion or text.
話の脈をたどれば、彼の本当の意図が見えてくる。
If you trace the thread of his remarks, his true intention becomes clear.
文章の脈を意識して書くと読みやすくなる。
If you write with the flow of the text in mind, it becomes easier to read.